We study S5-modal (monadic) expansions of extensions of Hájek's basic logic . Hájek proposed Hilbert-style systems axiomatizing these logics and we prove that completeness theorems for these logics follow from algebraic ...

In this chapter, we propose a definition of logical consequence based on the relation between the quantity of information present in a particular set of formulae and a particular formula. As a starting point, we use Shannon’s ...

In this chapter we give a detailed presentation of the most important aspects of Hajek´s basic Logic BL and their algebraic counterpart, BL-algebras.

The aim of this paper is to survey the tools needed to prove the standard completeness of Hájek Basic Logic with respect to continuous t-norms. In particular, decompositions of   totally ordered BL-algebras into simpler ...

Two questions are addressed in this article: 1) How to make the students realize the importance of logic; and 2) how to teach the logical rules. The teacher may begin their logic class with an attempt to answer 1. Logic ...

Graph databases make use of logics that combine traditional first-order features with navigation on paths, in the same way logics for model checking do. However, modern applications of graph databases impose a new requirement ...

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 ...

Relation-changing modal logics (RC for short) are extensions of the basic modal logic with dynamic operators that modify the accessibility relation of a model during the evaluation of a formula. These languages are equipped ...

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 investigate the expressive power of memory logics. These are modal logics extended with the possibility to store (or remove) the current node of evaluation in (or from) a memory, and to perform membership tests on the ...