Autoepistemic logic of minimal beliefs

More on Modal Aspects of Default Logic1

Fundamenta Informaticae ◽

10.3233/fi-1992-171-207 ◽

1992 ◽

Vol 17 (1-2) ◽

pp. 99-116

Author(s):

V. Wiktor Marek ◽

Miroslaw Truszczynski

Keyword(s):

Modal Logic ◽

Default Logic ◽

Nonmonotonic Logic ◽

Default Reasoning ◽

Default Theory ◽

Autoepistemic Logic ◽

The Relationship ◽

Natural Classes ◽

Weak Extension

Investigations of default logic have been so far mostly concerned with the notion of an extension of a default theory. It turns out, however, that default logic is much richer. Namely, there are other natural classes of objects that might be associated with default reasoning. We study two such classes of objects with emphasis on their relations with modal nonmonotonic formalisms. First, we introduce the concept of a weak extension and study its properties. It has long been suspected that there are close connections between default and autoepistemic logics. The notion of weak extension allows us to precisely describe the relationship between these two formalisms. In particular, we show that default logic with weak extensions is essentially equivalent to autoepistemic logic, that is, nonmonotonic logic KD45. In the paper we also study the notion of a set of formulas closed under a default theory. These objects are shown to correspond to stable theories and to modal logic S5. In particular, we show that skeptical reasoning with sets closed under default theories is closely related with provability in S5. As an application of our results we determine the complexity of reasoning with weak extensions and sets closed under default theories.

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Formalization of Inheritance Reasoning in Autoepistemic Logic

Fundamenta Informaticae ◽

10.3233/fi-1990-13403 ◽

1990 ◽

Vol 13 (4) ◽

pp. 403-443

Author(s):

Michael Gelfond ◽

Halina Przymusinska

Keyword(s):

General Framework ◽

Nonmonotonic Reasoning ◽

Commonsense Reasoning ◽

Autoepistemic Logic

Current research in the area of nonmonotonic reasoning suggests that autoepistemic logic provides a general framework for formalizing commonsense reasoning in various domains of discourse. The goal of this paper is to investigate the suitability of autoepistemic logic for formalization of some forms of inheritance reasoning. To this end we propose a new semantics for inheritance networks with exceptions based on autoepistemic logic.

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Reflexive Autoepistemic Logic

Fundamenta Informaticae ◽

10.3233/fi-1992-171-209 ◽

1992 ◽

Vol 17 (1-2) ◽

pp. 157-173

Author(s):

Grigori Schwarz

Keyword(s):

Autoepistemic Logic ◽

New Variant ◽

Formal Properties

We propose a new variant of autoepistemic logic which, intuitively, corresponds to understanding a belief operator L as “is known”, in contrast to the interpretation of L as “is believed” in Moore’s autoepistemic logic. Formal properties of the new logic and relationship to Moore’s logic are studied in detail.

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