Uniform semantic treatment of default and autoepistemic logics

Marc Denecker, Victor W. Marek, Mirosław S. Truszczyński

Research output: Contribution to journalArticlepeer-review

73 Scopus citations

Abstract

We revisit the issue of epistemological and semantic foundations for autoepistemic and default logics, two leading formalisms in nonmonotonic reasoning. We develop a general semantic approach to autoepistemic and default logics that is based on the notion of a belief pair and that exploits the lattice structure of the collection of all belief pairs. For each logic, we introduce a monotone operator on the lattice of belief pairs. We then show that a whole family of semantics can be defined in a systematic and principled way in terms of fixpoints of this operator (or as fixpoints of certain closely related operators). Our approach elucidates fundamental constructive principles in which agents form their belief sets, and leads to approximation semantics for autoepistemic and default logics. It also allows us to establish a precise one-to-one correspondence between the family of semantics for default logic and the family of semantics for autoepistemic logic. The correspondence exploits the modal interpretation of a default proposed by Konolige. Our results establish conclusively that default logic can be viewed as a fragment of autoepistemic logic, a result that has been long anticipated. At the same time, they explain the source of the difficulty to formally relate the semantics of default extensions by Reiter and autoepistemic expansions by Moore. These two semantics occupy different locations in the corresponding families of semantics for default and autoepistemic logics.

Original languageEnglish
Pages (from-to)79-122
Number of pages44
JournalArtificial Intelligence
Volume143
Issue number1
DOIs
StatePublished - Jan 2003

Bibliographical note

Funding Information:
Marc Denecker was supported in part by the Research Fund of the K.U. Leuven, Belgium. Victor W. Marek and Mirosław Truszczyński were supported by the National Science Foundation under Grants No. 9874764 and 0097278. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Keywords

  • Approximations
  • Autoepistemic logic
  • Default logic
  • Fixpoint semantics
  • Lattice operators

ASJC Scopus subject areas

  • Language and Linguistics
  • Linguistics and Language
  • Artificial Intelligence

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