a computational approach to approximate and plausible reasoning with applications to expert systems the intended purpose of this paper is twofold proposing a common basis for the modeling of uncertainty and imprecision and discussing various kinds of approximate and plausible reasoning schemes in this framework together with probability different kinds of uncertainty measures credibility and plausibility functions in the sense of shafer possibility measures in the sense of zadeh and the dual measures of necessity sugeno s g fuzzy measures are introduced in a unified way the modeling of imprecision in terms of possibility distribution is then presented and related questions such as the measure of the uncertainty of fuzzy events the probability and possibility qualification of statements the concept of a degree of truth and the truth qualification of propositions are discussed at length deductive inference from premises weighted by different kinds of measures by uncertainty or by truth values in the framework of various multivalued logics is fully investigated then deductive inferences from imprecise or fuzzy premises are dealt with patterns of reasoning where both uncertainty and imprecision are present are also addressed the last section is devoted to the combination of uncertain or imprecise pieces of information given by different sources on the whole this paper is a tentative survey of quantitative approaches in the modeling of uncertainty and imprecision including recent theoretical proposals as well as more empirical techniques such as the ones developed in expert systems such as mycin or prospector the management of uncertainty and imprecision in reasoning patterns being a key issue in artificial intelligence

some representational issues in default reasoning abstract although most commonly occurring default rules are normal when viewed in isolation they can interact with each other in ways that lead to the derivation of anomalous default assumptions in order to deal with such anomalies it is necessary to re represent these rules in some cases by introducing non normal defaults the need to consider such potential interactions leads to a new concept of integrity distinct from the conventional integrity issues of first order data bases the non normal default rules required to deal with default interactions all have a common pattern default theories conforming to this pattern are considerably more complex than normal default theories for example they need not have extensions and they lack the property of semi monotonicity current semantic network representations fail to reason correctly with defaults however when viewed as indexing schemes on logical formulae networks can be seen to provide computationally feasible heuristics for the consistency checks required by default reasoning

a logic to reason about likelihood abstract we present a logic ll which uses a modal operator l to help capture the notion of being likely despite the fact that likelihood is not assigned quantitative values through probabilities ll captures many of the properties of likelihood in an intuitively appealing way we give a possible worlds style semantics to ll and using standard techniques of modal logic we give a complete axiomatization for ll and show that satisfiability of ll formulas can be decided in exponential time we discuss how the logic might be used in areas such as medical diagnosis where decision making in the face of uncertainties is crucial we conclude by using ll to give a formal proof of correctness of some aspects of a protocol for exchanging secrets

smooth centre manifolds for impulsive delay differential equations abstract the existence and smoothness of centre manifolds and a reduction principle are proven for impulsive delay differential equations several intermediate results of theoretical interest are developed including a variation of constants formula for linear equations in the phase space of right continuous regulated functions linear variational equation and smoothness of the nonautonomous process and a floquet theorem for periodic systems three examples are provided to illustrate the results

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

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

evaluating the effect of semi normality on the expressiveness of defaults normal default logic ndl and semi normal default logic sndl are syntactically restricted variants of reiter s default logic dl although semi normal defaults have only a slightly more general form than normal defaults sndl does not share the nice properties of ndl e g semi monotonicity in this note we address the effect of semi normality on the expressive power of defaults using a classification method based on polynomial faithful and modular pfm translation functions the resulting classification indicates that sndl and dl are of equal expressive power which strictly exceeds that of ndl this strengthens an earlier result achieved by marek and truszczynski who establish the equivalence of weak semi normal defaults with general defaults furthermore it is established that prerequisite free fragments of dl and sndl pdl and psndl are of equal expressive power consequently psndl is less expressive than dl and sndl incomparable with ndl and more expressive than preferential entailment a generalized form of circumscription the latter result is in sharp contrast with imielinski s result which states that prerequisite free and semi normal default theories can be modularly translated into preferential entailment

