Non-Boolean classical relevant logics II: Classicality through truth-constants

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

On expansions of t-norm based logics with truth-constants

This paper focuses on completeness results about generic expansions of logics of both continuous t-norms and Weak Nilpotent Minimum (WNM) with truth-constants. Indeed, we consider algebraic semantics for expansions of these logics with a set of truth-constants {r | r ∈ C}, for a suitable countable C ⊆ [0, 1], and provide a full description of completeness results when (i) either the t-norm is a...

Algebraic and Topological Methods in Non-Classical Logics II

Thanks also go to Professor Francesc Esteva, head of the Research Institute in Artificial Intelligence (IIIA) and to Professor`Angel Jorba, head of the Institute of Mathematics at the University of Barcelona (IMUB), for being so receptive to our needs and providing administrative support in different ways. The Oficina d'Activitats Institucionals of the University of Barcelona offered invaluable...