Default Logic

Default Logic is recognized as a powerful framework for knowledge representation and incomplete information management. Its expressive power is suitable for non monotonic reasoning, but the counterpart is its very high level of computational complexity. The purpose of this paper is to show how heuristics such as Genetic Algorithms, Ant Colony Optimization and Local Search can be used to elaborate an efficient non monotonic reasoning system.

A counterpossible conditional, or counterpossible for short, is a conditional proposition whose antecedent is impossible. The filioque doctrine is a dogma of western Christian Trinitarian theology according to which the Holy Spirit proceeds from the Father and the Son. The filioque doctrine was the principal theological reason for the Great Schism, the split between Eastern Orthodoxy and western Christianity, which continues today. In the paper, I review one of the earliest medieval defenses of the doctrine in Anselm of Canterbury, and I show that Anselm's treatment of counterpossible conditionals concerning the procession of the spirit from the son in Trinitarian theology represent an early foray into default logic. Thus, the mutual estrangement of eastern and western positions on the matter may not lie fundamentally in a change in dogma, but rather in a change in logic. Mathematics Subject Classification. Primary 01A35; Secondary 03B60, 03B80.

In Gärdenfors and Makinson (Artif Intell 65(2):197–245, 1994) and Gärdenfors (Knowledge representation and reasoning under uncertainty, Springer-Verlag, 1992) it was shown that it is possible to model nonmonotonic inference using a classical consequence relation plus an expectation-based ordering of formulas. In this article, we argue that this framework can be significantly enriched by adopting a conceptual spaces-based analysis of the role of expectations in reasoning. In particular, we show that this can solve various epistemological issues that surround nonmonotonic and default logics. We propose some formal criteria for constructing and updating expectation orderings based on conceptual spaces, and we explain how to apply them to nonmonotonic reasoning about objects and properties.

A non-monotonic logic, the Logic of Plausible Reasoning (LPR), capable of coping with the demands of what we call complex reasoning, is introduced. It is argued that creative complex reasoning is the way of reasoning required in many instances of scientific thought, professional practice and common life decision taking. For managing the simultaneous consideration of multiple scenarios inherent in these activities, two new modalities, weak and strong plausibility, are introduced as part of the Logic of Plausible Deduction (LPD), a deductive logic specially designed to serve as the monotonic support for LPR. Axiomatics and semantics for LPD, together with a completeness proof, are provided. Once LPD has been given, LPR may be defined via a concept of extension over LPD. Although the construction of LPR extensions is first presented in standard style, for the sake of comparison with existing non-monotonic formalisms, alternative more elegant and intuitive ways for constructing non-monotonic LPR extensions are also given and proofs of their equivalence are presented.

We propose a modificationL 1 of the action description languageA. The languageL 1 allows representation of hypothetical situations and hypothetical occurrence of actions (as inA) as well as representation of actual occurrences of actions and observations of the truth values of fluents in actual situations. The corresponding entailment relation formalizes various types of common-sense reasoning about actions and their effects not modeled by previous approaches. As an application of L1 we also present an architecture for intelligent agents capable of observing, planning and acting in a changing environment based on the entailment relation of L1 and use logic programming approximation of this entailment to implement a planning module for this architecture. We prove the soundness of our implementation and give a sufficient condition for its completeness.

This paper embedsdefaultloau into anextensio o Adams'prosabilitylo];0 called the system P+# D . DefaultreasotzW is furnishedwithtwo mechanisms:ongenerates(ir)relevanceassumptio)qandtheoez2projj]]z) lo werproWWz)qjy boWW;]ToW]qj3boq mechanismsmake defaultreasotz3protz3W;j]z)qq2reliable. There is an exactcoz2jjoz2jj betweenPo ofiqfi2z)q3]q[zand P+# D-extensioq] Thepro cedurefoP+# D-entailmentisco]]fiz)q2 incoq2W;WzywithPoo2]3procedure.1 Introduction and ...

