reasoning about action i a possible worlds approach abstract reasoning about change is an important aspect of commonsense reasoning and planning in this paper we describe an approach to reasoning about change for rich domains where it is not possible to anticipate all situations that might occur the approach provides a solution to the frame problem and to the related problem that it is not always reasonable to explicitly specify all of the consequences of actions the approach involves keeping a single model of the world that is updated when actions are performed the update procedure involves constructing the nearest world to the current one in which the consequences of the actions under consideration hold the way we find the nearest world is to construct proofs of the negation of the explicit consequences of the expected action and to remove a premise in each proof from the current world computationally this construction procedure appears to be tractable for worlds like our own where few things tend to change with each action or where change is regular

the complexity of logic based abduction abduction is an important form of nonmonotonic reasoning allowing one to find explanations for certain symptoms or manifestations when the application domain is described by a logical theory we speak about logic based abduction candidates for abductive explanations are usually subjected to minimality criteria such as subset minimality minimal cardinality minimal weight or minimality under prioritization of individual hypotheses this paper presents a comprehensive complexity analysis of relevant decision and search problems related to abduction on propositional theories our results indicate that abduction is harder than deduction in particular we show that with the most basic forms of abduction the relevant decision problems are complete for complexity classes at the second level of the polynomial hierarchy while the use of prioritization raises the complexity to the third level in certain cases

default reasoning from conditional knowledge bases complexity and tractable cases abstract conditional knowledge bases have been proposed as belief bases that include defeasible rules also called defaults of the form which informally read as generally if then such rules may have exceptions which can be handled in different ways a number of entailment semantics for conditional knowledge bases have been proposed in the literature however while the semantic properties and interrelationships of these formalisms are quite well understood about their computational properties only partial results are known so far in this paper we fill these gaps and first draw a precise picture of the complexity of default reasoning from conditional knowledge bases given a conditional knowledge base kb and a default does kb entail we classify the complexity of this problem for a number of well known approaches including goldszmidt et al s maximum entropy approach and geffner s conditional entailment where we consider the general propositional case as well as natural syntactic restrictions in particular to horn and literal horn conditional knowledge bases as we show the more sophisticated semantics for conditional knowledge bases are plagued with intractability in all these fragments we thus explore cases in which these semantics are tractable and find that most of them enjoy this property on feedback free horn conditional knowledge bases which constitute a new meaningful class of conditional knowledge bases furthermore we generalize previous tractability results from horn to q horn conditional knowledge bases which allow for a limited use of disjunction our results complement and extend previous results and contribute in refining the tractability intractability frontier of default reasoning from conditional knowledge bases they provide useful insight for developing efficient implementations

semantical considerations on nonmonotonic logic abstract commonsense reasoning is nonmonotonic in the sense that we often draw on the basis of partial information conclusions that we later retract when we are given more complete information some of the most interesting products of recent attempts to formalize nonmonotonic reasoning are the nonmonotonic logics of mcdermott and doyle 1 2 these logics however all have peculiarities that suggest they do not quite succeed in capturing the intuitions that prompted their development in this paper we reconstruct nonmonotonic logic as a model of an ideally rational agent s reasoning about his own beliefs for the resulting system called autoepistemic logic we define an intuitively based semantics for which we can show autoepistemic logic to be both sound and complete we then compare autoepistemic logic with the approach of mcdermott and doyle showing how it avoids the peculiarities of their nonmonotonic logic

spatial reasoning in a fuzzy region connection calculus although the region connection calculus rcc offers an appealing framework for modelling topological relations its application in real world scenarios is hampered when spatial phenomena are affected by vagueness to cope with this we present a generalization of the rcc based on fuzzy set theory and discuss how reasoning tasks such as satisfiability and entailment checking can be cast into linear programming problems we furthermore reveal that reasoning in our fuzzy rcc is np complete thus preserving the computational complexity of reasoning in the rcc and we identify an important tractable subfragment moreover we show how reasoning tasks in our fuzzy rcc can also be reduced to reasoning tasks in the original rcc while this link with the rcc could be exploited in practical reasoning algorithms we mainly focus on the theoretical consequences in particular using this link we establish a close relationship with the egg yolk calculus and we demonstrate that satisfiable knowledge bases can be realized by fuzzy regions in any dimension

radon and fourier transforms for d modules the fourier and radon hyperplane transforms are closely related and one such relation was established by brylinski 4 in the framework of holonomic d modules the integral kernel of the radon hyperplane transform is associated with the hypersurface scp p of pairs x y where x is a point in the n dimensional complex projective space p belonging to the hyperplane yap as it turns out a useful variant is obtained by considering the integral transform associated with the open complement u of s in p p in the first part of this paper we generalize brylinski s result in order to encompass this variant of the radon transform and also to treat arbitrary quasi coherent d modules as well as twisted abelian sheaves our proof is entirely geometrical and consists in a reduction to the onedimensional case by the use of homogeneous coordinates the second part of this paper applies the above result to the quantization of the radon transform in the sense of 7 first we deal with line bundles more precisely let p 1 4 p v be the projective space of lines in the vector spacev denote by 3 d r

stability result with application to adaptive control we prove a relatively simple stability result for a particular system of time varying difference equations we then display its usefulness in analysing the stability and convergence of discrete time adaptive control systems in particular we apply our result to demonstrate the stability and convergence of two disparate adaptive control schemes

temporal reasoning about fuzzy intervals traditional approaches to temporal reasoning assume that time periods and time spans of events can be accurately represented as intervals real world time periods and events on the other hand are often characterized by vague temporal boundaries requiring appropriate generalizations of existing formalisms this paper presents a framework for reasoning about qualitative and metric temporal relations between vague time periods in particular we show how several interesting problems like consistency and entailment checking can be reduced to reasoning tasks in existing temporal reasoning frameworks we furthermore demonstrate that all reasoning tasks of interest are np complete which reveals that adding vagueness to temporal reasoning does not increase its computational complexity to support efficient reasoning a large tractable subfragment is identified among others generalizing the well known ord horn subfragment of the interval algebra extended with metric constraints

first order logical filtering logical filtering is the process of updating a belief state set of possible world states after a sequence of executed actions and perceived observations in general it is intractable in dynamic domains that include many objects and relationships still potential applications for such domains e g semantic web autonomous agents and partial knowledge games encourage research beyond intractability results in this paper we present polynomial time algorithms for filtering belief states that are encoded as first order logic fol formulas our algorithms are exact in many cases of interest they accept belief states in fol without functions permitting arbitrary arity for predicates infinite universes of elements and equality they enable natural representation with explicit references to unidentified objects and partially known relationships still maintaining tractable computation previous results focus on more general cases that are intractable or permit only imprecise filtering our algorithms guarantee that belief state representation remains compact for strips actions among others with unbounded size domains this guarantees tractable exact filtering indefinitely for those domains the rest of our results apply to expressive modeling languages such as partial databases and belief revision in fol

