Bi-modal Gödel logic over [0,1]-valued Kripke frames

Details Bi-modal Gödel logic over [0,1]-valued Kripke frames Bi-modal Gödel logic over [0,1]-valued Kripke frames

2011-10-11

arxiv.org/abs/1110.2407v1

Mathematics

Logic

Scientific paper

We consider the G\"odel bi-modal logic determined by fuzzy Kripke models where both the propositions and the accessibility relation are infinitely valued over the standard G\"odel algebra [0,1] and prove strong completeness of Fischer Servi intuitionistic modal logic IK plus the prelinearity axiom with respect to this semantics. We axiomatize also the bi-modal analogues of $T,$ $S4,$ and $S5$ obtained by restricting to models over frames satisfying the [0,1]-valued versions of the structural properties which characterize these logics. As application of the completeness theorems we obtain a representation theorem for bi-modal G\"odel algebras.

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