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 -