Paraconsistent logic

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

Natural Deduction: An Introduction to Logic with Real Arguments, a Little History, and Some Humour

Abstract: Richard Arthur's Natural Deduction provides a wide-ranging introduction to logic. In lively and readable prose, Arthur presents a new approach to the study of logic, one that seeks to integrate methods of argument analysis developed in modern "informal logic" with natural deduction techniques. The dry bones of logic are given flesh by unusual attention to the history of the subject, from Pythagoras, the Stoics, and Indian Buddhist logic, through Lewis Carroll, Venn, and Boole, to Russell, Frege, and Monty Python.

An embedding-based completeness proof for nelson's paraconsistent logic

Abstract: It is known that a syntactical embedding theorem of Nelson’s paraconsistent logic N4 into the positive intuitionistic logic LJ is useful to show the cut-elimination and decidability theorems for N4. In this paper, a semantical embedding theorem of N4 into LJ is shown. An alternative proof of the Kripke-completeness theorem for N4 is obtained by combining both the syntactical and semantical embedding theorems. Thus, the completeness, cut-elimination and decidability theorems can uniformly be obtained from these embedding theorems. A singleconsequence Kripke semantics for N4 is also addressed based on a modication of the semantical embedding theorem.

Logical Formalization and the Formation of Logic(s)

Abstract: The project of logic as a theoretical tool useful for the sciences and humanities involves, as a crucial step, logical formalization – the conversion of sentences of natural language to formulas of a formal language. But what do we do, exactly, when we do logical formalization? What are the criteria of adequacy of the conversion? In how far is logic normative? The paper offers answers to these central (but surprisingly rather neglected) questions and shows that getting a proper grasp on the process of formalization is important for understanding the nature of logic. The key point is that logic as a theoretical tool manages to consolidate our linguistic – in particular argumentative – practices by means of attaining a specific sort of reflective equilibrium. The paper provides a detailed discussion of the answers to the above questions implied by this understanding of logic.

Adaptive Logics and the Integration of Induction and Deduction

Abstract: The aim of this paper is twofold. First, I want to argue that the distinction between induction and deduction is less clear-cut than traditionally assumed, and that, moreover, most reasoning processes in the sciences involve an integration of inductive and deductive steps. Next, I want to show how so-called adaptive logics may lead to a better understanding of this integrated use of induction and deduction.