logic based ontology comparison and module extraction with an application to dl lite we develop a formal framework for comparing different versions of ontologies and apply it to ontologies formulated in terms of dl lite a family of lightweight description logics designed for data intensive applications the main feature of our approach is that we take into account the vocabulary signature with respect to which one wants to compare ontologies five variants of difference and inseparability relations between ontologies are introduced and their respective applications for ontology development and maintenance discussed these variants are obtained by generalising the notion of conservative extension from mathematical logic and by distinguishing between differences that can be observed among concept inclusions answers to queries over aboxes by taking into account additional context ontologies and by considering a model theoretic language independent notion of difference we compare these variants study their meta properties determine the computational complexity of the corresponding reasoning tasks and present decision algorithms moreover we show that checking inseparability can be automated by means of encoding into qbf satisfiability and using off the shelf general purpose qbf solvers inseparability relations between ontologies are then used to develop a formal framework for minimal module extraction we demonstrate that different types of minimal modules induced by these inseparability relations can be automatically extracted from real world medium size dl lite ontologies by composing the known tractable syntactic locality based module extraction algorithm with our non tractable extraction algorithms and using the multi engine qbf solver aqme finally we explore the relationship between uniform interpolation or forgetting and inseparability

preprocessing of intractable problems some computationally hard problems e g deduction in logical knowledge bases are such that part of an instance is known well before the rest of it and remains the same for several subsequent instances of the problem in these cases it is useful to preprocess off line this known part so as to simplify the remaining on line problem in this paper we investigate such a technique in the context of intractable i e np hard problems recent results in the literature show that not all np hard problems behave in the same way for some of them preprocessing yields polynomial time on line simplified problems we call them compilable while for other ones their compilability implies some consequences that are considered unlikely our primary goal is to provide a sound methodology that can be used to either prove or disprove that a problem is compilable to this end we define new models of computation complexity classes and reductions we find complete problems for such classes completeness meaning they are the less likely to be compilable we also investigate preprocessing that does not yield polynomial time on line algorithms but generically decreases complexity this leads us to define hierarchies of compilability that are the analog of the polynomial hierarchy a detailed comparison of our framework to the idea of parameterized tractability shows the differences between the two approaches

semantic forgetting in answer set programming the notion of forgetting also known as variable elimination has been investigated extensively in the context of classical logic but less so in nonmonotonic logic programming and nonmonotonic reasoning the few approaches that exist are based on syntactic modifications of a program at hand in this paper we establish a declarative theory of forgetting for disjunctive logic programs under answer set semantics that is fully based on semantic grounds the suitability of this theory is justified by a number of desirable properties in particular one of our results shows that our notion of forgetting can be entirely captured by classical forgetting we present several algorithms for computing a representation of the result of forgetting and provide a characterization of the computational complexity of reasoning from a logic program under forgetting as applications of our approach we present a fairly general framework for resolving conflicts in inconsistent knowledge bases that are represented by disjunctive logic programs and we show how the semantics of inheritance logic programs and update logic programs from the literature can be characterized through forgetting the basic idea of the conflict resolution framework is to weaken the preferences of each agent by forgetting certain knowledge that causes inconsistency in particular we show how to use the notion of forgetting to provide an elegant solution for preference elicitation in disjunctive logic programming

non monotonic logic i abstract non monotonic logical systems are logics in which the introduction of new axioms can invalidate old theorems such logics are very important in modeling the beliefs of active processes which acting in the presence of incomplete information must make and subsequently revise assumptions in light of new observations we present the motivation and history of such logics we develop model and proof theories a proof procedure and applications for one non monotonic logic in particular we prove the completeness of the non monotonic predicate calculus and the decidability of the non monotonic sentential calculus we also discuss characteristic properties of this logic and its relationship to stronger logics logics of incomplete information and truth maintenance systems

on the relationship between circumscription and negation as failure abstract the aim of this paper is to investigate two powerful methods of handling negative information in logic based knowledge representation systems the logical minimization in the form of circumscription and the negation as failure rule formalized by various closures or completions of original theories we suggest a new more powerful form of the negation as failure rule and describe an important class of theories for which this form of negation as failure is equivalent to particular forms of circumscription these results establish a close relationship between the two important formalizations of nonmonotonic reasoning and provide a syntactic characterization of the corresponding circumscriptive theories this allows us to apply existing methods of deduction using various negation as failure rules to answering queries in a broad class of circumscriptive theories

on the measure of conflicts shapley inconsistency values there are relatively few proposals for inconsistency measures for propositional belief bases however inconsistency measures are potentially as important as information measures for artificial intelligence and more generally for computer science in particular they can be useful to define various operators for belief revision belief merging and negotiation the measures that have been proposed so far can be split into two classes the first class of measures takes into account the number of formulae required to produce an inconsistency the more formulae required to produce an inconsistency the less inconsistent the base the second class takes into account the proportion of the language that is affected by the inconsistency the more propositional variables affected the more inconsistent the base both approaches are sensible but there is no proposal for combining them we address this need in this paper our proposal takes into account both the number of variables affected by the inconsistency and the distribution of the inconsistency among the formulae of the base our idea is to use existing inconsistency measures in order to define a game in coalitional form and then to use the shapley value to obtain an inconsistency measure that indicates the responsibility contribution of each formula to the overall inconsistency in the base this allows us to provide a more reliable image of the belief base and of the inconsistency in it

an algorithm to compute circumscription abstract mccarthy s theory of circumscription appears to be the most powerful among various formalizations of nonmonotonic reasoning designed to handle incomplete and negative information in knowledge representation systems in this paper we describe a query answering algorithm for circumscriptive theories the closed world assumption cwa and its generalizations the generalized closed world assumption gcwa and the extended closed world assumption ecwa can be considered as special forms of circumscription consequently our algorithm also applies to answering queries in theories using the closed world assumption and its generalizations similarly since prioritized circumscription is equivalent to a conjunction of parallel circumscriptions our algorithm can be used to answer queries in theories circumscribed by prioritized circumscription

da 2 merging operators a new framework for propositional merging is presented da2 merging operators parameterized by a distance between interpretations and two aggregation functions are introduced many distances and aggregation functions can be used and many merging operators already defined in the literature including both model based ones and syntax based ones can be encoded as specific da2 operators both logical and complexity properties of those operators are studied an important result is that under very weak assumptions query entailment from merged bases is only at the first level of the polynomial hierarchy when any of the da2 operators is used as a by product complexity results for several existing merging operators are derived as well

