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

multi observation blind deconvolution with an adaptive sparse prior this paper describes a robust algorithm for estimating a single latent sharp image given multiple blurry and or noisy observations the underlying multi image blind deconvolution problem is solved by linking all of the observations together via a bayesian inspired penalty function which couples the unknown latent image along with a separate blur kernel and noise variance associated with each observation all of which are estimated jointly from the data this coupled penalty function enjoys a number of desirable properties including a mechanism whereby the relative concavity or sparsity is adapted as a function of the intrinsic quality of each corrupted observation in this way higher quality observations may automatically contribute more to the final estimate than heavily degraded ones while troublesome local minima can largely be avoided the resulting algorithm which requires no essential tuning parameters can recover a sharp image from a set of observations containing potentially both blurry and noisy examples without knowing a priori the degradation type of each observation experimental results on both synthetic and real world test images clearly demonstrate the efficacy of the proposed method

defeasible inheritance with doubt index and its axiomatic characterization this article introduces and uses a representation of defeasible inheritance networks where links in the network are viewed as propositions and where defeasible links are tagged with a quantitative indication of the proportion of exceptions called the doubt index this doubt index is used for restricting the length of the chains of inference the representation also introduces the use of defeater literals that disable the chaining of subsumption links the use of defeater literals replaces the use of negative defeasible inheritance links expressing most a are not b the new representation improves the expressivity significantly inference in inheritance networks is defined by a combination of axioms that constrain the contents of network extensions a heuristic restriction that also has that effect and a nonmonotonic operation of minimizing the set of defeater literals while retaining consistency we introduce an underlying semantics that defines the meaning of literals in a network and prove that the axioms are sound with respect to this semantics we also discuss the conditions for obtaining completeness traditional concepts assumptions and issues in research on nonmonotonic or defeasible inheritance are reviewed in the perspective of this approach

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

lexicographic priorities in default logic abstract resolving conflicts between default rules is a major subtask in performing default reasoning a declarative way of controlling the resolution of conflicts is to assign priorities to default rules and to prevent conflict resolution in ways that violate the priorities this work extends reiter s default logic with a priority mechanism that is based on lexicographic comparison given a default theory and a partial ordering on the defaults the preferred extensions are the lexicographically best extensions we discuss alternative ways of using lexicographic comparison and investigate their properties and relations between them the applicability of the priority mechanism to inheritance reasoning is investigated by presenting two translations from inheritance networks to prioritized default theories and relating them to inheritance theories presented earlier by gelfond and przymusinska and by brewka

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

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

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

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

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

operational characterization of extensions in some logics for default reasoning default reasoning is one of the most common forms of nonmonotonic reasoning and is found in many application domains default logic and its variants have been proposed as knowledge representation methods capable of default reasoning one problem of all these methods is that their concepts are given in terms of fixed point equations thus making them difficult to understand and use in this paper we present simple constructive approaches for the semantics of some default logic variants and show their correctness

expressing preferences in default logic we address the problem of reasoning about preferences among properties outcomes desiderata etc in reiter s default logic preferences are expressed using an ordered default theory consisting of default rules world knowledge and an ordering reflecting preference on the default rules in contrast with previous work in the area we do not rely on prioritised versions of default logic but rather we transform an ordered default theory into a second standard default theory wherein the preferences are respected in that defaults are applied in the prescribed order this translation is accomplished via the naming of defaults so that reference may be made to a default rule from within a theory in an elaboration of the approach we allow an ordered default theory where preference information is specified within a default theory here one may specify preferences that hold by default in a particular context or give preferences among preferences in the approach one essentially axiomatises how different orderings interact within a theory and need not rely on metatheoretic characterisations as well we can immediately use existing default logic theorem provers for an implementation from a theoretical point of view this shows that the explicit representation of priorities among defaults adds nothing to the overall expressibility of default logic

a note on the model theoretic semantics of fuzzy logic programming for dealing with inconsistency inconsistency is likely to exist in a knowledge base built up from various sources of information especially in the presence of uncertainty and fuzziness in such a case inconsistency is often local and thus should not cause the entire knowledge base to collapse for a fuzzy logic system to be able to deal with local inconsistency an appropriate model theoretic semantics is required this paper analyses and shows that the model theoretic semantics approach of possibilistic logic which has recently become popular to be applied to the development of fuzzy set logic whose formulas can have fuzzy set constants cannot deal with local inconsistency we then introduce the annotated logic based approach as a solution and analyse the difference and relation between the two approaches

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

an argument based approach to reasoning with specificity we present a new priority based approach to reasoning with specificity which subsumes inheritance reasoning the new approach differs from other priority based approaches in the literature in the way priority between defaults is handled here it is conditional rather than unconditional as in other approaches we show that any unconditional handling of priorities between defaults as advocated in the literature until now is not sufficient to capture general defeasible inheritance reasoning we propose a simple and novel argumentation semantics for reasoning with specificity taking the conditionality of the priorities between defaults into account since the proposed argumentation semantics is a form of stable semantics of nonmonotonic reasoning it inherits a common problem of the latter where it is not always defined for every default theory we propose a class of stratified default theories for which the argumentation semantics is always defined we also show that acyclic and consistent inheritance networks are stratified we prove that the argumentation semantics satisfies the basic properties of a nonmonotonic consequence relation such as deduction reduction conditioning and cumulativity for well defined and stratified default theories we give a modular and polynomial transformation of default theories with specificity into semantically equivalent reiter default theories

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

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

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

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

an abstract argumentation theoretic approach to default reasoning abstract we present an abstract framework for default reasoning which includes theorist default logic logic programming autoepistemic logic non monotonic modal logics and certain instances of circumscription as special cases the framework can be understood as a generalisation of theorist the generalisation allows any theory formulated in a monotonic logic to be extended by a defeasible set of assumptions an assumption can be defeated or attacked if its contrary can be proved possibly with the aid of other conflicting assumptions we show that given such a framework the standard semantics of most logics for default reasoning can be understood as sanctioning a set of assumptions as an extension of a given theory if and only if the set of assumptions is conflict free in the sense that it does not attack itself and it attacks every assumption not in the set we propose a more liberal argumentation theoretic semantics based upon the notion of admissible extension in logic programming we regard a set of assumptions in general as admissible if and only if it is conflict free and defends itself by attacking every set of assumptions which attacks it we identify conditions for the existence of extensions and for the equivalence of different semantics

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

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

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