Proof theory of Nelson's paraconsistent logic: A uniform perspective
Norihiro Kamide,Heinrich Wansing +1 more
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In this paper, proof systems for Nelson's paraconsistent logic N4 are comprehensively studied and some basic theorems including cut-elimination, normalization and completeness are uniformly proved using various embedding theorem.About:
This article is published in Theoretical Computer Science.The article was published on 2012-01-01 and is currently open access. It has received 48 citations till now. The article focuses on the topics: Paraconsistent logic & Principle of explosion.read more
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Classical Negation and Expansions of Belnap---Dunn Logic
Michael De,Hitoshi Omori +1 more
TL;DR: The notion of classical negation is investigated from a non-classical perspective and an axiomatic expansion BD+ of four-valued Belnap–Dunn logic is considered, showing the expansion complete and maximal.
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Paraconsistent Logic, Evidence, and Justification
TL;DR: A modal logic, KX4, in which $$\square X$$□X can be read as asserting there is implicit evidence for X, where the authors understand evidence to permit contradictions in a formal sense, is introduced, and BLE is shown to be equivalent to Nelson's paraconsistent logic N4.
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From Paraconsistent Logic to Dialetheic Logic
Hitoshi Omori,Hitoshi Omori +1 more
TL;DR: This paper proposes an account of negation, and explores some of its implications, and introduces a special kind of paraconsistent logic, called dialetheic logic, obtained by combining connectives from different traditions ofParaconsistency, and has some distinctive features such as its propositional fragment being Post complete.
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A Useful Four-Valued Logic
TL;DR: It is argued that a sophisticated question-answering machine that has the capability of making inferences from its data base should employ a certain four-valued logic, the motivating consideration being that minor inconsistencies in its data should not be allowed to lead to irrelevant conclusions.
Book
Entailment : the logic of relevance and necessity
TL;DR: The Description for this book, Entailment: The Logic of Relevance and Necessity, will be forthcoming.
Book
Basic proof theory
TL;DR: N- systems and H-systems and Gentzen systems, proof theory of arithmetic, second-order logic, and solutions to selected exercises.
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