fuzzy logic in commercial expert system results and prospects abstract this paper surveys the use of fuzzy methods in commercial applications of the technology of expert systems and in commercial products which aim to support such applications it attempts to evaluate the utility of such an approach to uncertainty management compared to other well known methods of handling uncertainty in expert systems starting from this base it attempts an evaluation of the prospects for fuzzy expert systems in the medium term as a survey it attempts to list applications and commercial products as comprehensively as is practical and includes an extensive bibliography on the topic

results on translating defaults to circumscription abstract in this paper we define different concepts of translating a set of defaults into circumscription the most important of these modular translation requires that additive changes of specific facts not defaults of default theory translate to additive changes of the simple abnormality theory corresponding to circumscription we show that surprisingly enough an important class of defaults normal defaults with prerequisites does not have such a modular translation into circumscription abnormality theory we also establish the classes of defaults which are translatable into circumscription

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

the anomalous extension problem in default reasoning abstract in their recent celebrated paper hanks and mcdermott presented a simple problem in temporal reasoning which showed that a seemingly natural representation of a frame axiom in nonmonotonic logic can give rise to an anomalous extension i e one which is counter intuitive in that it does not appear to be supported by the known facts an alternative less formal approach to nonmonotonic reasoning uses the mechanism of a truth maintenance system tms surprisingly when reformulated in terms of a tms the anomalous extension noted by hanks and mcdermott disappears we analyze the reasons for this first it is seen that anomalous extensions are not limited to temporal reasoning but can occur in simple nontemporal default reasoning as well in these cases also the natural tms representation avoids the problem exploring further it is observed that the form of the tms justifications resembles that of nonnormal default rules nonnormal rules have already been proposed as a means of avoiding anomalous extensions in some nontemporal reasoning situations it appears that suitably formulated they can exclude the anomalous extension in the hanks mcdermott case also although the representation does not adjust smoothly to fresh information as does the tms some variant of default logic appears to be required to provide a correct semantic basis for truth maintenance systems

embedding in factorisable restriction monoids abstract each restriction semigroup is proved to be embeddable in a factorisable restriction monoid or equivalently in an almost factorisable restriction semigroup it is also established that each restriction semigroup has a proper cover which is embeddable in a semidirect product of a semilattice by a group

smooth center manifolds for nonuniformly partially hyperbolic trajectories abstract we establish the existence of unique smooth center manifolds for ordinary differential equations v a t v f t v in banach spaces assuming that v a t v admits a nonuniform exponential trichotomy this allows us to show the existence of unique smooth center manifolds for the nonuniformly partially hyperbolic trajectories in addition we prove that the center manifolds are as regular as the vector field our proof of the c k smoothness of the manifolds uses a single fixed point problem in an appropriate complete metric space to the best of our knowledge we establish in this paper the first smooth center manifold theorem in the nonuniform setting

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

a revisited approach to linear fuzzy regression using trapezoidal fuzzy intervals conventional fuzzy regression using possibilistic concepts allows the identification of models from uncertain data sets however some limitations still exist this paper deals with a revisited approach for possibilistic fuzzy regression methods indeed a new modified fuzzy linear model form is introduced where the identified model output can envelop all the observed data and ensure a total inclusion property moreover this model output can have any kind of spread tendency in this framework the identification problem is reformulated according to a new criterion that assesses the model fuzziness independently from the collected data distribution the potential of the proposed method with regard to the conventional approach is illustrated by simulation examples

