An Algebraic Investigation of the Connexive Logic C

In this paper we show that axiomatic extensions of H. Wansing's connexive logic C (C-?) are algebraizable (in the sense of J.W. Blok and D. Pigozzi) with respect to sub-varieties of C(C-?)-algebras. We develop the structure theory of C(C-?)-algebras, and we prove their representability in terms of twist-like constructions over implicative lattices (Heyting algebras). As a consequence, we further clarify the relationship between the aforementioned classes. Finally, taking advantage of the above machinery, we provide some preliminary remarks on the lattice of axiomatic extensions of C (C-?) as well as on some properties of their equivalent algebraic semantics

Some adaptive contributions to logics of formal inconsistency

Some insights were gained from the study of inconsistency-adaptive logics. The aim of the present paper is to put some of these insight to work for the study of logics of formal inconsistency. The focus of attention are application contexts of the aforementioned logics and their theoretical properties in as far as they are relevant for applications. As the questions discussed are difficult but important, a serious attempt was made to make the paper concise but transparent

A four-valued hybrid logic with non-dual modal operators

Hybrid logics are an extension of modal logics where it is possible to refer to a specific state, thus allowing the description of what happens at specific states, equalities and transitions between them. This makes hybrid logics very desirable to work with relational structures. However, as the amount of information grows, it becomes increasingly more common to find inconsistencies. Information collected about a particular hybrid structure is not an exception. Rather than discarding all the data congregated, working with a paraconsistent type of logic allows us to keep it and still make sensible inferences. In this paper we introduce a four-valued semantics for hybrid logic, where contradictions are allowed both at the level of propositional variables and accessibility relations. A distinguishing feature of this new logic is the fact that the classical equivalence between modal operators will be broken. A sound and complete tableau system is also presented.publishe

Tutorial on inconsistency-adaptive logics

This paper contains a concise introduction to a few central features of inconsistency-adaptive logics. The focus is on the aim of the program, on logics that may be useful with respect to applications, and on insights that are central for judging the importance of the research goals and the adequacy of results. Given the nature of adaptive logics, the paper may be read as a peculiar introduction to defeasible reasoning

Two Consistent Many-Valued Logics for Paraconsistent Phenomena

In this reviewing paper, we recall the main results of our papers [24, 31] where we introduced two paraconsistent semantics for Pavelka style fuzzy logic. Each logic formula a is associated with a 2 x 2 matrix called evidence matrix. The two semantics are consistent if they are seen from 'outside'; the structure of the set of the evidence matrices M is an MV-algebra and there is nothing paraconsistent there. However, seen from "inside,' that is, in the construction of a single evidence matrix paraconsistency comes in, truth and falsehood are not each others complements and there is also contradiction and lack of information (unknown) involved. Moreover, we discuss the possible applications of the two logics in real-world phenomena