Document Type : Research

Author

• javid jafari

Department of Philosophy, Faculity of Humanity, Tarbiat Modares University, Tehran

Abstract

The logic {LP} is a paraconsistent logic that bears strong structural and semantic similarities to the LP logic introduced by Graham Priest. It is defined using Nmatrices, a semantic tool that plays a significant role in the study of paraconsistent logics by allowing for the analysis of contradictory statements without collapsing the entire logical system. In this paper, we first present the semantic framework of this logic and then develop a proof theory for it based on Gentzen-type sequent calculus. We show that this proof system is both sound and complete with respect to the proposed matrix semantics. Another focus of this study is the analysis of certain distinctive features of the {LP} logic, where noticeable differences from the original LP logic emerge. In particular, we examine the non-standard behavior of the conjunction operator in this logic, which functions in such a radically different way from common logics that the term “conjunction” barely seems appropriate.

Keywords

• Paraconsistent logics
• non-deterministic matrix
• sequent calculus
• proof-theory
• Gentzen-type systems

Main Subjects

• Non-Standard Mathematical Logic