TY - JOUR

T1 - Semantic interpolation

AU - Gabbay, Dov M.

AU - Schlechta, Karl

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - Interpolation

KW - Non-monotonic logic

KW - Semantics

UR - http://www.scopus.com/inward/record.url?scp=84886683164&partnerID=8YFLogxK

U2 - 10.3166/JANCL.20.345-371

DO - 10.3166/JANCL.20.345-371

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AN - SCOPUS:84886683164

SN - 1166-3081

VL - 20

SP - 345

EP - 371

JO - Journal of Applied Non-Classical Logics

JF - Journal of Applied Non-Classical Logics

IS - 4

ER -