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

center manifolds for impulsive equations under nonuniform hyperbolicity abstract we establish the existence of smooth center manifolds under sufficiently small perturbations of an impulsive linear equation in particular we obtain the c 1 smoothness of the manifolds outside the jumping times we emphasize that we consider the general case of nonautonomous equations for which the linear part has a nonuniform exponential trichotomy

grounded fixpoints and their applications in knowledge representation in various domains of logic researchers have made use of a similar intuition that facts or models can be derived from the ground up they typically phrase this intuition by saying e g that the facts should be grounded or that they should not be unfounded or that they should be supported by cycle free arguments et cetera in this paper we formalise this intuition in the context of algebraical fixpoint theory we define when a lattice element x l is grounded for lattice operator o l l on the algebraical level we investigate the relationship between grounded fixpoints and the various classes of fixpoints of approximation fixpoint theory including supported minimal kripke kleene stable and well founded fixpoints on the logical level we investigate groundedness in the context of logic programming autoepistemic logic default logic and argumentation frameworks we explain what grounded points and fixpoints mean in these logics and show that this concept indeed formalises intuitions that existed in these fields we investigate which existing semantics are grounded we study the novel semantics for these logics that is induced by grounded fixpoints which has some very appealing properties not in the least its mathematical simplicity and generality our results unveil a remarkable uniformity in intuitions and mathematics in these fields

definability and commonsense reasoning abstract the definition of concepts is a central problem in commonsense reasoning many themes in nonmonotonic reasoning concern implicit and explicit definability implicit definability in nonmonotonic logic is always relative to the context the current theory of the world we show that fixed point equations provide a generalization of explicit definability which correctly captures the relativized context theories expressed within this logical framework provide implicit definitions of concepts moreover it is possible to derive these fixed points entirely within the logic

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

partial monoid actions and a class of restriction semigroups abstract we study classes of proper restriction semigroups determined by properties of partial actions underlying them these properties include strongness antistrongness being defined by a homomorphism being an action etc of particular interest is the class determined by homomorphisms primarily because we observe that its elements while being close to semidirect products serve as mediators between general restriction semigroups and semidirect products or w products in an embedding covering construction it is remarkable that this class does not have an adequate analogue if specialized to inverse semigroups f restriction monoids of this class called ultra f restriction monoids are determined by homomorphisms from a monoid t to the munn monoid of a semilattice y we show that these are precisely the monoids y m t considered by fountain gomes and gould we obtain a mcalister type presentation for the class given by strong dual prehomomorphisms and apply it to construct an embedding of ultra f restriction monoids for which the base monoid t is free into w products of semilattices by monoids our approach yields new and simpler proofs of two recent embedding covering results by szendrei

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

all i know a study in autoepistemic logic abstract current approaches to formalizing nonmonotonic reasoning using logics of belief require the definition of new metalogical properties over sets of sentences this research attempts to show how some of these patterns of reasoning can be captured using only the classical notions of logic satisfiability validity implication this is done by extending a logic of belief so that it is possible to say that only a certain proposition or finite set of them is believed this research also extends previous approaches to handle quantifiers and equality provides a semantic account of certain types of nonmonotonicity and through a simple proof theory allows formal derivations to be generated

possible world semantics and autoepistemic reasoning abstract the possible world semantics of modal logic has been employed to study the nonmonotonic reasoning formalism moore s autoepistemic logic only kripke structure which is also known as a standard model has been used to represent the autoepistemic expansions of modal theories here we argue that the mode of autoepistemic reasoning which is formalized by autoepistemic logic is not necessarily associated with a standard model another model of the possible world semantics the minimal model is helpful in knowledge representation and belief reasoning in particular the minimal model can be used as a structure to represent all the autoepistemic expansions of a modal theory we extend the minimal model with standard model to deal with both knowledge and belief and introduce a null value called unknown to provide a refined model for knowledge and belief we also present a notion of epistemic base of basic sentences to identify the possible worlds in a minimal model by reformulating moore s autoepistemic logic with respect to epistemic base some reasonable modal theories that do not have any autoepistemic expansion will have generalized autoepistemic expansions

