Paraconsistent logic

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

Pros and Cons of Physics in Logics

Abstract: The article examines the relation between physics and logics. It is claimed that well known logics can serve as a basis for an analytical examination of a physical theory, but that also physical theories can add to logics a synthetical aspect by allowing them inspiration by real world behaviour. Examples are mentioned for each of these cases, namely the Nemeti groups axiomatic relativity theory, Belnap’s branching models, and Orthologic. Thereafter, two options are presented where this observation was explicitly put to use. The first is the attempt to axiomatize Branching continuation models and the second is a logic inspired by classical mechanics’ vectors to describe doxastic models. The article then closes with a general discussion about the topic of influence between logic and physics based on the presented examples.

Paraconsistent Reasoning in Science and Mathematics: Introduction

Abstract: In this book we present a collection of papers on the topic of applying paraconsistent logic to solve inconsistency related problems in science, mathematics and computer science. The goal is to develop, compare, and evaluate different ways of applying paraconsistent logic. After more than 60 years of mainly theoretical developments in many independent systems of paraconsistent logic, we believe the time has come to compare and apply the developed systems in order to increase our philosophical understanding of reasoning when faced with inconsistencies. This book wants to be a first step toward an application based, constructive debate to tackle the question which systems are best applied for which kind of problems and which philosophical conclusions can be drawn from such applications.

Normativity and its vindication: The case of Logic 1

Abstract: Physical laws are irresistible. Logical rules are not. That is why logic is said to be normative. Given a sys- tem of logic we have a Norma, a standard of correctness. The problem is that we need another Norma to establish when the standard of correctness is to be applied. Subsequently we start by clarifying the senses in which the term 'logic' and the term 'normativity' are being used. Then we explore two different epistemo- logies for logic to see the sort of defence of the normativity of logic they allow for; if any. The analysis concentrates on the case of classical logic. In particular the issue will be appraised from the perspective put forward by the epistemology based on the methodology of wide reflective equilibrium and the scientific one underlying the view of logic as model. 1. Logic is normative It is clear that logic has traditionally been considered as normative. But, let us not take anything for granted and try to understand what this means. First, we need to state what we understand by logic. The term 'logic' is ambiguous in that it can be under- stood as what Peirce called, following medieval logicians, logica utens the rules that a given subject, or community of subjects, usesor as what he called logica docensthe set of theories that logicians have developed. In what follows we will use the term 'lo- gic' in the second sense given above. The task of logical theories (logica docens) has been frequently depicted as that of de- veloping theories for the evaluations of arguments. Following Burgess, the Kneales, and many others we claim that it should be obvious that "logic as a discipline could not develop until the practice of rational argumentation had flourished" (Resnik, 1985, p. 230). In the same line, Corcoran (Corcoran 1973) has claimed that before Aristotle developed his conception of proof a large amount of proofs had already been ob- tained. Therefore, since logical theories developed after rational argumentative prac- tice, in what follows, our bank of data will consist in a certain type of rational argu- mentative practice: The arguments and proofs in classical mathematical practice. My emphasis on mathematical practice intends to leave aside the problems pointed out by Resnik (Resnik, 1985, p. 227) in relation to the issue of using logical theories to de- scribe a "natural practice":

Remarks on Vasiľiev's investigations of contradictions

Abstract: Looking at Vasiľiev’s works we notice the influence of Neo-Kantians’ views, why we have to separate the real world from the world of thought before we start philosophical-logical investigations. From the point of view of logic, Vasiľiev adopted two assumptions. First, the essence of logic is the division into truth and falsehood. It is not possible to deal with logic if we cannot differentiate between the two. The second assumption is that logic comprises two types of rules: the first are rules of a purely rational nature, they are absolute and form a part of metalogic — the universal part of logic, which is not subject for change.