Semantic interpolation

Dov M. Gabbay, Karl Schlechta

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

The problem of interpolation is a classical problem in logic. Given a consequence relation ̃ and two formulas φ and with ψ ̃ we try to find a "simple" formula ψ such that φ ̃ ψ ̃. "Simple" is defined here as "expressed in the common language of φ and &psin ". Non-monotonic logics like preferential logics are often a mixture of a non-monotonic part with classical logic. In such cases, it is natural examine also variants of the interpolation problem, like: is there "simple" α such that φ ψ ̃, where is classical consequence? We translate the interpolation problem from the syntactic level to the semantic level. For example, the classical interpolation problem is now the question whether there is some "simple" model set X such that M(φ) X M(ψ). We can show that such X always exist for monotonic and antitonic logics. The case of non-monotonic logics is more complicated, there are several variants to consider, and we mostly have only partial results.

Original languageEnglish
Pages (from-to)345-371
Number of pages27
JournalJournal of Applied Non-Classical Logics
Volume20
Issue number4
DOIs
StatePublished - 2010

Keywords

  • Interpolation
  • Non-monotonic logic
  • Semantics

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