Decidability results in non-classical logics

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...

Labelled non-classical logics

Decidability Results for Metric and Layered Temporal Logics

We study the decidability problem for metric and layered temporal logics. The logics we consider are suitable to model time granularity in various contexts, and they allow one to build granular temporal models by referring to thènatural scale' in any component of the model and by properly constraining the interactions between diierently-grained components. A monadic second-order language combin...

Automated Reasoning in Quantified Non-Classical Logics

This paper introduces a non-clausal connection calculus for intuitionistic first-order logic. It is an extension of the non-clausal connection calculus for classical logic by prefixes and an additional prefix unification, which encode the Kripke semantics of intuitionistic logic. nanoCoP-i is a first implementation of this intuitionistic non-clausal connection calculus. Details of the compact P...