minimal belief and negation as failure abstract fangzhen lin and yoav shoham defined a propositional nonmonotonic logic which uses two independent modal operators one of them represents minimal knowledge the other is related to the ideas of justification as understood in default logic and of negation as failure we describe a simplified version of that system show how quantifiers can be included in it and study its relation to circumscription and default logic to logic programming and to the theory of epistemic queries developed by hector levesque and ray reiter

adaptive gpc based on laguerre filters modelling abstract a state space model based on laguerre filters is proposed to design an adaptive generalized predictive controller gpc for stable plants a sufficient stability condition is derived to study the convergence and stability of the proposed controller in case of a plant model match robustness conditions are also given for the case of plant model mismatch the results are applicable to gpc schemes based on moving average models in the presence of plant model mismatch illustrative examples show the robustness of the controller and compare it with other gpc versions

logical representation and fusion of prioritized information based on guaranteed possibility measures in the possibility theory framework prioritized information can be logically expressed in different formats the most usual way used in standard possibilistic logic is to associate necessity degrees with propositional formulas this paper considers another representation and fusion of prioritized information using guaranteed possibility measures prioritized pieces of information are then represented by sets of weighted formulas called knowledge bases where weights are lower bounds of guaranteed possibility degrees of formulas we first show that the basic notions of standard possibilistic logic have natural counterparts when dealing with knowledge bases in particular we present the inference machinery and provide syntactic but semantically meaningful merging of knowledge bases in the second part of the paper we show that distance based merging propositional knowledge bases can be naturally encoded using knowledge bases moreover this encoding is more efficient than the necessity based encoding of distance based merging operator

results on the propositional μ calculus abstract in this paper we define and study a propositional calculus l which consists essentially of propositional modal logic with a least fixpoint operator l is syntactically simpler yet strictly more expressive than propositional dynamic logic pdl for a restricted version we give an exponential time decision procedure small model property and complete deductive system theory subsuming the corresponding results for pdl

more complicated questions about maxima and minima and some closures of np abstract starting from np complete problems defined by questions of the kind max m and min m we consider problems defined by more complicated questions about these maxima and minima as for example max m min m and is max odd this continues a work started by papadimitriou and yannakakis 1982 it is shown that these and other problems are complete in certain subclasses of the boolean closure of np and other classes in the interesting area below the class p 2 of the polynomial time hierarchy special methods are developed to prove such completeness results for this it is necessary to establish some properties of the classes in question which might be interesting in their own right

lost in translation language independence in propositional logic application to belief change while propositional logic is widely used as a representation framework for many ai applications the concept of language independence in the propositional setting has not received much attention so far in this paper we define language independence for a propositional operator as robustness w r t symbol translation we motivate the need to focus on symbol translations of restricted types introduce and study several families of translations of interest and provide a number of characterization results we also identify the computational complexity of recognizing symbol translations from those families then we investigate the robustness of belief merging belief revision and belief update operators w r t translations of different types it turns out that some rational merging revision update operators are not guaranteed to offer the most basic yet non trivial form of language independence

a consistency based approach for belief change this paper presents a general consistency based framework for expressing belief change the framework has good formal properties while being well suited for implementation for belief revision informally in revising a knowledge base k by a sentence we begin with and include as much of k as consistently possible this is done by expressing k and in disjoint languages asserting that the languages agree on the truth values of corresponding atoms wherever consistently possible and then re expressing the result in the original language of k there may be more than one way in which the languages of k and can be so correlated in choice revision one such extension represents the revised state alternately skeptical revision consists of the intersection of all such extensions contraction is similarly defined although interestingly it is not interdefinable with revision the framework is general and flexible for example one could go on and express other belief change operations such as update and erasure and the merging of knowledge bases further the framework allows the incorporation of static and dynamic integrity constraints the approach is well suited for implementation belief change can be equivalently expressed in terms of a finite knowledge base and the scope of a belief change operation can be restricted to just those propositions common to the knowledge base and sentence for change we give a high level algorithm implementing the procedure and an expression of the approach in default logic lastly we briefly discuss two implementations of the approach

forgetting in multi agent modal logics abstract in the past decades forgetting has been investigated for many logics and has found many applications in knowledge representation and reasoning in this paper we study forgetting in multi agent modal logics we adopt the semantic definition of existential bisimulation quantifiers as that of forgetting we resort to canonical formulas of modal logics introduced by moss an arbitrary modal formula is equivalent to the disjunction of a unique set of satisfiable canonical formulas we show that for the logics of k n d n t n k 45 n kd 45 n and s 5 n the result of forgetting an atom from a satisfiable canonical formula can be computed by simply substituting the literals of the atom with thus we show that these logics are closed under forgetting and hence have uniform interpolation finally we generalize the above results to include common knowledge of propositional formulas

reasoning with partially ordered information in a possibilistic logic framework in many applications the reliability relation associated with available information is only partially defined while most of existing uncertainty frameworks deal with totally ordered pieces of knowledge partial pre orders offer more flexibility than total pre orders to represent incomplete knowledge possibilistic logic which is an extension of classical logic deals with totally ordered information it offers a natural qualitative framework for handling uncertain information priorities are encoded by means of weighted formulas where weights are lower bounds of necessity measures this paper proposes an extension of possibilistic logic for dealing with partially ordered pieces of knowledge we show that there are two different ways to define a possibilistic logic machinery which both extend the standard one

belief revision in horn theories this paper investigates belief revision where the underlying logic is that governing horn clauses we show that classical agm belief revision doesn t immediately generalise to the horn case in particular a standard construction based on a total preorder over possible worlds may violate the accepted agm postulates conversely in the obvious extension to the agm approach horn revision functions are not captured by total preorders over possible worlds we address these difficulties by introducing two modifications to the agm approach first the semantic construction is restricted to well behaved orderings what we call horn compliant orderings second the revision postulates are augmented by an additional postulate both restrictions are redundant in the agm approach but not in the horn case in a representation result we show that the class of revision functions captured by horn compliant total preorders over possible worlds is precisely that given by the extended set of horn revision postulates further we show that horn revision is compatible with work in iterated revision and work concerning relevance in revision we also consider specific revision operators arguably this work is interesting for several reasons it extends agm revision to inferentially weaker horn theories hence it sheds light on the theoretical underpinnings of belief change as well as generalising the agm paradigm thus this work is relevant to revision in areas that employ horn clauses such as deductive databases and logic programming as well as areas in which inference is weaker than classical logic such as in description logic

