Modal logic for default reasoning

W. Marek, M. Truszczyński

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


In the paper we introduce a variant of autoepistemic logic that is especially suitable for expressing default reasonings. It is based on the notion of iterative expansion. We show a new way of translating default theories into the language of modal logic under which default extensions correspond exactly to iterative expansions. Iterative expansions have some attractive properties. They are more restrictive than autoepistemic expansions, and, for some classes of theories, than moderately grounded expansions. At the same time iterative expansions avoid several undesirable properties of strongly grounded expansions, for example, they are grounded in the whole set of the agent's initial assumptions and do not depend on their syntactic representation. Iterative expansions are defined syntactically. We define a semantics which leads to yet another notion of expansion - weak iterative expansion - and we show that there is an important class of theories, that we call ℐ-programs, for which iterative and weak iterative expansions coincide. Thus, for ℐ-programs, iterative expansions can be equivalently defined by semantic means.

Original languageEnglish
Pages (from-to)275-302
Number of pages28
JournalAnnals of Mathematics and Artificial Intelligence
Issue number1-4
StatePublished - Sep 1990


  • Autoepistemic logic
  • default logic
  • expansion
  • iterative expansion
  • logic of necessitation
  • nonmonotonic reasoning

ASJC Scopus subject areas

  • Artificial Intelligence
  • Applied Mathematics


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