a causal approach to nonmonotonic reasoning we introduce logical formalisms of production and causal inference relations based on input output logics of makinson and van der torre j philos logic 29 2000 383 408 these inference relations will be assigned however both standard semantics giving interpretation to their rules and natural nonmonotonic semantics based on the principle of explanation closure the resulting nonmonotonic formalisms will be shown to provide a logical representation of abductive reasoning and a complete characterization of causal nonmonotonic reasoning from mccain and turner proc aaai 97 providence ri 1997 pp 460 465 the results of the study suggest production and causal inference as general nonmonotonic formalisms providing an alternative representation for a significant part of nonmonotonic reasoning

rationality transitivity and contraposition abstract the purpose of this note is to compare the rule of rational monotonicity proposed in 3 and different rules expressing some weak forms of transitivity and contraposition we present four weak forms of transitivity that in preferential logic are equivalent to rational monotonicity and a weak form of contraposition that is strictly weaker than rational monotonicity but equivalent to it in the presence of disjunctive rationality

active logic semantics for a single agent in a static world for some time we have been developing and have had significant practical success with a time sensitive contradiction tolerant logical reasoning engine called the active logic machine alma the current paper details a semantics for a general version of the underlying logical formalism active logic central to active logic are special rules controlling the inheritance of beliefs in general and of beliefs about the current time in particular very tight controls on what can be derived from direct contradictions email protected p and mechanisms allowing an agent to represent and reason about its own beliefs and past reasoning furthermore inspired by the notion that until an agent notices that a set of beliefs is contradictory that set seems consistent and the agent therefore reasons with it as if it were consistent we introduce an apperception function that represents an agent s limited awareness of its own beliefs and serves to modify inconsistent belief sets so as to yield consistent sets using these ideas we introduce a new definition of logical consequence in the context of active logic as well as a new definition of soundness such that when reasoning with consistent premises all classically sound rules remain sound in our new sense however not everything that is classically sound remains sound in our sense for by classical definitions all rules with contradictory premises are vacuously sound whereas in active logic not everything follows from a contradiction

from ordering based nonmonotonic reasoning to conditional logics as ga rdenfors and makinson have recently shown a nonmonotonic inference relation can be generated from a total pre ordering on the set of formulas or equivalently from an uncertainty valuation we build here on these results we include the pre ordering in the language by introducing a conditional operator and we extend the generation of a nonmonotonic inference relation by allowing the use of incompletely specified pre orderings this allows effective procedures for computing nonmonotonic inferences by translating nonmonotonic reasoning into deduction in a conditional logic authors abstract

how does a box work a study in the qualitative dynamics of solid objects this paper is an in depth study of qualitative physical reasoning about one particular scenario using a box to carry a collection of objects from one place to another specifically we consider the plan plan1 load objects ucargo into box obox one by one carry obox from location l1 to location l2 we present qualitative constraints on the shape starting position and material properties of ucargo and obox and on the characteristics of the motion that suffice to make it virtually certain that plan1 can be successfully executed we develop a theory consisting mostly of first order statements together with two default rules that supports an inference of the form if conditions xyz hold and the agent attempts to carry out plan1 then presumably he will succeed our theory is elaboration tolerant in the sense that carrying out the analogous inference for carrying objects in boxes with lids in boxes with small holes or on trays can reuse much of the same knowledge the theory integrates reasoning about continuous time euclidean space commonsense dynamics of solid objects and semantics of partially specified plans

mappings of finite distortion discreteness and openness we establish a sharp integrability condition on the partial derivatives of a mapping with l p integrable distortion for some p n 1 to guarantee discreteness and openness we also show that a mapping with exponentially integrable distortion and integrable jacobian determinant is either constant or both discrete and open we give an example demonstrating the preciseness of our criterion

a polynomial time subsumption algorithm for nominal safe elo under rational closure abstract description logics dls under rational closure rc is a well known framework for non monotonic reasoning in dls in this paper we address the concept subsumption decision problem under rc for nominal safe e l o a notable and practically important dl representative of the owl 2 profile owl 2 el our contribution here is to define a polynomial time subsumption procedure for nominal safe e l o under rc that relies entirely on a series of classical monotonic e l subsumption tests therefore any existing classical monotonic e l reasoner can be used as a black box to implement our method we then also adapt the method to one of the known extensions of rc for dls namely defeasible inheritance based dls without losing the computational tractability

two counterexamples related to baker s approach to the frame problem abstract andrew baker s approach to reasoning about actions is the most robust circumscriptive approach currently known investigation of its applicability to nondeterministic actions reveals that this approach does not allow us to draw some intuitively plausible conclusions also it does not always generate the proper existence of situations axiom the limitations are traced to an unexpected interference of the axioms encoding observations with the minimization a modification that avoids the shortcomings is suggested

nonmonotonic causal theories the nonmonotonic causal logic defined in this paper can be used to represent properties of actions including actions with conditional and indirect effects nondeterministic actions and concurrently executed actions it has been applied to several challenge problems in the theory of commonsense knowledge we study the relationship between this formalism and other work on nonmonotonic reasoning and knowledge representation and discuss its implementation called the causal calculator

