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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TL;DR: This note criticises arguments against the central inference rules for the logic of ‘because’, and presents an independent argument in favour of the rules used in the logic.
Abstract: The present author developed a calculus for the logic of ‘because’. In a recent paper in this journal, it has been claimed that the central inference rules for the logic are invalid and that the intuition upon which the rules are based is not accounted for. This note criticises these arguments and presents an independent argument in favour of the rules used in the logic.
7 citations
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TL;DR: In this paper, a paraconsistent higher-order logic with countable infinite indeterminacy is presented, where each basic formula can get its own indeterminate truth value (or as we prefer: truth code).
Abstract: Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to achieve there are many potential applications of paraconsistent logics in knowledge-based systems, logical semantics of natural language, etc. Higher order logics have the advantages of being expressive and with several automated theorem provers available. Also the type system can be helpful. We present a concise description of a paraconsistent higher order logic with countable infinite indeterminacy, where each basic formula can get its own indeterminate truth value (or as we prefer: truth code). The meaning of the logical operators is new and rather different from traditional many-valued logics as well as from logics based on bilattices. The adequacy of the logic is examined by a case study in the domain of medicine. Thus we try to build a bridge between the HOL and MVL communities. A sequent calculus is proposed based on recent work by Muskens.
7 citations
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TL;DR: It is shown herein that probability can be comprehended in terms of a set of formal theories built in similar language, and explained how logical probabilistic methods relate to such techniques, and shows that the perfect formalization of a domain of knowledge requires them.
Abstract: The uncertainty of knowledge, in contrast to that of data, can be assessed by its probability in the logical sense. The logical concept of probability has been developed since the 1930s but, to date, no complete and accepted framework has been found. This paper approaches this problem from the point of view of logical entailment and natural sequential calculus of Classical logic. It is shown herein that probability can be comprehended in terms of a set of formal theories built in similar language. This measure is compliant with general understanding of probability, can be both conditional and unconditional, accounts for learning new evidence and complements Bayes’s rule. The approach suggested is practically infeasible at present and requires further theoretical research in the domain of geoscience. Nevertheless, even within the framework of existing methods of expert judgement processing, there is a way of implementing logic that will improve the quality of judgements. Also, to reach the state of formalization necessary to use logical probability, techniques of knowledge engineering are required; this paper explains how logical probabilistic methods relate to such techniques, and shows that the perfect formalization of a domain of knowledge requires these methods. Hence, the lines for future research should be: (1) the development of a strategy of co-application of existing expert judgement-processing techniques, knowledge engineering and classical logic; and (2) further research into logic enabling the development of formal languages and theories in
7 citations
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TL;DR: The paper traces this particular conception of logic back to the influence of his teachers in set theory and topology in Warsaw, and then details how it affected his explication of the notions of satisfaction, truth, logical consequence and logical term.
7 citations
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TL;DR: It is claimed that dialogue logic is the best-suited instrument to analyse paradoxes of the Sorites type.
Abstract: The first part of this paper presents asympathetic and critical examination of the approachof Shahid Rahman and Walter Carnielli, as presented intheir paper “The Dialogical Approach toParaconsistency”. In the second part, possibleextensions are presented and evaluated: (a) top-downanalysis of a dialogue situation versus bottom-up, (b)the specific role of ambiguities and how to deal withthem, and (c) the problem of common knowledge andbackground knowledge in dialogues. In the third part,I claim that dialogue logic is the best-suitedinstrument to analyse paradoxes of the Sorites type.All these considerations lead to philosophicallyrelevant observations concerning principles of charityon the one hand, and compactness on the other.
7 citations