The capability of drawing defeasible conclusions in presence of partial information is a crucial factor of intelligent behavior. To achieve this capability, human beings resort to a particular kind of knowledge, called default knowledge. The most significant property of default knowledge is that it can be exploited in the reasoning process even if there is only partial information about the satisfaction of the preconditions which allow its application, on condition that there is no reason to believe that such preconditions are not satisfied. If new information becomes available from which the falsity of such preconditions can be deduced, the conclusions derived from the application of default knowledge have to be retracted. This particular form of reasoning, involving the use of default knowledge, may be called defeasible reasoning. In order to build automated reasoning systems including defeasible reasoning capabilities, many extensions of classical logic have been proposed as mode...

Practical use of default logics requires mechanisms to select the more suitable extensions from out of the several often allowed by a classical default theory. An obvious solution is to order defaults in a preference hierarchy, and use this ordering to select preferred extensions. The literature contains many suggestions on how to implement such a scheme. The problem is that they yield different results: all authors agree that preferred extensions employ preferred defaults, but this apparent agreement hides differences in lower level decisions. While motivations for these are rarely discussed, their consequences for overall behaviour are wide-ranging. This paper points towards standardisation, discussing principles that ought to hold and then working top-down to determine lower level details. We present characterisations, uncover anomalies of existing approaches, and suggest repairs. We build on work by Brewka and Eiter [4], who first identified some of the desiderata discussed here. A slightly modified version of the notion of preferred extension proposed by these authors, and one by Delgrande and Schaub [5], are identified as the most and least inclusive notions of extension satisfying all desiderata. We point out that these two (in the literature previously termed “descriptive” and “prescriptive”, respectively) differ along two rather independent dimensions, and two additional notions are then identified, representing the remaining possibilities.

In this paper we consider goal generation in cognitive agent architectures. We show how goal generation can be described in terms of interaction between mental attitudes biased by agent types such as realistic, social, selfish and stable. We introduce a generic BOID architecture and agent type specific BOID architectures, in which goals are generated from conditional beliefs, obligations, intentions and desires. We implement the BOID architectures by relating conditional mental attitudes to components, goal generation to extension ...

In this talk - based on the results of a forthcoming paper (Coletti, Scozzafava and Vantaggi 2002), presented also by one of us at the Conference on "Non Classical Logic, Approximate Reasoning and Soft-Computing" (Anacapri, Italy, 2001) - we discuss the problem of representing default rules by means of a suitable coherent conditional probability, defined on a family of conditional events. An event is singled-out (in our approach) by a proposition, that is a statement that can be either true or false; a conditional event is consequently defined by means of two propositions and is a 3-valued entity, the third value being (in this context) a conditional probability.

There is a wide agreement on the use of norms in order to specify the expected behaviour of agents in open MAS. However, cur- rent norm formalisms focus on the declarative nature of norms. In order to be implemented, these norms should be translated into operational representations. In this paper we present our preliminary work on im- plementation of norm

A logical formalization to the process of theory revision when it is confronted by a scientific anomaly is presented. By “scientific anomaly” we mean an observed fact falling into the explanatory scope of a theory that cannot be explained by the theory and the accepted auxiliary ...

A non-monotonic logic, the Logic of Plausible Reasoning (LPR), capable of coping with the demands of what we call complex reasoning, is introduced. It is argued that creative complex reasoning is the way of reasoning required in many instances of scientific thought, professional practice and common life decision taking. For managing the simultaneous consideration of multiple scenarios inherent in these activities, two new modalities, weak and strong plausibility, are introduced as part of the Logic of Plausible Deduction (LPD), a deductive logic specially designed to serve as the monotonic support for LPR. Axiomatics and semantics for LPD, together with a completeness proof, are provided. Once LPD has been given, LPR may be defined via a concept of extension over LPD. Although the construction of LPR extensions is first presented in standard style, for the sake of comparison with existing non-monotonic formalisms, alternative more elegant and intuitive ways for constructing non-monotonic LPR extensions are also given and proofs of their equivalence are presented.