On an algebraic and Kripke semantics for intermediate logics

Kripke Completeness for Intermediate Logics

Kripke semantics for fuzzy logics

Kripke frames (and models) provide a suitable semantics for sub-classical logics; for example Intuitionistic Logic (of Brouwer and Heyting) axiomatizes the reflexive and transitive Kripke frames (with persistent satisfaction relations), and the Basic Logic (of Visser) axiomatizes transitive Kripke frames (with persistent satisfaction relations). Here, we investigate whether Kripke frames/models...

Subintuitionistic Logics with Kripke Semantics

The subintuitionistic logics introduced by Corsi and Restall are developed in a uniform manner. Proof systems are given for derivations without and with assumptions. The results are applied to give conservation theorems for intuitionistic logic IPC over Corsi’s system F. For Visser’s basic logic strong completeness is proved and additional conservation results are obtained.

Kripke Semantics for Logics with Bck Implication

We present Kripke semantics for some substructural logics with weakening, known as logics with BCK implication. This work is a continuation of the work of Allwein and Dunn on Kripke semantics for Linear Logic, which in turn rested on Dunn’s Gaggle Theory and on Urquhart’s Representation Theory for nondistributive lattices. The basic idea in the representation theory is to use maximally disjoint...

Categorical and Kripke Semantics for Constructive Modal Logics

We consider two systems of constructive modal logic which are computationally motivated. Their modalities admit several computational interpretations and are used to capture intensional features such as notions of computation, constraints, concurrency design, etc. Both systems have so far been studied mainly from a type-theoretic and category-theoretic perspectives, but Kripke models for simila...