THE MODAL LOGICS OF KRIPKE-FEFERMAN TRUTH

On Kripke completeness of some modal predicate logics

Let us recall some basic definitions and notation; most of them are the same as in the book [3]. Atomic formulas are constructed from predicate letters P k (countably many for each arity n ≥ 0) and a countable set of individual variables V ar, without constants and function letters. Modal (predicate) formulas are obtained from atomic formulas by applying classical propositional connectives, qua...

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...

A General Proof of Kripke-completeness for Quantified Modal Logics

Relating Categorical and Kripke Semantics for Intuitionistic Modal Logics

We consider two systems of intuitionistic modal logic which are com-putationally motivated: rst, they have a constructive proof theory, and second, their modalities allow several computational interpretations. Both systems have so far been studied from a type-theoretic and category-theoretic perspectives. In this paper, we prove some duality results which show how to relate Kripke models to the...

On the density of truth in modal logics

The aim of this paper is counting the probability that a random modal formula is a tautology. We examine {→, 2} fragment of two modal logics S5 and S4 over the language with one propositional variable. Any modal formula written in such a language may be interpreted as a unary binary tree. As it is known, there are finitely many different formulas written in one variable in the logic S5 and this...