representing action indeterminacy and ramifications abstract we define and study a high level language for describing actions more expressive than the action language a introduced by gelfond and lifschitz the new language ar allows us to describe actions with indirect effects ramifications nondeterministic actions and actions that may be impossible to execute it has symbols for nonpropositional fluents and for the fluents that are exempt from the commonsense law of inertia temporal projection problems specified using the language ar can be represented as nested abnormality theories based on the situation calculus

inductive situation calculus temporal reasoning has always been a major test case for knowledge representation formalisms in this paper we develop an inductive variant of the situation calculus in id logic classical logic extended with inductive definitions this logic has been proposed recently and is an extension of classical logic it allows for a uniform representation of various forms of definitions including monotone inductive definitions and non monotone forms of inductive definitions such as iterated induction and induction over well founded posets we show that the role of such complex forms of definitions is not limited to mathematics but extends to commonsense knowledge representation in the id logic axiomatization of the situation calculus fluents and causality predicates are defined by simultaneous induction on the well founded poset of situations the inductive approach allows us to solve the ramification problem for the situation calculus in a uniform and modular way our solution is among the most general solutions for the ramification problem in the situation calculus using previously developed modularity techniques we show that the basic variant of the inductive situation calculus without ramification rules is equivalent to reiter style situation calculus

dynamic belief revision operators the agm approach to belief change is not geared to provide a decent account of iterated belief change darwiche and pearl have sought to extend the agm proposal in an interesting way to deal with this problem we show that the original darwiche pearl approach is on the one hand excessively strong and on the other rather limited in scope the later darwiche pearl approach we argue although it addresses the first problem still remains rather permissive we address both these issues by 1 assuming a dynamic revision operator that changes to a new revision operator after each instance of belief change and 2 strengthening the darwiche pearl proposal moreover we provide constructions of this dynamic revision operator via entrenchment kinematics as well as a simple form of lexicographic revision and prove representation results connecting these accounts

the suprem architecture a new intelligent paradigm abstract we investigate the model theory of the notion of circumscription and find completeness theorems that provide a partial converse to a result of mccarthy we show that the circumscriptive theorems are precisely the truths of the minimal models in the case of various classes of theories and for various versions of circumscription we also present an example of commonsense reasoning in which first order circumscription does not achieve the intuitive and desired minimization

note about cardinality based circumscription abstract in a very interesting paper liberatore and schaerf showed how to express the leading proposals of belief revision using a circumscription in order to deal with one of the belief revision theories they had to introduce a new circumscription based on the cardinality instead of the classical set inclusion we give a few properties of this new circumscription in doing so we prove that in the finite case there is inter definability between ordinary circumscription and cardinality based circumscription we show why a technical result published in the initial paper cannot be true and we give a related result which is true instead where the respective roles of the varying or fixed propositions are reversed this result could help automatic computation we use the logical properties of circumscriptions and cardinality based circumscriptions in order to highlight the behavior of cardinality based circumscription and the importance of the fixed propositions this study allows a full description of the expressive power of cardinality based circumscription in the finite case and it provides some limitations in the infinite case

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

a defeasible reasoning model of inductive concept learning from examples and communication this paper introduces a logical model of inductive generalization and specifically of the machine learning task of inductive concept learning icl we argue that some inductive processes like icl can be seen as a form of defeasible reasoning we define a consequence relation characterizing which hypotheses can be induced from given sets of examples and study its properties showing they correspond to a rather well behaved non monotonic logic we will also show that with the addition of a preference relation on inductive theories we can characterize the inductive bias of icl algorithms the second part of the paper shows how this logical characterization of inductive generalization can be integrated with another form of non monotonic reasoning argumentation to define a model of multiagent icl this integration allows two or more agents to learn in a consistent way both from induction and from arguments used in the communication between them we show that the inductive theories achieved by multiagent induction plus argumentation are sound i e they are precisely the same as the inductive theories built by a single agent with all data

a non monotonic description logic for reasoning about typicality in this paper we propose a non monotonic extension of the description logic alc for reasoning about prototypical properties and inheritance with exceptions the resulting logic called alc t m i n is built upon a previously introduced monotonic logic alc t that is obtained by adding a typicality operator t to alc the operator t is intended to select the most normal or most typical instances of a concept so that knowledge bases may contain subsumption relations of the form t c d t c is subsumed by d expressing that typical c members are instances of concept d from a knowledge representation point of view the monotonic logic alc t is too weak to perform inheritance reasoning in alc t m i n in order to perform non monotonic inferences we define a minimal model semantics over alc t the intuition is that preferred or minimal models are those that maximize typical instances of concepts by means of alc t m i n we are able to infer defeasible properties of explicit or implicit individuals we also present a tableau calculus for deciding alc t m i n entailment that allows to give a complexity upper bound for the logic namely that query entailment is in co nexp n p