a generalized lqg approach to self tuning control part ii implementation and simulation implementation aspects of the lq self tuner proposed in part i are discussed the method involves solution of a riccati equation through u d factorization and state estimation through transmittance matrices simplified vector formulations of the u d time update and the transmittance matrix are presented simulation results demonstrate the superiority of this algorithm over pole placement and the generalized minimum variance controllers incorporation of the auxiliary variable t instead of y t and the incremental control law u t in the cost function ascribes the right servo properties to this algorithm with offset free control performance the algorithmic stability and numerical robustness without sacrifice of implement ational simplicity make the proposed lq self tuner attractive

a hypergeometric modules and gauss manin systems abstract let a be a d n integer matrix gel fand et al proved that most a hypergeometric systems have an interpretation as a fourier laplace transform of a direct image the set of parameters for which this happens was later identified by schulze and walther as the set of not strongly resonant parameters of a a similar statement relating a hypergeometric systems to exceptional direct images was proved by reichelt in this article we consider a hybrid approach involving neighborhoods u of the torus of a and consider compositions of direct and exceptional direct images our main results characterize for which parameters the associated a hypergeometric system is the inverse fourier laplace transform of such a mixed gauss manin system in order to describe which u work for such a parameter we introduce the notions of fiber support and cofiber support of a d module if the semigroup ring c n a is normal we show that every a hypergeometric system is mixed gauss manin we also give an explicit description of the neighborhoods u which work for each parameter in terms of primitive integral support functions

propositional circumscription and extended closed world reasoning are p p 2 complete abstract circumscription and the closed world assumption with its variants are well known nonmonotonic techniques for reasoning with incomplete knowledge their complexity in the propositional case has been studied in detail for fragments of propositional logic one open problem is whether the deduction problem for arbitrary propositional theories under the extended closed world assumption or under circumscription is p 2 complete i e complete for a class of the second level of the polynomial hierarchy we answer this question by proving these problems p 2 complete and we show how this result applies to other variants of closed world reasoning

reasoning under inconsistency a forgetting based approach in this paper a fairly general framework for reasoning from inconsistent propositional bases is defined variable forgetting is used as a basic operation for weakening pieces of information so as to restore consistency the key notion is that of recoveries which are sets of variables whose forgetting enables restoring consistency several criteria for defining preferred recoveries are proposed depending on whether the focus is laid on the relative relevance of the atoms or the relative entrenchment of the pieces of information or both our framework encompasses several previous approaches as specific cases including reasoning from preferred consistent subsets and some forms of information merging interestingly the gain in flexibility and generality offered by our framework does not imply a complexity shift compared to these specific cases

nonmonotonic reasoning preferential models and cumulative logics abstract many systems that exhibit nonmonotonic behavior have been described and studied already in the literature the general notion of nonmonotonic reasoning though has almost always been described only negatively by the property it does not enjoy i e monotonicity we study here general patterns of nonmonotonic reasoning and try to isolate properties that could help us map the field of nonmonotonic reasoning by reference to positive properties we concentrate on a number of families of nonmonotonic consequence relations defined in the style of gentzen 13 both proof theoretic and semantic points of view are developed in parallel the former point of view was pioneered by gabbay 10 while the latter has been advocated by shoham 38 five such families are defined and characterized by representation theorems relating the two points of view one of the families of interest that of preferential relations turns out to have been studied by adams 2 the preferential models proposed here are a much stronger tool than adams probabilistic semantics the basic language used in this paper is that of propositional logic the extension of our results to first order predicate calculi and the study of the computational complexity of the decision problems described in this paper will be treated in another paper

propositional belief base update and minimal change abstract in this paper we examine ten concrete propositional update operations of the literature we start by completely characterizing their relative strength and their computational complexity then we evaluate the competing update operations with respect to the postulates proposed by katsuno and mendelzon it turns out that the majority violates most of the postulates we argue that all violated postulates are undesirable except one after that we evaluate the update operations with respect to another property which has been investigated extensively in the literature viz that disjunctive updates should not be identified with the exclusive disjunction we argue that this is desirable and show that the argument gives further support to the rejection of two of the postulates finally we study how the different approaches accommodate general laws governing the world alias integrity constraints summing up our results we conclude that only two of the update operations are satisfactory

foundations of instance level updates in expressive description logics in description logic dl aboxes are used for describing the state of affairs in an application domain we consider the problem of updating aboxes when the state changes assuming that update information is described at an atomic level i e in terms of possibly negated abox assertions that involve only atomic concepts and roles we analyze such basic abox updates in several standard dls in particular addressing questions of expressibility and succinctness can updated aboxes always be expressed in the dl in which the original abox was formulated and if so what is the size of the updated abox it turns out that dls have to include nominals and the constructor of hybrid logic for updated aboxes to be expressible and that this still holds when updated aboxes are approximated moreover the size of updated aboxes is exponential in the role depth of the original abox and the size of the update we also show that this situation improves when updated aboxes are allowed to contain additional auxiliary symbols then dls only need to include nominals for updated aboxes to exist and the size of updated aboxes is polynomial in the size of both the original abox and the update

semantical and computational aspects of horn approximations abstract selman and kautz proposed a method called horn approximation for speeding up inference in propositional knowledge bases their technique is based on the compilation of a propositional formula into a pair of horn formulae a horn greatest lower bound glb and a horn least upper bound lub in this paper we focus on glbs and address two questions that have been only marginally addressed so far 1 what is the semantics of the horn glbs 2 what is the exact complexity of finding them we obtain semantical as well as computational results the major semantical result is the set of minimal models of a propositional formula and the set of minimum models of its horn glbs are the same the major computational result is finding a horn glb of a propositional formula in cnf is np equivalent

propositional distances and compact preference representation abstract distances between possible worlds play an important role in logic based knowledge representation especially in belief change reasoning about action belief merging and similarity based reasoning we show here how they can be used for representing in a compact and intuitive way the preference profile of an agent following the principle that given a goal g then the closer a world w to a model of g the better w we give an integrated logical framework for preference representation which handles weighted goals and distances to goals in a uniform way then we argue that the widely used hamming distance which merely counts the number of propositional symbols assigned a different value by two worlds is generally too rudimentary and too syntax sensitive to be suitable in real applications therefore we propose a new family of distances based on choquet integrals in which the hamming distance has a position very similar to that of the arithmetic mean in the class of choquet integrals

the size of a revised knowledge base abstract in this paper we address a specific computational aspect of belief revision the size of the propositional formula obtained by means of the revision of a formula with a new one in particular we focus on the size of the smallest formula which is logically equivalent to the revised knowledge base the main result of this paper is that not all formalizations of belief revision are equal from this point of view for some of them we show that the revised knowledge base can be represented by a polynomial size formula we call these results compactability results on the other hand for other ones the revised knowledge base does not always admit a polynomial space representation unless the polynomial hierarchy collapses at a sufficiently low level non compactability results we also show that the time complexity of query answering for the revised knowledge base has definitely an impact on being able to represent the result of the revision compactly nevertheless formalisms with the same complexity may have different compactability properties we also study compactability properties for a weaker form of equivalence called query equivalence which allows to introduce new propositional symbols moreover we extend our analysis to the special case in which the new formula has constant size and to the case of sequences of revisions i e iterated belief revision a complete analysis along these four coordinates is shown

