Paraconsistent logic

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

Break of Logic Symmetry by Self-conflicting Agents: Descriptive vs. Prescriptive Rules

Abstract: Classical axiomatic uncertainty theories (probability theory and others) model reasoning of rational agents. These theories are prescriptive, i.e., prescribe how a rational agent should reason about uncertainties. In particular, it is prescribed that (1) uncertainty P of any sentencep is evaluated by a single scalar P(p) value, (2) the truth-value of any tautology (por-p) is true, and (3) the truth-value of any contradiction (pnland-p) is false for every proposition p. However, real agents can be quite irrational in many aspects and do not follow rational prescriptions. In this paper, we build a logic of irrational and conflicting agents called I-agent logic of uncertainty (IALU) as a vector logic of evaluations of sentences. This logic does not prescribe rules on how an agent should reason rationally, but describe rules on how agents reason irrationally. This is a descriptive not prescriptive theory in contrast with the classical logic and the probability theories. This provides a new possibility to better understand and model uncertainties associated with social conflict phenomena. We show that the fuzzy logic has a potential to become a scalar version of a descriptive logic of irrational agents because it satisfies several necessary conditions of IALU

A Formal Bi-Logic Framework for the Mental Processes.

Abstract: This paper addresses questions of the transition related to conscious processes and unconscious processes, namely aims to substantiating a primary framework to the following open question: The vast majority of brain activity is non-conscious. What is the criterion to distinguish the non-conscious activities from conscious ones? To support our answers in a principled way, we present a general framework for the study of mental processes resting on two main principles: firstly, we endorse Matte Blanco’s principle of symmetry by giving central stage to the concept of unconscious processes. Secondly, to structure and combine the notions of infinity and partwhole equivalence in a mathematical logic method, moreover we base our work on modern non-classical logics in the disposition of context-dependency, as forcefully put forward by CJS Clarke. In particular, we employ the paraconsistent logic as the underlying logical system for defining the general framework for mental processes, highly structural and formal representation, called bi-logic framework.

The RM paraconsistent refutation system

Abstract: The aim of this paper is to study the refutation system consisting of the refutation axiom p ∧ ¬p → q and the refutation rules: reverse substitution and reverse modus ponens (B/A, if A → B ∈ RM). It is shown that the refutation system is characteristic for the logic of the 3-element RM algebra.

On Priest on Nonmonotonic and Inductive Logic

Abstract: Graham Priest defends the use of a nonmonotonic logic, LPm, in his analysis of reasoning in the face of true contradictions, such as those arising from the paradoxes of self-reference. In the course of defending this choice of logic in the face of the criticism that this logic is not truth preserving, Priest argued (2012) that requirement is too much to ask: since LPm is a nonmonotonic logic, it necessarily fails to preserve truth. In this article, I show that this assumption is incorrect, and I explain why nonmonotonic logics can nonetheless be truth preserving. Finally, I diagnose Priest's error, to explain when nonmonotonic logics do indeed fail to preserve truth.

On Quantum Logic

Abstract: The author holds that while effectively applied in a variety of fields, quantum mechanics has been the controversial topic under dispute, ever since its advent, in terms of definition, conceptual and philosophical implications. The paper is thus an attempt to invetigate the origin of quantum logic and the difference between classical logic and quantum logic so as to guide the research in this field.