defeasible reasoning with variable degrees of justification the question addressed in this paper is how the degree of justification of a belief is determined a conclusion may be supported by several different arguments the arguments typically being defeasible and there may also be arguments of varying strengths for defeaters for some of the supporting arguments what is sought is a way of computing the on sum degree of justification of a conclusion in terms of the degrees of justification of all relevant premises and the strengths of all relevant reasons i have in the past defended various principles pertaining to this problem in this paper i reaffirm some of those principles but propose a significantly different final analysis specifically i endorse the weakest link principle for the computation of argument strengths according to this principle the degree of justification an argument confers on its conclusion in the absence of other relevant arguments is the minimum of the degrees of justification of its premises and the strengths of the reasons employed in the argument i reaffirm my earlier rejection of the accrual of reasons according to which two arguments for a conclusion can result in a higher degree of justification than either argument by itself this paper diverges from my earlier theory mainly in its treatment of defeaters first it argues that defeaters that are too weak to defeat an inference outright may still diminish the strength of the conclusion second in the past i have also denied that multiple defeaters can result in the defeat of an argument that is not defeated by any of the defeaters individually in this paper i urge that there are compelling examples that support a limited version of this collaborative defeat the need to accommodate diminishers and collaborative defeat has important consequences for the computation of degrees of justification the paper proposes a characterization of degrees of justification that captures the various principles endorsed and constructs an algorithm for computing them

the value of the four values in his well known paper how computer should think belnap 1977 argues that four valued semantics is a very suitable setting for computerized reasoning in this paper we vindicate this thesis by showing that the logical role that the four valued structure has among ginsberg s bilattices is similar to the role that the two valued algebra has among boolean algebras specifically we provide several theorems that show that the most useful bilattice valued logics can actually be characterized as four valued inference relations in addition we compare the use of three valued logics with the use of four valued logics and show that at least for the task of handling inconsistent or uncertain information the comparison is in favor of the latter

mappings of finite distortion monotonicity and continuity we study mappings f f1 fn rn in the sobolev space w loc r n where is a connected open subset of rn with n 2 thus for almost every x we can speak of the linear transformation d f x rn rn called differential of f at x its norm is defined by d f x sup d f x h h sn 1 we shall often identify d f x with its matrix and denote by j x f det d f x the jacobian determinant thus using the language of differential forms we can write

a maximum entropy approach to nonmonotonic reasoning an approach to nonmonotonic reasoning that combines the principle of infinitesimal probabilities with that of maximum entropy thus extending the inferential power of the probabilistic interpretation of defaults is proposed a precise formalization of the consequences entailed by a conditional knowledge base is provided the computational machinery necessary for drawing these consequences is developed and the behavior of the maximum entropy approach is compared to related work in default reasoning the resulting formalism offers a compromise between two extremes the cautious approach based on the conditional interpretations of defaults and the bold approach based on minimizing abnormalities

impediments to universal preference based default theories research on nonmonotonic and default reasoning has identified several important criteria for preferring alternative default inferences the theories of reasoning based on each of these criteria may uniformly be viewed as theories of rational inference in which the reasoner selects maximally preferred states of belief though researchers have noted some cases of apparent conflict between the preferences supported by different theories it has been hoped that these special theories of reasoning may be combined into a universal logic of nonmonotonic reasoning we show that the different categories of preferences conflict more than has been realized and adapt formal results from social choice theory to prove that every universal theory of default reasoning will violate at least one reasonable principle of rational reasoning our results can be interpreted as demonstrating that within the preferential framework we cannot expect much improvement on the rigid lexicographic priority mechanisms that have been proposed for conflict resolution

double preference relations for generalised belief change many belief change formalisms employ plausibility orderings over the set of possible worlds to determine how the beliefs of an agent ought to be modified after the receipt of a new epistemic input while most such possible world semantics rely on a single ordering we investigate the use of an additional preference ordering representing for instance the epistemic context the agent finds itself in to guide the process of belief change we show that the resultant formalism provides a unifying semantics for a wide variety of belief change operators by varying the conditions placed on the second ordering different families of known belief change operators can be captured including agm belief contraction and revision rott and pagnucco s severe withdrawal the systematic withdrawal of meyer et al as well as the linear liberation and s liberation operators of booth et al our approach also identifies novel classes of belief change operators worthy of further investigation

qualitative decision theory from savage s axioms to nonmonotonic reasoning this paper investigates to what extent a purely symbolic approach to decision making under uncertainty is possible in the scope of artificial intelligence contrary to classical approaches to decision theory we try to rank acts without resorting to any numerical representation of utility or uncertainty and without using any scale on which both uncertainty and preference could be mapped our approach is a variant of savage s where the setting is finite and the strict preference on acts is a partial order it is shown that although many axioms of savage theory are preserved and despite the intuitive appeal of the ordinal method for constructing a preference over acts the approach is inconsistent with a probabilistic representation of uncertainty the latter leads to the kind of paradoxes encountered in the theory of voting it is shown that the assumption of ordinal invariance enforces a qualitative decision procedure that presupposes a comparative possibility representation of uncertainty originally due to lewis and usual in nonmonotonic reasoning our axiomatic investigation thus provides decision theoretic foundations to the preferential inference of lehmann and colleagues however the obtained decision rules are sometimes either not very decisive or may lead to overconfident decisions although their basic principles look sound this paper points out some limitations of purely ordinal approaches to savage like decision making under uncertainty in perfect analogy with similar difficulties in voting theory