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

almost perfect restriction semigroups abstract we call a restriction semigroup almost perfect if it is proper and the least congruence that identifies all its projections is perfect we show that any such semigroup is isomorphic to a w product w t y where t is a monoid y is a semilattice and there is a homomorphism from t into the inverse semigroup ti y of isomorphisms between ideals of y conversely all such w products are almost perfect since we also show that every restriction semigroup has an easily computed cover of this type the combination yields a mcalister type theorem for all restriction semigroups it is one of the theses of this work that almost perfection and perfection the analogue of this definition for restriction monoids are the appropriate settings for such a theorem that these theorems do not reduce to a general theorem for inverse semigroups illustrates a second thesis of this work that restriction and by extension ehresmann semigroups have a rich theory that does not consist merely of generalizations of inverse semigroup theory it is then with some ambivalence that we show that all the main results of this work easily generalize to encompass all proper restriction semigroups the notation w t y recognizes that it is a far reaching generalization of a long known similarly titled construction as a result our work generalizes szendrei s description of almost factorizable semigroups while at the same time including certain classes of free restriction semigroups in its realm

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

model preference default theories most formal theories of default inference have very poor computational properties and are easily shown to be intractable or worse undecidable we are therefore investigating limited but eciently computable theories of default reasoning this paper defines systems of propositional model preference defaults which provide a true modeltheoretic account of default inference with exceptions the most general system of model preference defaults is decidable but still intractable inspired by the very good linear complexity of propositional horn theories we consider systems of horn defaults surprisingly finding a most preferred model in even this very limited system is shown to be np hard tractability can be achieved in two ways by eliminating the specificity ordering among default rules thus limiting the system s expressive power and by restricting our attention to systems of acyclic horn defaults these acyclic theories can encode acyclic defeasible inheritance hierarchies but are strictly more general this analysis suggests several directions for future research finding other syntactic restrictions which permit ecient computation or more

on usual values in commonsense reasoning abstract in many cases commonsense knowledge consists of knowledge of what is usual in this paper we develop a system for reasoning with usual information this system is based upon the fact that these pieces of commonsense information involve both a probabilistic aspect and a granular aspect we implement this system with the aid of probabilistic possibilistic granules

any world assumptions in logic programming due to the usual incompleteness of information representation any approach to assign a semantics to logic programs has to rely on a default assumption on the missing information the stable model semantics that has become the dominating approach to give semantics to logic programs relies on the closed world assumption cwa which asserts that by default the truth of an atom is false there is a second well known assumption called open world assumption owa which asserts that the truth of the atoms is supposed to be unknown by default however the cwa the owa and the combination of them are extremal though important assumptions over a large variety of possible assumptions on the truth of the atoms whenever the truth is taken from an arbitrary truth space the topic of this paper is to allow any assignment i e interpretation over a truth space to be a default assumption our main result is that our extension is conservative in the sense that under the everywhere false default assumption cwa the usual stable model semantics is captured due to the generality and the purely algebraic nature of our approach it abstracts from the particular formalism of choice and the results may be applied in other contexts as well

modal nonmonotonic logics ranges characterization computation many nonmonotonic formalism including default logic logic programming with stable models and autoepistemic logic can be represented faithfully by means of modal nonmonotonic logics in the family proposed by mcdermott and doyle in this paper properties of logics in this family are thoroughly investigated we present several results on characterization of expansions these results are applicable to a wide class of nonmonotonic modal logics using these characterization results algorithms for computing expansions for finite theories are developed perhaps the most important finding of this paper is that the structure of the family of modal nonmonotonic logics is much simpler than that of the family of underlying modal monotonic logics namely it is often the case that different monotonic modal logics collapse to the same nonmonotonic system we exhibit four families of logics whose nonmonotonic variants coincide 5 kd45 tw5 sw5 n wk and w5 d4wb these nonmonotonic logics naturally represent logics related to commonsense reasoning and knowledge representation such as autoepistemic logic reflexive autoepistemic logic default logic and truth maintenance with negation

