Journal Article

Characterizing Interpolation Pairs in Infinitary Graded Logics

Giovanna D'Agostino

in Journal of Logic and Computation

Volume 13, issue 2, pages 173-193
Published in print April 2003 | ISSN: 0955-792X
Published online April 2003 | e-ISSN: 1465-363X | DOI: http://dx.doi.org/10.1093/logcom/13.2.173
Characterizing Interpolation Pairs in Infinitary Graded Logics

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In this paper the problem of interpolation for the family of countable infinitary graded modal logics is considered. It is well known that interpolation fails in general for these logics and it is then natural to ask for a semantical characterization (stronger than entailment) of pairs of graded formulae having an interpolant. This is obtained using the notion of entailment along elementary equivalence. More precisely, we prove that if L is a graded modal logic then a pair (ø, ψ) of graded formulae in L have an interpolant in L if, and only if, ø entails ψ along elementary equivalence with respect to L. This characterization is obtained by adapting to graded modal logics the method of consistency property modulo bisimulation, which was previously used in Infinitary Logic and Infinitary Modal Logic. In the case of full Countable Infinitary Graded Modal Logic we improve this result and show that this logic enjoys Craig interpolation. This is done using a characterization of graded bisimulation between models via isomorphism of their unravellings.

Keywords: Interpolation; graded modalities; consistency property; infinitary lgoic; bisimulation

Journal Article.  0 words. 

Subjects: Computing ; Logic

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