conditional entailment bridging two approaches to default reasoning abstract in recent years two conceptually different interpretations of default expressions have been advanced extensional interpretations in which defaults are regarded as prescriptions for extending one s set of beliefs and conditional interpretations in which defaults are regarded as beliefs whose validity is bound to a particular context the two interpretations possess virtues and limitations that are practically orthogonal to each other the conditional interpretations successfully resolve arguments of different specificity e g penguins don t fly in spite of being birds but fail to capture arguments of irrelevance e g concluding red birds fly from birds fly the opposite is true for the extensional interpretations this paper develops a new account of defaults called conditional entailment which combines the benefits of the two interpretations like prioritized circumscriptions conditional entailment resolves arguments by enforcing priorities among defaults however instead of having to be specified by the user these priorities are extracted automatically from the knowledge base similarly conditional entailment possesses a sound and complete proof theory based on interacting arguments and amenable to implementation in conventional atmss

an axiomatic analysis of structured argumentation with priorities several systems of semantics have been proposed for structured argumentation with priorities as the proposed semantics often sanction contradictory conclusions even for skeptical reasoners there is a fundamental need for guidelines for understanding and evaluating them especially their conceptual foundation and relationship in this paper we present an axiomatic analysis of the semantics of structured defeasible argumentation both with and without preferences by introducing a class of ordinary attack relations satisfying a set of simple and intuitive properties we show that there exists a normal form for ordinary attack relations in the sense that stable extensions wrt any ordinary attack relation are stable extensions wrt the normal attack relations we relate the ordinary semantics to other approaches especially to the aspic framework and the prioritized approaches in logic programming

motivated action theory a formal theory of causal reasoning when we reason about change over time it causation provides an implicit preference we prefer sequences of situations in which one situation leads causally to the next rather than sequences in which one situation follows another at random and without causal connections in this paper we explore the problem of temporal reasoning reasoning about change over time and the crucial role that causation plays in our intuitions we examine previous approaches to temporal reasoning and their shortcomings in light of this analysis we propose a new system for it causal reasoning motivated action theory which builds upon causation as a crucial preference criterion motivated action theory solves the traditional problems of both forward and backward reasoning and additionally provides a basis for a new theory of explanation

provably correct theories of action we investigate logical formalization of the effects of actions in the situation calculus we propose a formal criterion against which to evaluate theories of deterministic actions we show how the criterion provides us a formal foundation upon which to tackle the frame problem as well as its variant in the context of concurrent actions our main technical contributions are in formulating a wide class of monotonic causal theories that satisfy the criterion and showing that each such theory can be reformulated succinctly in circumscription

probabilistic horn abduction and bayesian networks this paper presents a simple framework for horn clause abduction with probabilities associated with hypotheses the framework incorporates assumptions about the rule base and independence assumptions amongst hypotheses it is shown how any probabilistic knowledge representable in a discrete bayesian belief network can be represented in this framework the main contribution is in finding a relationship between logical and probabilistic notions of evidential reasoning this provides a useful representation language in its own right providing a compromise between heuristic and epistemic adequacy it also shows how bayesian networks can be extended beyond a propositional language this paper also shows how a language with only unconditionally independent hypotheses can represent any probabilistic knowledge and argues that it is better to invent new hypotheses to explain dependence rather than having to worry about dependence in the language

on first order conditional logics abstract conditional logics have been developed as a basis from which to investigate logical properties of weak conditionals representing for example counterfactual and default assertions this work has largely centred on propositional approaches however it is clear that for a full account a first order logic is required existing or obvious approaches to first order conditional logics are inadequate in particular various representational issues in default reasoning are not addressed by extant approaches further these problems are not unique to conditional logic but arise in other nonmonotonic reasoning formalisms i argue that an adequate first order approach to conditional logic must admit domains that vary across possible worlds as well the most natural expression of the conditional operator binds variables although this binding may be eliminated by definition a possible worlds approach based on kripke structures is developed and it is shown that this approach resolves various problems that arise in a first order setting including specificity arising from nested quantifiers in a formula and an analogue of the lottery paradox that arises in reasoning about default properties

modeling a dynamic and uncertain world i symbolic and probabilistic reasoning about change abstract intelligent agency requires some ability to predict the future an agent must ask itself what is presently its best course of action given what it now knows about what the world will be like when it intends to act this paper presents a system that uses a probabilistic model to reason about the effects of an agent s proposed actions on a dynamic and uncertain world computing the probability that relevant propositions will hold at a specified point in time the model allows for incomplete information about the world the occurrence of exogenous unplanned events unreliable sensors and the possibility of an imperfect causal theory the system provides an application program with answers to questions of the form is the probability that will hold in the world at time t greater than it is unique among algorithms for probabilistic temporal reasoning in that it tries to limit its inference according to the proposition time and probability threshold provided by the application the system will also notify the application if subsequent evidence invalidates its answer to a query

