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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01 Jan 2004
TL;DR: The main point is that the rise of logic is both a matter of development and the matter of instantaneous creation, and the required vocabulary must have a historical process preceding it.
Abstract: In comparison with other disciplines, logic moves on a higher level of abstraction. In logic, individual statements needs to be analyzed and evaluated, and such analyses are generalized in terms of consistency and validity. The natural sciences can be viewed as forming theories by talking about entities that give causal or other types of explanation of sensible particulars. Logic obviously cannot be viewed this way. Logic is not some sort of an abstraction from sensory experience nor can it be defined in terms of other disciplines or interest. Logic has like mathematics autonomy and the highest level of abstractness. The main point is that the rise of logic is both a matter of development and the matter of instantaneous creation. The required vocabulary must have a historical process preceding it. Once that is in place, the possibility of constructing logic is there. Aristotle has been the first to understand the autonomy of logic, and the way it opens up a magic world of endless explorations of a unique mode of reflection, construction, justification, and argument evaluation.
1 citations
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23 Oct 2008
TL;DR: A connection of two techniques applied in Artificial Intelligence to solve problems of restoration of electrical power substations are presented: Case-based Reasoning --- CBR and the Four-Valued Annotated Paraconsistent Logic --- 4vAPL.
Abstract: This paper presents a connection of two techniques applied in Artificial Intelligence to solve problems of restoration of electrical power substations The techniques are: Case-based Reasoning --- CBR and the Four-Valued Annotated Paraconsistent Logic --- 4vAPL This linking process happens in the manipulation of the functions of belief, disbelief, expertise and temporality of the 4vAPL for the recovery of cases to determine process diagnostics of a CBR The domain of CBR is applied in the restoration of an electrical power substation The 4vAPL is the support applied to the problems that present inconsistent, partial, undefined information Thus, it approaches the system under study to real situations
1 citations
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03 Oct 2018TL;DR: The classic propositional tableau method is extended in order to compute the models given by the semantics of the Priest’s paraconsistent logic of paradox, and multisets are considered to represent branches of the tableau tree.
Abstract: We extend the classic propositional tableau method in order to compute the models given by the semantics of the Priest’s paraconsistent logic of paradox. Without loss of generality, we assume that the knowledge base is represented through propositional statements in NNF, which leads to use only two rules from the classical propositional tableau calculus for computing the paraconsistent models. We consider multisets to represent branches of the tableau tree and we extend the classical closed branches in order to compute the paradoxical models of formulas of the knowledge base. A sound and complete algorithm is provided.
1 citations
01 Jan 2008
TL;DR: In this article, a direct semantics and axiomatization of Jaskowski's adjunctive discursive logic and two additional connectives of negation are presented, one of which is a connective of the discursive conjunction.
Abstract: In the logical literature, Discursive (or Discussive) Logic introduced by Stanis law Jaskowski is seen as one of the earliest examples of the so-called paraconsistent logic. Nevertheless, there is some confusion over what discursive logic actually is. One of the possible sources of the confusion may be easily discerned; it comes from the fact that Jaskowski published his two papers in Polish and their English translations appeared many years later. 1 Up till 1999, no one but a Polish reader was able to read Jaskowski's paper on the discursive conjunction and, consequently some authors took discursive logic to be a foremost example of a non-adjunctive logic. 2 The situation became even more complicated when da Costa, Dubikajtis and Kotas presented an axiomatization with discursive connectives as primitive symbols. It turned out that a connective of the discursive conjunction they considered did not correspond to any of Jaskowski's connectives. Thus, their axiomatization contained some axiom schemata that were not generally valid in Jaskowski's logic. 3 The purpose of this paper is to clarify the confusion surrounding the discur- sive logic. We will present a direct semantics and axiomatization of Jaskowski's adjunctive discursive logic and show how to define and axiomatize two additional connectives of negation.
1 citations
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TL;DR: The distinction between analytic and synthetic as a partition of propositions, proofs, programs and definitions, and main results obtained in mathematical logic as answers to the logical questions concerning the relationships between analytical and synthetic are introduced.
Abstract: First, I will introduce the distinction between analytic and synthetic as a partition of propositions, proofs, programs and definitions, as an extension of the distinction between analytic categorical propositions and synthetic categorical propositions in ancient Logic. Secondly, I will discuss some logical questions concerning the distinction between analytic and synthetic, and I will present main results obtained in mathematical logic as answers to the logical questions concerning the relationships between analytic and synthetic.
1 citations