Topic
Paraconsistent logic
About: Paraconsistent logic is a research topic. Over the lifetime, 1610 publications have been published within this topic receiving 28842 citations.
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Book•
01 Jan 2004
TL;DR: The authors The Mathematical Turn in Logic: From General to Transcendental Logic (M. Tiles) is a seminal work in the history of logic, with a focus on algebraic logic.
Abstract: Preface (D.M. Gabbay, J. Woods). List of Contributors. Leibniz's Logic (W. Lenzen). Kant: From General to Transcendental Logic (M. Tiles). Hegel's Logic (J.W. Burbidge). Bolzano as Logician (P. Rusnock, R. George). Husserl's Logic (R. Tieszen). Algebraical Logic 1685-1900 (T. Hailperin). The Algebra of Logic (V.S. Valencia). The Mathematical Turn in Logic (I. Grattan-Guinness). Schroder's Logic (V. Peckhaus). Peirce's Logic (R. Hilpinen). Frege's Logic (P. Sullivan). Index.
35 citations
TL;DR: In this paper, the authors present a theory of belief revision that allows people to come to believe in contradictions by replacing consistency maintenance with a weaker property called coherence, which is defined as the property that a set of statements are coherent if they do not overlap.
Abstract: This paper presents a theory of belief revision that allows people to come tobelieve in contradictions. The AGM theory of belief revision takes revision,in part, to be consistency maintenance. The present theory replacesconsistency with a weaker property called “coherence”. In addition to herbelief set, we take a set of statements that she rejects. These two sets arecoherent if they do not overlap. On this theory, belief revision maintains coherence.
35 citations
Proceedings Article•
09 Aug 2003TL;DR: This paper provides a general characterization of inconsistency, based on quasi-classical logic (a form of paraconsistent logic with a more expressive semantics than Belnap's four-valued logic, and unlike otherParaconsistent logics, allows the connectives to appear to behave as classical connectives).
Abstract: Inconsistencies frequently occur in knowledge about the real-world. Some of these inconsistencies may be more significant than others, and some knowledgebases (sets of formulae) may contain more inconsistencies than others. This creates problems of deciding whether to act on these inconsistencies, and if so how. To address this, we provide a general characterization of inconsistency, based on quasi-classical logic (a form of paraconsistent logic with a more expressive semantics than Belnap's four-valued logic, and unlike other paraconsistent logics, allows the connectives to appear to behave as classical connectives). We analyse inconsistent knowledge by considering the conflicts arising in the minimal quasi-classical models for that knowledge. This is used for a measure of coherence for each knowledgebase, and for a measure of significance of inconsistencies in each knowledgebase. In this paper, we formalize this framework, and consider applications in managing heterogeneous sources of knowledge.
35 citations
01 Jan 1985
TL;DR: In this article, the meaning and function of negation are disentangled from ontological issues with which they have been long entangled, by separating relevant and paraconsistent logics from classical theories.
Abstract: The problems of the meaning and function of negation are disentangled from ontological issues with which they have been long entangled. The question of the function of negation is the crucial issue separating relevant and paraconsistent logics from classical theories.
34 citations
05 Jun 1995
TL;DR: This paper introduces and discusses sound and complete proof systems in Natural Deduction style for representing various “truth” consequence relations of Dynamic Logic and derives in Dynamic Logic a set of rules representing a ND-style system for Hoare Logic.
Abstract: Natural Deduction style presentations of program logics are useful in view of the implementation of such logics in interactive proof development environments, based on type theory, such as LEGO, Coq, etc. In fact, ND-style systems are the kind of systems which can take best advantage of the possibility of reasoning “under assumptions” offered by proof assistants generated by Logical Frameworks. In this paper we introduce and discuss sound and complete proof systems in Natural Deduction style for representing various “truth” consequence relations of Dynamic Logic. We discuss the design decisions which lead to adequate encodings of these logics in Coq. We derive in Dynamic Logic a set of rules representing a ND-style system for Hoare Logic.
34 citations