similarity between preferential models the notion of bisimulation is an important concept in process algebra and modern modal logic this paper explores the notion of b similarity which is a kind of bisimulation between preferential models we characterize the equivalence of preferential models in terms of b similarity however this result is applicable only for preferential models of finite depth to overcome this defect we introduce a weak notion of similarity called m similarity and obtain a result corresponding to hennessy milner theorem and keisler shelah s isomorphism theorem in modal logic and first order logic respectively as its application we investigate the expressive power of boolean combinations of conditional assertions bca for short and prove that bcas are the fragments of first order language preserved under m similarity moreover we obtain a characterization for elementary classes defined by bcas a notion of first order translation originating from modal logic plays an important role in this paper in order to illustrate that first order translation is a powerful tool in the study of nonmonotonic logic some model theoretic results about preferential models are proved based on this translation

on the satisfiability of circumscription abstract etherington mercer and reiter showed on the basis of ideas of bossu and siegel that circumscription cannot lead to inconsistency for universal formulas we extend this result in three directions to formulas of a more general syntactic form to circumscription with some predicate symbols allowed to vary and to prioritized circumscription

a unifying action calculus mccarthy s situation calculus is arguably the oldest special purpose knowledge representation formalism designed to axiomatize knowledge of actions and their effects four decades of research in this area have led to a variety of alternative formalisms while some approaches can be considered instances or extensions of the classical situation calculus like reiter s successor state axioms or the fluent calculus there are also special planning languages like adl and approaches based on a linear rather than branching time structure like the event calculus the co existence of many different calculi has two main disadvantages the formal relations among them is a largely open issue and a lot of today s research concerns the transfer of specific results from one approach to another in this paper we present a unifying action calculus which encompasses well defined classes of all of the aforementioned formalisms our calculus not only facilitates comparisons and translations between specific approaches it also allows to solve interesting problems for various calculi at once we exemplify this by providing a general calculus independent solution to a problem of practical relevance which is intimately related to mccarthy s quest for elaboration tolerant formalisms the modularity of domain axiomatizations

reasoning by cases in default logic reiter s default logic is one of the most popular formalisms for describing default reasoning one important defect of default logic is however the inability to reason by cases over the years several solutions for this problem have been proposed all these proposals deal with deriving new propositions through reasoning by cases none however discuss the propositions that should no longer be derivable as a result of reasoning by cases this paper discusses the latter subject it shows that an intuitively plausible way of dealing with propositions that should no longer be derivable as a result of reasoning by cases can have far reaching consequences one of the consequences is that disjunctions must be viewed as describing possible extensions

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

ramification and causality abstract in formal systems for reasoning about actions the ramification problem denotes the problem of handling indirect effects these effects are not explicitly represented in action specifications but follow from general laws describing dependencies among components of the world state an adequate treatment of indirect effects requires a suitably weakened version of the general law of persistence it also requires a method to avoid unintuitive changes suggested by the aforementioned dependency laws we propose a solution to the ramification problem that uses directed relations between two single effects stating the circumstances under which the occurrence of the first causes the second we argue for the necessity of an approach based on causality by elaborating the limitations of common paradigms employed to handle ramifications the principle of categorization and the policy of minimal change our abstract solution is realized on the basis of a particular action calculus namely the fluent calculus

from statistical knowledge bases to degrees of belief an intelligent agent will often be uncertain about various properties of its environment and when acting in that environment it will frequently need to quantify its uncertainty for example if the agent wishes to employ the expected utility paradigm of decision theory to guide its actions it will need to assign degrees of belief subjective probabilities to various assertions of course these degrees of belief should not be arbitrary but rather should be based on the information available to the agent this paper describes one approach for inducing degrees of belief from very rich knowledge bases that can include information about particular individuals statistical correlations physical laws and default rules we call our approach the random worlds method the method is based on the principle of indifference it treats all of the worlds the agent considers possible as being equally likely it is able to integrate qualitative default reasoning with quantitative probabilistic reasoning by providing a language in which both types of information can be easily expressed our results show that a number of desiderata that arise in direct inference reasoning from statistical information to conclusions about individuals and default reasoning follow directly from the semantics of random worlds for example random worlds captures important patterns of reasoning such as specificity inheritance indifference to irrelevant information and default assumptions of independence furthermore the expressive power of the language used and the intuitive semantics of random worlds allow the method to deal with problems that are beyond the scope of many other nondeductive reasoning systems

nonmonotonic reasoning in the framework of situation calculus abstract most of the solutions proposed to the yale shooting problem have either introduced new nonmonotonic reasoning methods generally involving temporal priorities or completely reformulated the domain axioms to represent causality explicitly this paper presents a new solution based on the idea that since the abnormality predicate takes a situational argument it is important for the meanings of the situations to be held constant across the various models being compared this is accomplished by a simple change in circumscription policy when ab is circumscribed result rather than holds is allowed to vary in addition we need an axiom ensuring that every consistent situation is included in the domain of discourse ordinary circumscription will then produce the intuitively correct answer beyond its conceptual simplicity the solution proposed here has additional advantages over the previous approaches unlike the approach that uses temporal priorities it can support reasoning backward in time as well as forward and unlike the causal approach it can handle ramifications in a natural manner

an approach to default reasoning based on a first order conditional logic revised report abstract an approach to default reasoning based on an extension to classical first order logic is presented in this approach first order logic is augmented with a variable conditional operator for representing default statements the statement is read as if then normally truth in the resulting logic is based on a possible worlds semantics is true just when is true in the least exceptional worlds in which is true this system provides a basis for representing and reasoning about default statements inferences of default properties of individuals rely on two assumptions first that the world being modelled is as unexceptional as consistently possible and second that sentences that may consistently be assumed to be irrelevant to a default inference are in fact irrelevant to the inference two formulations of default inferencing are developed the first involves extending the set of default statements to include all combinations of irrelevant properties the second involves assuming that the world being modelled is among the simplest worlds consistent with the defaults and with what is contingently known in the end the two approaches prove to be equivalent with respect to their respective set of default inferences finally it is shown how the approach treats two current problems in default reasoning the first problem concerns the ordering of default statements the second concerns a problem of hanks and mcdermott for dealing with multiple extensions of a set of defaults

