Paraconsistent logic

About: Paraconsistent logic is a research topic. Over the lifetime, 1610 publications have been published within this topic receiving 28842 citations.

Negation and Partial Axiomatizations of Dependence and Independence Logic Revisited

Abstract: In this paper, we axiomatize the negatable consequences in dependence and independence logic by extending the natural deduction systems of the logics given in [10, 20]. We give a characterization for negatable formulas in independence logic and negatable sentences in dependence logic, and identify an interesting class of formulas that are negatable in independence logic. Dependence and independence atoms, first-order formulas belong to this class.

The logic determined by Smiley’s matrix for Anderson and Belnap’s first-degree entailment logic

Abstract: The aim of this paper is to define the logical system Sm4 characterised by the degree of truth-preserving consequence relation defined on the ordered set of values of Smiley’s four-element matrix MSm4. The matrix MSm4 has been of considerable importance in the development of relevant logics and it is at the origin of bilattice logics. It will be shown that Sm4 is a most interesting paraconsistent logic which encloses a sound theory of logical necessity similar to that of Anderson and Belnap’s logic of entailment E. Intuitively, Sm4 can be described as a four-valued expansion of the positive fragment of Lewis’ S5 or, alternatively, as a four-valued version of S5.

N.A. Vasil'ev's Logical Ideas and the Categorical Semantics of Many-Valued Logic

Abstract: Here we suggest a formal using of N.A. Vasil’ev’s logical ideas in categorical logic: the idea of “accidental” assertion is formalized with topoi and the idea of the notion of nonclassical negation, that is not based on incompatibility, is formalized in special cases of monoidal categories. For these cases, the variant of the law of “excluded n-th” suggested by Vasil’ev instead of the tertium non datur is obtained in some special cases of these categories. The paraconsistent law suggested by Vasil’ev is also demonstrated with linear and tensor logics but in a form weaker than he supposed. As we have, in fact, many truth-values in linear logic and topos logic, the admissibility of the traditional notion of inference in the categorical interpretation of linear and intuitionistic proof theory is discussed.

Analysis and Diagnosis of Cardiovascular Diseases through the Paraconsistent Annotated Logic

Abstract: All over the world cardiovascular diseases are responsible for a great number of clinical problems that result in death. Arterial Hypertension is considered one of the main agents of such diseases and, for that reason, the correct detection of Hypertension symptoms is very important for the medical area. In this work we use the Paraconsistent Logic (PL) as a method of treatment of uncertainties to help health professionals that act in this medical area. With base in the concepts of the Paraconsistent Logic we created a Expert System for the help in the analysis and diagnosis in cardiovascular diseases. This computational system is called “ParaHyper Analyzer” and it uses Algorithms of the Paraconsistent Logic, a non-classical kind of logic, for the treatment of contradictory information. The algorithms are obtained through the interpretation of the representative Lattice of Paraconsistent Annotated Logic with annotation of two values (PAL2v), where the certainty degree (DC) and the contradiction degree (Dct) are calculated, according to the logical methodology. The PAL2v algorithms are called Paraconsistent Analysis Nodes (PAN). The PAN allows the analysis of propositions which are related to changes in the blood pressure, so that the patient can be classified in a certain risk group. The ParaHyper Analyzer studies this information and presents a result which shows the possibility of developing a serious cardiovascular disease.