an optimum time scale for discrete laguerre network any discrete time stable transfer function can be expressed by a discrete time laguerre series with a chosen time scale an optimum time scale such that an index is minimized is derived this index ensures that the coefficients of higher order laguerre functions go toward zero quickly the solution derived requires the knowledge of the impulse response of the discrete plant cases of first order plants second order underdamped plants and plants with multiunit delay are also discussed

propositional belief base merging or how to merge beliefs goals coming from several sources and some links with social choice theory abstract we give in this paper new results on merging operators those operators aim to define the goals or beliefs of an agents group after the individuals goals beliefs using the logical framework of konieczny and pino perez proceedings of the fifth european conference on symbolic and quantitative approaches to reasoning with uncertainty ecsqaru 99 lecture notes in artificial intelligence 1638 1999 pp 233 244 we study the relationships between two important sub families of merging operators majority operators and arbitration operators an open question was to know if those two families were disjoint or not we show that there are operators that belong simultaneously to the two families furthermore the new family introduced allows the user to choose the consensual level he wants for his majority operator we show at the end of this work some relationships between logical belief merging operators and social choice rules

leray s quantization of projective duality 2 review on correspondences for sheaves and d modules 4 2 1 notations 4 2 1 1 geometry 4 2 1 2 sheaves 4 2 1 3 d modules 5 2 1 4 e modules 6 2 2 correspondences for sheaves and d modules 6

an assumption based tms abstract this paper presents a new view of problem solving motivated by a new kind of truth maintenance system unlike previous truth maintenance systems which were based on manipulating justifications this truth maintenance system is in addition based on manipulating assumption sets as a consequence it is possible to work effectively and efficiently with inconsistent information context switching is free and most backtracking and all retraction is avoided these capabilities motivate a different kind of problem solving architecture in which multiple potential solutions are explored simultaneously this architecture is particularly well suited for tasks where a reasonable fraction of the potential solutions must be explored

stability and convergence analyses of an adaptive gpc based on state space modeling a generalized predictive controller gpc is derived based on a general state space model the equivalence of the predictive control problem to a perturbation problem is revealed in the case of a small perturbation the closed loop poles are calculated with high accuracy for the case of a general perturbation an upper bound on the permissible perturbation norm is derived assuming an open loop stable system both the plant model match and plant model mismatch cases are analysed the controller is proven to be robust and an adaptive implementation is motivated for open loop stable systems the convergence and stability of the control scheme are ensured by proper tuning of the control weight and prediction horizon the results are applicable to a wide range of predictive controllers the main contribution of this paper is not a new control algorithm but new techniques to analyse the gpc as well as new stability and convergence results

using local search to find msses and muses in this paper a new complete technique to compute maximal satisfiable subsets msses and minimally unsatisfiable subformulas muses of sets of boolean clauses is introduced the approach improves the currently most efficient complete technique in several ways it makes use of the powerful concept of critical clause and of a computationally inexpensive local search oracle to boost an exhaustive algorithm proposed by liffiton and sakallah these features can allow exponential efficiency gains to be obtained accordingly experimental studies show that this new approach outperforms the best current existing exhaustive ones

solving logic program conflict through strong and weak forgettings we consider how to forget a set of atoms in a logic program intuitively when a set of atoms is forgotten from a logic program all atoms in the set should be eliminated from this program in some way and other atoms related to them in the program might also be affected we define notions of strong and weak forgettings in logic programs to capture such intuition reveal their close connections to the notion of forgetting in classical propositional theories and provide a precise semantic characterization for them based on these notions we then develop a general framework for conflict solving in logic programs we investigate various semantic properties and features in relation to strong and weak forgettings and conflict solving in the proposed framework we argue that many important conflict solving problems can be represented within this framework in particular we show that all major logic program update approaches can be transformed into our framework under which each approach becomes a specific conflict solving case with certain constraints we also study essential computational properties of strong and weak forgettings and conflict solving in the framework

a guide to completeness and complexity for modal logics of knowledge and belief abstract we review and re examine possible worlds semantics for propositional logics of knowledge and belief with three particular points of emphasis 1 we show how general techniques for finding decision procedures and complete axiomatizations apply to models for knowledge and belief 2 we show how sensitive the difficulty of the decision procedure is to such issues as the choice of modal operators and the axiom system and 3 we discuss how notions of common knowledge and distributed knowledge among a group of agents fit into the possible worlds framework as far as complexity is concerned we show among other results that while the problem of deciding satisfiability of an s5 formula with one agent is np complete the problem for many agents is pspace complete adding a distributed knowledge operator does not change the complexity but once a common knowledge operator is added to the language the problem becomes complete for exponential time

integral transforms with exponential kernels and laplace transform let x z y be a correspondence of complex manifolds f g we study integral transforms associated to kernels exp o with p meromor phic on z acting on formal or moderate cohomologies our main application is the laplace transform in this case x is the projective compactification of the vector space v c y is its dual space z x x y and o z w z w we obtain the isomorphisms f 0 ov f n f ov thom f v thom far n ov this content downloaded from 207 46 13 59 on mon 13 jun 2016 05 54 06 utc all use subject to http about jstor org terms 972 masaki kashiwara and pierre schapira where f is a conic and rll constructible sheaf on v and fa is its fourier sato transform some applications are discussed rims kyoto university kyoto 606 01 japan institut de mathematiques universit9 paris vi case 82 4 pl jussieu 75252 paris france e mail address schapirafmath jussieu fr this content downloaded from 207 46 13 59 on mon 13 jun 2016 05 54 06 utc all use subject to http about jstor org terms

the computational complexity of propositional strips planning abstract i present several computational complexity results for propositional strips planning i e strips planning restricted to ground formulas different planning problems can be defined by restricting the type of formulas placing limits on the number of pre and postconditions by restricting negation in pre and postconditions and by requiring optimal plans for these types of restrictions i show when planning is tractable polynomial and intractable np hard in general it is pspace complete to determine if a given planning instance has any solutions extremely severe restrictions on both the operators and the formulas are required to guarantee polynomial time or even np completeness for example when only ground literals are permitted determining plan existence is pspace complete even if operators are limited to two preconditions and two postconditions when definite horn ground formulas are permitted determining plan existence is pspace complete even if operators are limited to zero preconditions and one postcondition one of the interesting tractable problems is if each operator is restricted to positive preconditions and one postcondition only ground literals the blocks world problem slightly modified is a subproblem of this restricted planning problem these results in combination with previous analyses are not encouraging for domain independent planning

