UNIFICATION IN INTERMEDIATE LOGICS

Unification in Intermediate Logics

This paper contains a proof–theoretic account of unification in intermediate logics. It is shown that many existing results can be extended to fragments that at least contain implication and conjunction. For such fragments, the connection between valuations and most general unifiers is clarified, and it is shown how from the closure of a formula under the Visser rules a proof of the formula und...

Unification in modal and description logics

Unification was originally introduced in automated deduction and term rewriting, but has recently also found applications in other fields. In this article, we give a survey of the results on unification obtained in two closely related, yet different, application areas of unification: description logics and modal logics.

Proof analysis in intermediate logics

Using labelled formulae, a cut-free sequent calculus for intuitionistic propositional logic is presented, together with an easy cut-admissibility proof; both extend to cover, in a uniform fashion, all intermediate logics characterised by frames satisfying conditions expressible by one or more geometric implications. Each of these logics is embedded by the Gödel-McKinsey-Tarski translation into ...

Kripke Completeness for Intermediate Logics

Krlpke Models and Intermediate Logics

In [10], Kripke gave a definition of the semantics of the intuitionistic logic. Fitting [2] showed that Kripke's models are equivalent to algebraic models (i.e., pseudo-Boolean models) in a certain sense. As a corollary of this result, we can show that any partially ordered set is regarded as a (characteristic) model of a intermediate logic ̂ We shall study the relations between intermediate log...