Skolem Functions in Non-Classical Logics

Löwenheim-Skolem theorems for non-classical first-order algebraizable logics

This paper is a contribution to the model theory of non-classical firstorder predicate logics. In a wide framework of first-order systems based on algebraizable logics, we study several notions of homomorphisms between models and find suitable definitions of elementary homomorphism, elementary substructure and elementary equivalence. Then we obtain (downward and upward) Löwenheim–Skolem theorem...

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

Possibility and Necessity Functions over Non-Classical Logics

We propose an integration of possibility the­ ory into non-classical logics. We obtain many formal results that generalize the case where possibility and necessity functions are based on classical logic. We show how useful such an approach is by applying it to reasoning un­ der uncertain and inconsistent information.