a formal model of diagnostic inference i problem formulation and decomposition abstract this paper which is part i of a two part series introduces a new model of diagnostic problem solving based on a generalization of the set covering problem the model formalizes the concepts of 1 1 whether or not a set of one or more disorders is sufficient to explain a set of occurring manifestations 2 2 what a solution is for a diagnostic problem and 3 3 how to generate all of the alternative explanations in a problem s solution in addition conditions for decomposing a diagnostic problem into independent subproblems are stated and proven this model is of interest because it captures several intuitively plausible features of human diagnostic inference it directly addresses the issue of multiple simultaneous causative disorders it can serve as a theoretical basis for expert systems for diagnostic problem solving and it provides a conceptual framework within which to view some recent ai work on diagnostic problem solving in general in part ii the concepts developed in this paper will be used to present algorithms for diagnostic problem solving

deterministic adaptive control based on laguerre series representation the behaviour of adaptive controllers in the presence of unmodelled dynamics and the need for reduced a priori information have led us to abandon the usual arma transfer function representation for a representation by an orthonormal series the appeal of our new approach is that it eliminates the need for assumptions about the plant order and the time delay the plant is modelled by an orthonormal laguerre network put in state space form a simple predictive control law is proposed an explicit deterministic adaptive controller is then designed simulations show that it is easy to use able to handle non minimum phase plants and more robust than the conventional model based approach although we chose laguerre functions other orthonormal functions may be used we have already tested some with success

answer set programming and plan generation abstract the idea of answer set programming is to represent a given computational problem by a logic program whose answer sets correspond to solutions and then use an answer set solver such as smodels or dlv to find an answer set for this program applications of this method to planning are related to the line of research on the frame problem that started with the invention of formal nonmonotonic reasoning in 1980

propositional knowledge base revision and minimal change abstract the semantics of revising knowledge bases represented by sets of propositional sentences is analyzed from a model theoretic point of view a characterization of all revision schemes that satisfy the gardenfors rationality postulates is given in terms of minimal change with respect to an ordering among interpretations revision methods proposed by various authors are surveyed and analyzed in this framework the correspondences between gardenfors like rationality postulates and minimal changes with respect to other orderings are also investigated

autoepistemic logic autoepistemic logic is one of the principal modes of nonmonotonic reasoning it unifies several other modes of nonmonotonic reasoning and has important application in logic programming in the paper a theory of autoepistemic logic is developed this paper starts with a brief survey of some of the previously known results then the nature of nonmonotonicity is studied by investigating how membership of autoepistemic statements in autoepistemic theories depends on the underlying objective theory a notion similar to set theoretic forcing is introduced expansions of autoepistemic theories are also investigated expansions serve as sets of consequences of an autoepistemic theory and they can also be used to define semantics for logic programs with negation theories that have expansions are characterized and a normal form that allows the description of all expansions of a theory is introduced our results imply algorithms to determine whether a theory has a unique expansion sufficient conditions stratification that imply existence of a unique expansion are discussed the definition of stratified theories is extended and under some additional assumptions efficient algorithms for testing whether a theory is stratified are proposed the theorem characterizing expansions is applied to two classes of theories k1 theories and ae programs in each case simple hypergraph characterization of expansions of theories from each of these classes is given finally connections with stable model semantics for logic programs with negation is discussed in particular it is proven that the problem of existence of stable models is np complete authors abstract

perturbation analysis of gpc with one step control horizon abstract a generalized predictive controller is derived based on a state space model the special but commonly used case of a one step control horizon is analyzed it is shown that the predictive control problem is actually a perturbation problem where there exist easy relations to calculate the closed loop poles in case of a plant model match the perturbed eigenvalues of a stable system as well as a system having one unstable pole are studied the results do not necessarily require the infinite prediction horizon or the zero control weighting assumptions in case of a plant model mismatch stability is studied for general plant representations using operators as well as for a linear time invariant representation it is shown that the generalized predictive controller still yields a mean level controller under some assumptions

cumulative default logic finite characterization algorithms and complexity abstract brewka s cumulative default logic cdl a new version of reiter s default logic puts emphasis on the joint consistency among the justifications of all applied defaults to obtain cumulativity in this paper a finite characterization of cdl extensions using sets of generating defaults is given from this characterization we derive new algorithms for various reasoning tasks in cdl moreover we show that propositional cumulative default reasoning has the same complexity as classical default reasoning

applications of circumscription to formalizing common sense knowledge we present a new and more symmetric version of the circumscription method of nonmonotonic reasoning first described in mccarthy 1980 and some applications to formalizing common sense knowledge the applications in this paper are mostly based on minimizing the abnormality of different aspects of various entities included are nonmonotonic treatments of is a hierarchies the unique names hypothesis and the frame problem the new circumscription may be called formula circumscription to distinguish it from the previously defined domain circumscription and predicate circumscription a still more general formalism called prioritized circumscription is briefly explored

an interpretation of fuzzy measures and the choquet integral as an integral with respect to a fuzzy measure abstract in this paper the non additivity of sugeno s fuzzy measures is interpreted in terms of addition and the rationality of the choquet integral is discussed it is pointed out that a fuzzy measure on a set x expresses the interaction between the subsets of x and can be represented by an additive measure it is shown through concrete examples that the choquet integral is reasonable as an integral with respect to a fuzzy measure it is also found that the choquet integral is closely related with the representation of a fuzzy measure

knowledge updates semantics and complexity issues we consider the problem of updating of an agent s knowledge we propose a formal method of knowledge update on the basis of the semantics of modal logic s5 in our method an update is specified according to the minimal change on both the agent s actual world and knowledge we discuss general minimal change properties of knowledge update and show that our knowledge update operator satisfies all the update postulates of katsuno and mendelzon we characterize several specific forms of knowledge update which have important applications in reasoning about change of agents knowledge we also examine the persistence property of knowledge and ignorance associated with knowledge update we then investigate the computational complexity of model checking for knowledge update we first show that in general the model checking for knowledge update is s 2 p complete we then identify a subclass of knowledge update problems that has polynomial time complexity for model checking we point out that some important knowledge update problems belong to this subclass we further address another interesting subclass of knowledge update problems for which the complexity of model checking is np complete