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

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

conditional logics of normality a modal approach abstract several conditional theories of default reasoning have recently been proposed for the representation of statements about normal states of affairs or prototypical properties the natural semantics of these systems and their ability to reason about default rules make these approaches quite appealing we present a family of modal logics in which we define a conditional connective for statements of normality and examine its properties we also demonstrate that two of the most important conditional approaches are equivalent to fragments of our conditional logics of normality and to standard modal logics the approach we take is general enough to allow the expression of a number of different forms of defeasible reasoning and can be used to illustrate the relationship between these types of reasoning e g belief revision subjunctive and autoepistemic reasoning and our default logics this relationship is explored in a companion paper

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

analytical expression of explicit mpc solution via lattice piecewise affine function an analytical expression of the explicit solution to linear model predictive control mpc is proposed by the introduction of a lattice piecewise affine pwa function a systematic procedure is developed for building a lattice pwa representation from a continuous explicit mpc solution obtained by a multi parametric program a simple method is presented to remove the redundant parameters in the lattice expression of mpc control laws the effectiveness of this approach is supported by the study of three benchmark mpc problems the proposed analytical expression provides a very efficient and practically viable method for implementing the explicit mpc solutions regarding its online calculation and memory space requirements

nonmonotonic logic and temporal projection abstract nonmonotonic formal systems have been proposed as an extension to classical first order logic that will capture the process of human default reasoning or plausible inference through their inference mechanisms just as modus ponens provides a model for deductive reasoning but although the technical properties of these logics have been studied in detail and many examples of human default reasoning have been identified for the most part these logics have not actually been applied to practical problems to see whether they produce the expected results we provide axioms for a simple problem in temporal reasoning which has long been identified as a case of default reasoning thus presumably amenable to representation in nonmonotonic logic upon examining the resulting nonmonotonic theories however we find that the inferences permitted by the logics are not those we had intended when we wrote the axioms and in fact are much weaker this problem is shown to be independent of the logic used nor does it depend on any particular temporal representation upon analyzing the failure we find that the nonmonotonic logics we considered are inherently incapable of representing this kind of default reasoning the first part of the paper is an expanded version of one that appeared in the 1986 aaai proceedings the second part reports on several responses to our result that have appeared since the original paper was published

comments on analytical expression of explicit mpc solution via lattice piecewise affine function automatica 45 2009 910 917 the simplification conditions for lattice representation of the pwa control law in the explicit mpc suggested in the aforementioned article are shown by means of a counterexample not to be sufficient in view of this a modified lemma is proposed in this note for ensuring the sufficiency

quatum logic hilbert space revision theory our starting point is the observation that with a given hilbert space h we may in a way to be made precise associate a class of non monotonic consequence relations in such a way that there exists a one to one correspondence between the rays of h and these consequence relations the projectors in hilbert space may then be viewed as a sort of revision operators the lattice of closed subspaces appears as a natural generalisation of the concept of a lindenbaum algebra in classical logic the logics presentable by hilbert spaces are investigated and characterised moreover the individual consequence relations are studied a key concept in this context is that of a consequence relation having a pointer to itself it is proved that such consequence relations have certain remarkable properties in that they reflect their metatheory at the object level to a surprising extent the tools used in the investigation stem from two different areas of research namely from the disciplines of non monotonic logic on the one hand and from hilbert space theory on the other there exist surprising connections between these two fields of research the investigation of which constitutes the purpose of this pape

a first order conditional logic for prototypical properties abstract an approach for representing knowledge about defaults and prototypical properties is presented this is accomplished by adding to first order logic a variable conditional operator to express relations between entities and prototypical properties of such entities truth conditions for this operator are based on a possible worlds semantics a proof theory is provided and the logic is shown to be sound and complete properties of the resultant formal system are argued to correspond to common intuitions concerning defaults and prototypical properties moreover the system is argued to provide a more appropriate basis for representing knowledge about such entities than other existing approaches

a nonmonotonic observation logic a variant of reiter s default logic is proposed as a logic for reasoning with defeasible observations traditionally default rules are assumed to represent generic information and the facts are assumed to represent specific information about the situation but in this paper the specific information derives from defeasible observations represented by normal free default rules and the facts represent hard background knowledge whenever the evidence underlying some observation is more refined than the evidence underlying another observation this is modelled by means of a priority between the default rules representing the observations we thus arrive at an interpretation of prioritized normal free default logic as an observation logic and we propose a semantics for this observation logic finally we discuss how the proposed observation logic relates to the multiple extension problem and the problem of sensor fusion

