Paraconsistent logic

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

Reasoning with contradictory information using quasi-classical logic

Abstract: The proof theory of quasi-classical logic (QC logic) allows the derivation of non-trivializable classical inferences from inconsistent information. A non-trivializable, or paraconsistent, logic is, by necessity, a compromise, or weakening, of classical logic. The compromises on QC logic seem to be more appropriate than other paraconsistent logics for applications in computing. In particular, the connectives behave in a classical manner. Here we motivate the need for QC logic, present a proof theory, and semantics for the logic, and compare it to other paraconsistent logics.

The completeness and compactness of a three-valued first-order logic

Abstract: The strong completeness and the compactness of a three-valued first order predicate calculus with two distinguished truth-values are obtained. The system was introduced in Sur un prcb leme de Jaskowski, I .M.L. D.'Ottaviano and N.C. A. da Costa, C.R. Acad.Sc. Paris 270A (1970) , pp.1349-1353, and has several applications, especially in paraconsistent logics.

A Comparative Study of Various Model-Theoretic Treatments of Negation: A History of Formal Negation

Abstract: There are different treatments of the semantics of negation in non-classical logics, the most familiar of which is probably the Kripke definition of negation for intuitionistic logic. In two recent papers I have explored generalizations of Goldblatt’s semantics for negation in orthologic (which uses the perp relation), and related these to the Kripke definition of negation for intuitonistic logic, and to the definition of De Morgan negation in relevance logic (which standardly uses the ‘star operator’ *). The present paper in part surveys this earlier work, but the main focus is to connect the alternative four-valued semantics of De Morgan negation (using ‘overdetermined’ and ‘underdetermined’ truth values) to the star semantics (and hence indirectly to the perp semantics). This connection is based on semi-published work of mine from the 1960’s.

An ensemble design of intrusion detection system for handling uncertainty using Neutrosophic Logic Classifier

Abstract: In the real world it is a routine that one must deal with uncertainty when security is concerned. Intrusion detection systems offer a new challenge in handling uncertainty due to imprecise knowledge in classifying the normal or abnormal behaviour patterns. In this paper we have introduced an emerging approach for intrusion detection system using Neutrosophic Logic Classifier which is an extension/combination of the fuzzy logic, intuitionistic logic, paraconsistent logic, and the three-valued logics that use an indeterminate value. It is capable of handling fuzzy, vague, incomplete and inconsistent information under one framework. Using this new approach there is an increase in detection rate and the significant decrease in false alarm rate. The proposed method tripartitions the dataset into normal, abnormal and indeterministic based on the degree of membership of truthness, degree of membership of indeterminacy and degree of membership of falsity. The proposed method was tested up on KDD Cup 99 dataset. The Neutrosophic Logic Classifier generates the Neutrosophic rules to determine the intrusion in progress. Improvised genetic algorithm is adopted in order to detect the potential rules for performing better classification. This paper exhibits the efficiency of handling uncertainty in Intrusion detection precisely using Neutrosophic Logic Classifier based Intrusion detection System.