A.I. Arruda, R. Chuaqui y N.C.A. da Costa (eds.), Non-Classical Logics, Model Theory and Computability

Truth Values and Connectives in Some Non-Classical Logics

The question as to whether the propositional logic of Heyting, which was a formalization of Brouwer's intuitionistic logic, is finitely many valued or not, was open for a while (the question was asked by Hahn). Kurt Gödel (1932) introduced an infinite decreasing chain of intermediate logics, which are known nowadays as Gödel logics, for showing that the intuitionistic logic is not finitely (man...

Non-classical Metatheory for Non-classical Logics

A number of authors have objected to the application of non-classical logic to problems in philosophy on the basis that these non-classical logics are usually characterised by a classical meta-theory. In many cases the problem amounts to more than just a discrepancy; the very phenomena responsible for non-classicality occur in the field of semantics as much as they do elsewhere. The phenomena o...

Analytic Calculi for Non-Classical Logics: Theory and Applications

The possession of a suitable proof-calculus is the starting point for many investigations into a logic, including decidability and complexity, computational interpretations and automated theorem proving. By suitable proof-calculus we mean a calculus whose proofs exhibit some notion of subformula property (‘analyticity’). In this talk we describe a method for the algorithmic introduction of anal...

Labelled non-classical logics

CTL Model-Checking over Logics with Non-Classical Negations

In earlier work [9], we defined CTL model-checking over finite-valued logics with De Morgan negation. In this paper, we extend this work to logics with intuitionistic, Galois and minimal negations, calling the resulting language CTL. We define CTL operators and show that they can be computed using fixpoints. We further discuss how to extend our existing multi-valued model-checker Chek [8] to re...