qualitative decision theory with preference relations and comparative uncertainty an axiomatic approach this paper investigates a purely qualitative approach to decision making under uncertainty since the pioneering work of savage most models of decision under uncertainty rely on a numerical representation where utility and uncertainty are commensurate giving up this tradition we relax this assumption and introduce an axiom of ordinal invariance requiring that the decision maker s preference between two acts only depends on the relative position of their consequences for each state within this qualitative framework we determine the only possible form of the corresponding decision rule then assuming the transitivity of the strict preference the underlying partial confidence relations are those at work in non monotonic inference and thus satisfy one of the main properties of possibility theory the satisfaction of additional postulates of unanimity and anonymity enforces the use of a necessity measure unique up to a monotonic transformation for encoding the relative likelihood of events

measuring the incremental information value of documents the incremental searcher satisfaction model for information retrieval has been introduced to capture the incremental information value of documents in this paper from various cognitive perspectives searcher requirements are derived in terms of the increment function different approaches for the construction of increment functions are identified such as the individual and the collective approach translating the requirements to similarity functions leads to the so called base similarity features and the monotonicity similarity features we show that most concrete similarity functions in ir such as inclusion jaccard s dice s and cosine coefficient and some other approaches to similarity functions possess the base similarity features the inclusion coefficient also satisfies the monotonicity features

a characterization theorem for injective model classes axiomatized by general rules we continue the work in zhu et al normal conditions for inference relations and injective models theoret comput sci 309 2003 287 311 a class of strict partial order structures posets for short is said to be axiomatizable if the class of all injective preferential models from may be characterized in terms of general rules this paper aims to obtain some characteristics of axiomatizable classes to do this a monadic second order frame language is presented the relationship between 0 axiomatizability and second order definability is explored then a notion of an admissible set is introduced based on this notion we show that any preferential model which does not contain any four node substructure must be a reduct of some injective model furthermore we furnish a necessary and sufficient condition for the axiomatizability of classes of injective preferential models using general rules finally we show that in some sense the class of all posets without any four node substructure is the largest among axiomatizable classes

the expressive power of circumscription abstract circumscription is a form of nonmonotonic reasoning introduced by mccarthy 1997 as a way of characterizing defaults using second order logic the consequences of circumscription are those formulas true in the minimal models under a pre order on models in the case of domain circumscription the pre order was the sub model relation formula circumscription mccarthy 1980 1986 is characterized by minimizing a set of formulas one model is preferred to another model when the extensions of the minimized formulas in the first are subsets of the extensions in the second we show that the propositional version of formula circumscription can capture all pre orders on valuations of finite languages we consider the question of infinite languages and give the corresponding representation theorems we further show that there are natural defaults inertia in temporal projection captured by inductive definitions that cannot be captured by circumscription in the first order case finally contrary to previous claims we show that propositional formula circumscription can capture all preferential consequence relations over finite propositional languages as defined by kraus et al 1990 thus in the finite propositional case there is no restriction on the kinds of preferential defaults that circumscription can describe

mappings of finite distortion hausdorff measure of zero sets we prove that a for a mapping f of finite distortion k in l p n p the n p hausdorff measure of any point preimage is zero provided j f is integrable df in l s with s p and the multiplicity function of f is essentially bounded as a consequence for p n 1 we obtain that the mapping is then open and discrete

a new semantics for overriding in description logics abstract many modern applications of description logics dls for short such as biomedical ontologies and semantic web policies provide fresh motivations for extending dls with nonmonotonic inferences a topic that has attracted a significant amount of attention along the years despite this nonmonotonic inferences are not yet supported by dl technology due to a number of issues related to expressiveness computational complexity and optimizations this paper contributes to the practical support of nonmonotonic inferences in description logics by introducing a new semantics expressly designed to address knowledge engineering needs this formalism has appealing expressiveness enjoys nice computational properties and constitutes an interesting solution to an ample class of application needs the formalism is validated through extensive comparison with the other nonmonotonic dls and systematic scalability tests the test case generator and its novel validation methodology constitute a further contribution of this paper

a representation theorem for recovering contraction relations satisfying wci a notion of an image structure associated with the canonical epistemic state is introduced based on it we get a representation result for recovering contraction inference relations satisfying the condition weak conjunctive inclusion wci in terms of f standard epistemic agm states in effect this result establishes a representation theorem for belief contraction functions satisfying agm postulates k 1 k 7 and rott s wci and k 8c and hence generalizes rott s corresponding result in the finite framework

defaults in domain theory abstract this paper uses ideas from artificial intelligence to show how default notions can be defined over scott domains we combine these ideas with ideas arising in domain theory to shed some light on the properties of nonmonotonicity in a general model theoretic setting we consider in particular a notion of default nonmonotonic entailment between prime open sets in the scott topology of a domain we investigate in what ways this notion obeys the so called laws of cautious monotony and cautious cut proposed by gabbay kraus lehmann and magidor our notion of nonmonotonic entailment does not necessarily satisfy cautious monotony but does satisfy cautious cut in fact we show that any reasonable notion of nonmonotonic entailment on prime opens over a scott domain satisfying in particular the law of cautious cut can be concretely represented using our notion of default entailment we also give a variety of sufficient conditions for defaults to induce cumulative entailments those satisfying cautious monotony in particular we show that defaults with unique extensions are a representation of cumulative nonmonotonic entailment furthermore a simple characterization is given for those default sets which determine unique extensions in coherent domains finally a characterization is given for scott domains in which default entailment must be cumulative this is the class of daisy domains it is shown to be cartesian closed a purely domain theoretic result