saturation nonmonotonic reasoning and the closed world assumption abstract to deal with the problem of implicit negative information in databases it is necessary to use a nonmonotonic form of reasoning the form of reasoning described in this paper uses an ordering relation on interpretations of the type i is inferior to j if every elementary fact true in i is true in j in simple cases this rule may be defined by a set p of formulas implies a formula q if every minimal model of p satisfies q in more general cases this definition leads to paradox if p is consistent and has no minimal model p must not imply q and its negation we have 1 1 carefully formulated the definition of a special type of implication called sub implication to avoid this type of paradox 2 2 proved that if p is a set of clauses then p has a minimal model and more generally that every model of a set of clauses is minored by one of its minimal models 3 3 developed in this last case subject to certain conditions such as the use of a particular set of clauses called groundable clauses or g clauses a decidable algorithm to compute whether p implies q q being practically any formula

enhancing disjunctive logic programming systems by sat checkers disjunctive logic programming dlp with stable model semantics is a powerful nonmonotonic formalism for knowledge representation and reasoning reasoning with dlp is harder than with normal v free logic programs because stable model checking deciding whether a given model is a stable model of a propositional dlp program is co np complete while it is polynomial for normal logic programs this paper proposes a new transformation m p which reduces stable model checking to unsat i e to deciding whether a given cnf formula is unsatisfiable the stability of a model m of a program p thus can be verified by calling a satisfiability checker on the cnf formula m p the transformation is parsimonious i e no new symbol is added and efficiently computable as it runs in logarithmic space and therefore in polynomial time moreover the size of the generated cnf formula never exceeds the size of the input and is usually much smaller we complement this transformation with modular evaluation results which allow for efficient handling of large real world reasoning problems the proposed approach to stable model checking has been implemented in dlv a state of the art implementation of dlp a number of experiments and benchmarks have been run using satz as satisfiability checker the results of the experiments are very positive and confirm the usefulness of our techniques

solving conflicts in information merging by a flexible interpretation of atomic propositions although many techniques for merging conflicting propositional knowledge bases have already been proposed most existing work is based on the idea that inconsistency results from the presence of incorrect pieces of information which should be identified and removed in contrast we take the view in this paper that conflicts are often caused by statements that are inaccurate rather than completely false suggesting to restore consistency by interpreting certain statements in a flexible way rather than ignoring them completely in accordance with this view we propose a novel approach to merging which exploits extra logical background information about the semantic relatedness of atomic propositions several merging operators are presented which are based on different formalizations of this background knowledge ranging from purely qualitative approaches related to possibilistic logic to quantitative approaches with a probabilistic flavor both syntactic and semantic characterizations are provided for each merging operator and the computational complexity is analyzed

some remarks on the brylinski radon and the fourier transforms abstract we will study a relationship between the brylinski radon and the fourier transforms of a monodromic perverse sheaf in fact we will show that they are equivalent modulo a constant perverse sheaf as an application we will discuss a relation between the sklyanin transform and the brylinski radon transform

bounded query classes polynomial time machines having restricted access to an np oracle are investigated restricted access means that the number of queries to the oracle is restricted or the way in which the queries are made is restricted e g queries made during truth table reductions very different kinds of such restrictions result in the same or comparable complexity classes in particular the class p text np o log n can be characterized in very different ways furthermore the boolean hierarchy is generalized in such a way that it is possible to characterize p text np and p text np o log n in terms of the generalization

disjunctive merging quota and gmin merging operators when aggregating information from a group of agents accepting the pieces of information shared by all agents is a natural requirement in this paper we investigate such a unanimity condition in the setting of propositional merging we discuss two interpretations of the unanimity condition we show that the first interpretation is captured by existing postulates for merging but the second interpretation is not and this leads to the introduction of a new disjunction postulate disj it turns out that existing operators satisfying disj do not perform well with respect to the standard criteria used to evaluate merging operators logical properties computational complexity and strategy proofness to fill this gap we introduce two new families of propositional merging operators quota operators and gmin operators which satisfy disj and achieve interesting trade offs with respect to the logical computational and strategy proofness criteria

properties of generalized predictive control control design using long range prediction based on a dynamic model of the plant has become an important contender for high performance applications the model can be derived analytically but more typically it is provided by simple experiments or in the adaptive context by recursive estimation many methods have been proposed in the literature depending on the assumed model structure and the choice of cost function here the approach called generalized predictive control or gpc is reviewed of special interest is the derivation of prediction equations using an observer polynomial and a demonstration that the selection of particular horizons the costing horizons and the control horizon leads to well understood basic techniques such as dead beat pole placement and lq simulated examples show that gpc is suitable for controlling a complex plant such as unstable inverse unstable systems and how the observer polynomial independently tailors the response to the disturbances preprogrammed set points as with robot trajectory control and actuator nonlinearities can also be catered for a discussion of adaptive applications of gpc to several industrial process concludes that the method is easy to use and effective

a theory of diagnosis from first principles suppose one is given a description of a system together with an observation of the system s behaviour which conflicts with the way the system is meant to behave the diagnostic problem is to determine those components of the system which when assumed to be functioning abnormally will explain the discrepancy between the observed and correct system behaviour we propose a general theory for this problem the theory requires only that the system be described in a suitable logic moreover there are many such suitable logics e g first order temporal dynamic etc as a result the theory accommodates diagnostic reasoning in a wide variety of practical settings including digital and analogue circuits medicine and database updates the theory leads to an algorithm for computing all diagnoses and to various results concerning principles of measurement for discriminating among competing diagnoses finally the theory reveals close connections between diagnostic reasoning and nonmonotonic reasoning

reducing belief revision to circumscription and vice versa nonmonotonic formalisms and belief revision operators have been introduced as useful tools to describe and reason about evolving scenarios both approaches have been proven effective in a number of different situations however little is known about their relationship previous work by winslett has shown some correlations between a specific operator and circumscription in this paper we greatly extend winslett s work by establishing new relations between circumscription and a large number of belief revision operators this highlights similarities and differences between these formalisms furthermore these connections provide us with the possibility of importing results in one field into the other one

lazy narrowing strong completeness and eager variable elimination abstract narrowing is an important method for solving unification problems in equational theories that are presented by confluent term rewriting systems because narrowing is a rather complicated operation several authors studied calculi in which narrowing is replaced by more simple inference rules this paper is concerned with one such calculus contrary to what has been stated in the literature we show that the calculus lacks strong completeness so selection functions to cut down the search space are not applicable we prove completeness of the calculus and we establish an interesting connection between its strong completeness and the completeness of basic narrowing we also address the eager variable elimination problem it is known that many redundant derivations can be avoided if the variable elimination rule one of the inference rules of our calculus is given precedence over the other inference rules we prove the completeness of a restricted variant of eager variable elimination in the case of orthogonal term rewriting systems

