What is a logic? Which properties are preserved by maps between logics? What is the right notion for equivalence of logics? In order to give satisfactory answers we generalize and further develop the topological approach ...

In this article we introduce the variety of monadic BL-algebras as BL-algebras endowed with two monadic operators ∀ and ∃. After a study of the basic properties of this variety we show that this class is the equivalent ...

We consider the Σ1 0-fragment of second-order logic over the vocabulary h+, ×, 0, 1, <, S1, ..., Ski, interpreted over the reals, where the predicate symbols Si are interpreted as semi-algebraic sets. We show that, in this ...

It is well-known that Independence Friendly (IF) logic is equivalent to existential secondorder logic (Σ1 1 ) and, therefore, is not closed under classical negation. The Boolean closure of IF sentences, called Extended ...

In this paper we introduce a logic that we name semi Heyting–Brouwer logic, SHB, in such a way that the variety of double semi-Heyting algebras is its algebraic counterpart. We prove that, up to equivalences by translations, ...

The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (i.e. logics containing contradictory but nontrivial theories) having a consistency connective which allows to recover the ex falso quodlibet ...

The aim of this thesis is to study a family of logics, comprised of Nelson’s logic S, constructive logic with strong negation N 3, quasi-Nelson logic QN and quasi-Nelson implicative logic QN I. This is done in two ways. ...

We investigate dynamic modal operators that can change the model during evaluation. We define the logic SL by extending the basic modal language with the ♦ modality, which is a diamond operator that in addition has the ...

Semi-intuitionistic logic is the logic counterpart to semi-Heyting algebras, which were defined by H. P. Sankappanavar as a generalization of Heyting algebras. We present a new, more streamlined set of axioms for ...

We establish the Robinson joint consistency theorem for the infinite-valued propositional logic of Łukasiewicz. As a corollary we easily obtain the amalgamation property for MV-algebras-the algebras of Łukasiewicz logic: ...