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

acyclic logic programs and the completeness of sldnf resolution abstract this paper investigates the class of acyclic programs programs with the usual hierarchical condition imposed on ground instances of atoms rather than predicate symbols the acyclic condition seems to naturally capture much of the recursion that occurs in practice and many programs that arise in practical programming satisfy this condition we prove completeness of sldnf resolution for the acyclic programs and discuss several other desirable properties exhibited by programs belonging to this class

on decision theoretic foundations for defaults in recent years considerable effort has gone into understanding default reasoning most of this effort concentrated on the question of entailment i e what conclusions are warranted by a knowledge base of defaults surprisingly few works formally examine the general role of defaults we argue that an examination of this role is necessary in order to understand defaults and suggest a concrete role for defaults defaults simplify our decision making process allowing us to make fast approximately optimal decisions by ignoring certain possible states in order to formalize this approach we examine decision making in the framework of decision theory we use probability and utility to measure the impact of possible states on the decision making process more precisely we examine when a consequence relation which is the set of default inferences made by an inference system can be compatible with such a decision theoretic setup we characterize general properties that such consequence relations must satisfy and contrast them with previous analysis of default consequence relations in the literature in particular we show that such consequence relations must satisfy the properties of cumulative reasoning finally we compare our approach with poole s decision theoretic defaults and show how both can be combined to form an attractive framework for reasoning about decisions

on the consistency of defeasible databases abstract we propose a norm of consistency for a mixed set of defeasible and strict sentences which guided by a probabilistic interpretation of these sentences establishes a clear distinction between exceptions ambiguities and outright contradictions a notion of entailment is then defined which represents a minimal core of beliefs that must follow from the database if one is committed to avoid inconsistencies the paper establishes necessary and sufficient conditions for consistency and provides a simple decision procedure for testing the consistency of a database or whether a given sentence is entailed by the database it is also shown that if all sentences are of horn type consistency and entailment can be tested in polynomial time finally we discuss procedures for reasoning with inconsistent databases and identifying sentences directly responsible for the inconsistency

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

generalized possibilistic logic foundations and applications to qualitative reasoning about uncertainty this paper introduces generalized possibilistic logic gpl a logic for epistemic reasoning based on possibility theory formulas in gpl correspond to propositional combinations of assertions such as it is certain to degree that the propositional formula is true as its name suggests the logic generalizes possibilistic logic pl which at the syntactic level only allows conjunctions of the aforementioned type of assertions at the semantic level pl can only encode sets of epistemic states encompassed by a single least informed one whereas gpl can encode any set of epistemic states this feature makes gpl particularly suitable for reasoning about what an agent knows about the beliefs of another agent e g allowing the former to draw conclusions about what the other agent does not know we introduce an axiomatization for gpl and show its soundness and completeness w r t possibilistic semantics subsequently we highlight the usefulness of gpl as a powerful unifying framework for various knowledge representation formalisms among others we show how comparative uncertainty and ignorance can be modelled in gpl we also exhibit a close connection between gpl and various existing formalisms including possibilistic logic with partially ordered formulas a logic of conditional assertions in the style of kraus lehmann and magidor answer set programming and a fragment of the logic of minimal belief and negation as failure finally we analyse the computational complexity of reasoning in gpl identifying decision problems at the first second third and fourth level of the polynomial hierarchy

default extensions dealing with computer information a conditional knowledge base may be sometimes analyzed as a union of several pieces of information that are provided by independent sources in this case it is possible to extend separately each of these subbases via their rational closure and then glue the results together to get a rational extension of the whole base in which the specificity of its components is taken into account the resulting inference relation is free from the undesirable and counterintuitive results that can be encountered in the z system lex system or w system

explaining updates by minimal sums human reasoning about developments of the world involves always an assumption of inertia we discuss two approaches for formalizing such an assumption based on the concept of an explanation 1 there is a general preference relation given on the set of all explanations and 2 there is a notion of a distance between models and explanations are preferred if their sum of distances is minimal each distance dist naturally induces a preference relation dist we show exactly under which conditions the converse is true as well and therefore both approaches are equivalent modulo these conditions our main result is a general representation theorem in the spirit of kraus lehmann and magidor copyright 2001 elsevier science b v

extension of the concept of propositional deduction from classical logic to probability an overview of probability selection approaches abstract establishing a rigorous framework for propositional deduction which also agrees with what is termed commonsense reasoning poses a difficult challenge this paper is the first of a two part effort in considering the issue and proposing in future part 2 a particular approach via the use of second order probabilities i e distributions of probability measures as opposed to probability selection approaches especially that of maximum entropy and adams high probability schemes in the second order probability approach usually all probability distributions are assumed a priori to be either equally likely or more generally to be distributed via the dirichlet family up to the constraints involved in the premise set of the potential deduction considered

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