an explication of reasoning in multiple inheritance systems through non monotonic horn clause logic abstract in this paper we present a new approach to explicate the is a link and the inheritance of properties down through is a links we introduce the syntactic category of common nouns intended to represent kinds or prototypes of objects we describe two sentence forming operations the attribution of membership of kinds to objects or objects of a certain kind and the attribution of properties to objects or objects of a certain kind we then argue that the inferential behavior of sentences is different depending on how the sentence was formed although the attribution of membership in a kind will always hold true for any instance the attribution of a property may be overridden we explicate the inferential behavior of these sentences in non monotonic logic and present the proof theory and semantics for this non monotonic logic

fuzzy autoepistemic logic and its relation to fuzzy answer set programming autoepistemic logic is an important formalism for nonmonotonic reasoning it extends propositional logic by offering the ability to reason about an agent s lack of beliefs moreover it is well known to generalize the stable model semantics of answer set programming fuzzy logics on the other hand are multi valued logics which allow to model the intensity to which properties are satisfied we combine these ideas to a fuzzy autoepistemic logic which can be used to reason about one s beliefs in the degrees to which properties are satisfied we show that many properties from classical autoepistemic logic e g the equivalence between autoepistemic models and stable expansions remain valid under this generalization in this paper we consider a version of fuzzy answer set programming and show that its answer sets can be equivalently described as models in fuzzy autoepistemic logic we also define a fuzzy logic of minimal belief and negation as failure and use this as a tool to show that fuzzy autoepistemic logic generalizes fuzzy answer set programming

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

an overview of fuzzy quantifiers ii reasoning and applications abstract in the second part of the overview reasoning with fuzzily defined quantifiers and applications are presented possibility based reasoning is summarized in detail the widely used quantifier extension principle and various reasoning schemas derived from it are discussed some disadvantages of the quantifier extension principle are pointed out although intervalvalued quantifiers are only a special case of general quantifiers some specific properties and results arise from them furthermore they suggest another approach to interence with fuzzy quantifiers reasoning with quantification and several kinds of qualification is introduced this kind of reasoning requires a seamless synthesis of probability theory possibility theory fuzzy logic and belief theory at last the applications of fuzzily defined quantifiers in decision making and fuzzy database systems are introduced

the complexity of path based defeasible inheritance abstract touretzky 22 proposed a formalism for nonmonotonic multiple inheritance reasoning which is sound in the presence of ambiguities and redundant links we show that touretzky s inheritance notion is np hard and thus provided p np computationally intractable this result holds even when one only considers unambiguous totally acyclic inheritance networks a direct consequence of this result is that the conditioning strategy proposed by touretzky to allow for fast parallel inference is also intractable we also analyze the influence of various design choices made by touretzky we show that all versions of so called downward inheritance i e on path or off path preemption and skeptical or credulous reasoning are intractable however on the positive side tractability can be achieved when using upward inheritance finally we consider the problem of determining what holds in all extensions of an ambiguous inheritance network without any preemption corresponding to a very cautious form of inheritance this problem is tractable but when allowing even the most basic forms of preemption it becomes intractable

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

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

non monotomic fuzzy reasoning abstract fuzzy reasoning can provide techniques both for representing and managing the imprecision in commonsense reasoning but like human reasoning it conduces to inconsistencies inherent to the imprecise or incomplete knowledge that might be solved in the frame of fuzzy logic simulating human behavior in this paper we analyze this kind of conflicts and propose a non monotonic fuzzy logic in order to solve it moreover we show that many non monotonic human reasoning patterns can be modeled by means of this non monotonic fuzzy reasoning

improvement of the rate of convergence estimates for multigrid algorithm in this paper we present a new convergence rate for both symmetric and nonsymmetric positive definite problems in our theory regularity and approximation assumption is used a new rate of convergence estimate with a 12 is used where a is a regularity and approximation parameter also a new convergence rate is given by two grid schemes