Abstract This article investigates models of axiomatizations related to the semantic conception truth presented by Kripke (J Philos 72(19):690–716, 1975), so-called fixed-point semantics . Among various proof systems devised as a proof-theoretic characterization semantics, in recent years two alternatives have received particular attention: classical (i.e., based on logic) and nonclassical some...

Model checking [3] is a very popular paradigm for automatic verification of properties of finite state systems like those defined by circuits or communication protocols. A system is interpreted as a finite state labeled transition system or equivalently as a finite Kripke structure. If sys contains k concurrent components, each with m states, then the Kripke structure described by sys may have ...

The Gentzen-Kripke construction of the semantics for intermediate logic LQ, which is obtainable from the intuitionistic propositional logic H by adding the weak law of excluded middle -*A v —• —1>4, is presented. Our construction spans the Gentzen system and the Kripke semantics for LQ by providing the way from the cut-elimination theorem to model-theoretic results. The completeness and decidab...

We extend the algebraic-coalgebraic specification language CoCasl by full coalgebraic modal logic based on predicate liftings for functors. This logic is more general than the modal logic previously used in CoCasl and supports the specification of a variety of modal logics, such as graded modal logic, majority logic, and probabilistic modal logic. CoCasl thus becomes a modern modal language tha...

In [10] Osorio et al. introduced a paraconsistent three-valued logic, the logic CG3 which was named after the logic G ′ 3 due to the close relation between them. Authors defined CG3 via the three-valued matrix that defines G3 but changing the set of designated truth values. In this article we present a brief study of the Kripke-type semantics for some logics related with CG3 before constructing...

We give a simple intuitionistic completeness proof of Kripke semantics with constant domain for intuitionistic logic with implication and universal quantification. We use a cut-free intuitionistic sequent calculus as formal system and by combining soundness with completeness, we obtain an executable cut-elimination procedure. The proof, which has been formalised in the Coq proof assistant, easi...

Following the approaches and motivations given in recent works about constructive interpretation of description logics, we introduce the constructive description logic KALC. This logic is based on a Kripke-style semantics inspired by the Kripke semantics for Intuitionistic first order logic. In the paper we present the main features of our semantics and we study its relations with other approac...

What is the truth-value structure of realizability? How can realizability style models be integrated with forcing techniques from Kripke and Beth semantics, and conversely? These questions have received answers in Hyland’s [33], Läuchli’s [43] and in other, related or more syntactic developments cited below. Here we re-open the investigation with the aim of providing more constructive answers t...