on strongest neccessary and weakest sufficient conditions abstract given a propositional theory t and a proposition q a sufficient condition of q is one that will make q true under t and a necessary condition of q is one that has to be true for q to be true under t in this paper we propose a notion of strongest necessary and weakest sufficient conditions intuitively the strongest necessary condition of a proposition is the most general consequence that we can deduce from the proposition under the given theory and the weakest sufficient condition is the most general abduction that we can make from the proposition under the given theory we show that these two conditions are dual ones and can be naturally extended to arbitrary formulas we investigate some computational properties of these two conditions and discuss some of their potential applications

negation as failure careful closure procedure abstract the aim of this paper is a modification of minker s generalized closed world assumption that would allow application of the negation as failure rule with respect to a set p of not necessarily all predicates of a database db a careful closure procedure is introduced which when applied to a database db produces a new database db that is used to answer queries about predicates from db it is shown that db is consistent iff db is consistent if p is the set of all predicates from db and db does not contain functional symbols then db coincides with minker s gcwa the soundness and completeness of the careful closure procedure with respect to a minimal model style semantic is shown as an inference engine associated with db we propose a query evaluation procedure qep which is a combination of a method of splitting an indefinite database db into a disjunction of horn databases and clark s query evaluation procedure qep soundness of qep with respect to db is shown for a broad class of databases

nonmonotonic logic ii nonmonotonic modal theories tradmonal logics suffer from the monotomclty problem new axioms never mvahdate old theorems one way to get nd of this problem ts to extend traditional modal logic in the following way the operator m usually read possible is extended so that mp is true whenever p is consistent with the theory then any theorem of this form may be mvahdated if p s added as an axiom this extension results m nonmonotomc versions of the systems t 4 and 5 these systems are complete in that a theorem is provable in a theory based on one of them just if it is true m all noncommittal models of that theory where a noncommittal model ts one m which as many thmgs are possible as possible nonmonotomc 4 is probably the most interesting of the three since it is stronger than ordinary 4 but has all the usual inferential machinery of 4 there is a straightforward proof procedure for the sententlal subset of nonmonotomc 4 this approach to nonmonotonlc logic may be applied to several problems in knowledge representation for aruficml mtelhgence its main advantages over competmg approaches are that tt factors out problems of resource hmltattons and allows the symbol m to appear m any context since m is a meaningful part of the language

classical and weighted knowledgebase transformations abstract in this paper there is a review of some knowledgebase change operators namely the revision update symmetrical model fitting well known in the propositional case and some new problems concerning them there is an extended set of axioms to avoid a certain problem in connection with revision based on the propositional case we give some generalization of revision for first order case furthermore we define an extension of the propositional knowledgebase to weighted knowledgebase finally we deal with the weighted knowledgebase transformations

a logic for default reasoning the need to make default assumptions is frequently encountered in reasoning about incompletely specified worlds inferences sanctioned by default are best viewed as beliefs which may well be modified or rejected by subsequent observations it is this property which leads to the non monotonicity of any logic of defaults in this paper we propose a logic for default reasoning we then specialize our treatment to a very large class of commonly occuring defaults for this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover finally we provide criteria under which the revision of derived beliefs must be effected

assat computing answer sets of a logic program by sat solvers we propose a new translation from normal logic programs with constraints under the answer set semantics to propositional logic given a normal logic program we show that by adding for each loop in the program a corresponding loop formula to the program s completion we obtain a one to one correspondence between the answer sets of the program and the models of the resulting propositional theory in the worst case there may be an exponential number of loops in a logic program to address this problem we propose an approach that adds loop formulas a few at a time selectively based on these results we implement a system called assat x depending on the sat solver x used for computing one answer set of a normal logic program with constraints we test the system on a variety of benchmarks including the graph coloring the blocks world planning and hamiltonian circuit domains our experimental results show that in these domains for the task of generating one answer set of a normal logic program our system has a clear edge over the state of art answer set programming systems smodels and dlv

on the complexity of propositional knowledge base revision updates and counterfactuals abstract we study the complexity of several recently proposed methods for updating or revising propositional knowledge bases under the principle of minimal change in particular we derive complexity results for the following problem given a knowledge base t an update p and a formula q decide whether q is derivable from t p the updated or revised knowledge base note that this problem includes the evaluation of the counterfactual p q over t that is a conditional statement if p then q where p is known or expected to be false we consider the general case where t is an arbitrary propositional formula or theory as well as restricted versions of this problem in particular where t is a conjunction of horn clauses or where the size of the update p is bounded by a constant

a generalized lqg approach to self tuning control part i aspects of design implicit self tuners based on single stage cost function minimization schemes require exact knowledge of the dead time of the controlled plant explicit pole placement self tuners on the other hand though robust against variations of the time delay are very sensitive to the assumptions made about the model order of the plant wrong assumptions may result in very poor performance an explicit method based on minimization of a multistage cost function and a carima plant model formulated in state space is presented the method extends the design features of the generalized minimum variance scheme to the multistage case these can be used to tailor the closed loop response of the system the approach is shown to be robust against wrong a priori assumptions made about the plant dead time or order thus maintaining good servo and disturbance rejection properties see part ii

qualitative probabilities for default reasoning belief revision and causal modeling abstract this paper presents a formalism that combines useful properties of both logic and probabilities like logic the formalism admits qualitative sentences and provides symbolic machinery for deriving deductively closed beliefs and like probability it permits us to express if then rules with different levels of firmness and to retract beliefs in response to changing observations rules are interpreted as order of magnitude approximations of conditional probabilities which impose constraints over the rankings of worlds inferences are supported by a unique priority ordering on rules which is syntactically derived from the knowledge base this ordering accounts for rule interactions respects specificity considerations and facilitates the construction of coherent states of beliefs practical algorithms are developed and analyzed for testing consistency computing rule ordering and answering queries imprecise observations are incorporated using qualitative versions of jeffrey s rule and bayesian updating with the result that coherent belief revision is embodied naturally and tractably finally causal rules are interpreted as imposing markovian conditions that further constrain world rankings to reflect the modularity of causal organizations these constraints are shown to facilitate reasoning about causal projections explanations actions and change

brief optimal expansions of discrete time volterra models using laguerre functions this work is concerned with the optimization of laguerre bases for the orthonormal series expansion of discrete time volterra models the aim is to minimize the number of laguerre functions associated with a given series truncation error thus reducing the complexity of the resulting finite dimensional representation fu and dumont ieee trans automatic control 38 6 1993 934 indirectly approached this problem in the context of linear systems by minimizing an upper bound for the error resulting from the truncated laguerre expansion of impulse response models which are equivalent to first order volterra models a generalization of the work mentioned above focusing on volterra models of any order is presented in this paper the main result is the derivation of analytic strict global solutions for the optimal expansion of the volterra kernels either using an independent laguerre basis for each kernel or using a common basis for all the kernels