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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29 Jan 2001
TL;DR: In this article, the evolutionary derivation of logic has been studied in the context of science of reason, with a focus on the evolutionary base of classical logic and the evolution of non-classical logic.
Abstract: 1. The biology of logic 2. The evolutionary derivation of life-history strategy theory 3. The evolutionary derivation of decision logic 4. The evolutionary derivation of inductive logic (Part I) 5. The evolutionary derivation of deductive logic 6. The evolutionary derivation of inductive logic (Part II) 7. The evolutionary derivation of mathematics 8. Broadening the evolutionary base of classical logic 9. The evolutionary derivation of nonclassical logic 10. Radical reductionism in logic 11. Toward a unified science of reason Appendix: formal theory.
37 citations
TL;DR: This paper shows that all reasonable paraconsistent logics based on three-valued deterministic matrices are maximal in the authors' strong sense, and investigates the strongest possible notion of maximal paraconsistency, which is investigated in the context of logics that are based on deterministic or non-deterministicThree-valued matrices.
Abstract: Maximality is a desirable property of paraconsistent logics, motivated by the aspiration to tolerate inconsistencies, but at the same time retain from classical logic as much as possible. In this paper we introduce the strongest possible notion of maximal paraconsistency, and investigate it in the context of logics that are based on deterministic or non-deterministic three-valued matrices. We show that all reasonable paraconsistent logics based on three-valued deterministic matrices are maximal in our strong sense. This applies to practically all three-valued paraconsistent logics that have been considered in the literature, including a large family of logics which were developed by da Costa's school. Then we show that in contrast, paraconsistent logics based on three-valued properly nondeterministic matrices are not maximal, except for a few special cases (which are fully characterized). However, these non-deterministic matrices are useful for representing in a clear and concise way the vast variety of the (deterministic) three-valued maximally paraconsistent matrices. The corresponding weaker notion of maximality, called premaximal paraconsistency, captures the "core" of maximal paraconsistency of all possible paraconsistent determinizations of a non-deterministic matrix, thus representing what is really essential for their maximal paraconsistency.
36 citations
Book•
25 Sep 2002
TL;DR: In this article, the authors present a survey of formal approaches to practical logic and the Reconfiguration of Logic Programming (R.M. Woods, R.H. Johnson, D.M Gabbay, J.A. Pereira).
Abstract: Preface. List of Authors. Logic and The Practical Turn (J. Woods, R.H. Johnson, D.M. Gabbay, Hans Jurgen Ohlbach). Standard Logics as Theories of Argument and Inference: Deduction (J. Woods). Standard Logics as Theories of Argument and Inference: Induction (J. Woods). Internal Critique: A logic is not a Theory of Reasoning and a Theory of Reasoning is not a logic (G. Harman). Standard Logic as a Model of Reasoning: The Empirical Critique (D.N. Perkins). A Framework for Intersubjective Accountability: Dialogical Logic (E.M. Barth). Interrrogative Logic (J. Hintikka, I. Halonen, A. Mutanen). Informal Logic and the Reconfiguration of Logic (R.H. Johnson, J.A. Blair). Probability Logic (J. Williamson). Philosophical Incidence of Logic Programming (L.M. Pereira). Formal Approaches to Practical Reasoning: A Survey (D.M. Gabbay, J. Woods). Index.
36 citations
TL;DR: It is shown that this extended notion of fibring preserves completeness under certain reasonableconditions and is obtained using new techniques that explore the properties of a suitable meta-logic (conditional equational logic) where the (possibly) non-truth-functional valuations are specified.
Abstract: Fibring has been shown to be useful for combining logics endowed with truth-functional semantics. However, the techniques used so far are unable to cope with fibring of logics endowed with non-truth-functional semantics as, for example, paraconsistent logics. The first main contribution of the paper is the development of a suitable abstract notion of logic, that may also encompass systems with non-truth-functional connectives, and where fibring can still be dealt with. Furthermore, it is shown that this extended notion of fibring preserves completeness under certain reasonable conditions. This completeness transfer result, the second main contribution of the paper, generalizes the one established in Zanardo et al. (2001) but is obtained using new techniques that explore the properties of a suitable meta-logic (conditional equational logic) where the (possibly) non-truth-functional valuations are specified. The modal paraconsistent logic of da Costa and Carnielli (1988) is studied in the context of this novel notion of fibring and its completeness is so established.
36 citations