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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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Journal ArticleDOI
01 Dec 2013-Episteme
TL;DR: In this article, it is argued that it is open to a classical logician to make distinctions, also needed by the paraconsistent logician, which allow a more nuanced ranking of theories in which inconsistent theories can have different degrees of usefulness and productivity.
Abstract: Classical logic is explosive in the face of contradiction, yet we find ourselves using inconsistent theories. Mark Colyvan, one of the prominent advocates of the indispensability argument for realism about mathematical objects, suggests that such use can be garnered to develop an argument for commitment to inconsistent objects and, because of that, a paraconsistent underlying logic. I argue to the contrary that it is open to a classical logician to make distinctions, also needed by the paraconsistent logician, which allow a more nuanced ranking of theories in which inconsistent theories can have different degrees of usefulness and productivity. Facing inconsistency does not force us to adopt an underlying paraconsistent logic. Moreover we will see that the argument to best explanation deployed by Colyvan in this context is unsuccessful. I suggest that Quinean approach which Colyvan champions will not lead to the revolutionary doctrines Colyvan endorses.

4 citations

Proceedings ArticleDOI
22 May 2001
TL;DR: The notion of "molecular logic", of which all finite valued variants of LP are a type, is defined, which concludes that the logic LP and its many valued generalizations are paraconsistent because of expressive incompleteness.
Abstract: In contrast to most logics, in paraconsistent logic it is not true that everything followed from a contradiction. The semantics for one of the best known paraconsistent logics, LP, permits sentences to be both true and false; but at the same time, the semantic characterization of the logical particles is classical. We define the notion of "molecular logic", of which all finite valued variants of LP are a type. Generally paraconsistent logics do not contain extensional conditionals. Molecular logics of n values may be conservatively extended to standard many valued logics of 2/sup n/-1 values, in which it is easy to define extensional conditionals with the usual detachment rules. The extension, while paraconsistent relative to a negation satisfying standard conditions on the original n values, is not paraconsistent relative to a negation satisfying standard conditions on the 2/sup n/-1 values of the extension. We conclude that the logic LP and its many valued generalizations are paraconsistent because of expressive incompleteness.

4 citations

Proceedings ArticleDOI
26 Jul 2004
TL;DR: An application of the Para‐analyzer, a logical analyzer based on the Paraconsistent Annotated Logic Pτ, introduced by Da Silva Filho and Abe in the decision‐making systems is presented and an example is analyzed in detail showing how uncertainty, inconsistency and paracompleteness can be elegantly handled with this logical system.
Abstract: In this paper we present an application of the Para‐analyzer, a logical analyzer based on the Paraconsistent Annotated Logic Pτ, introduced by Da Silva Filho and Abe in the decision‐making systems An example is analyzed in detail showing how uncertainty, inconsistency and paracompleteness can be elegantly handled with this logical systemAs application for the Para‐analyzer in decision‐making, we developed the BAM — Baricenter Analysis Method In order to make the presentation easier, we present the BAM applied in the viability analysis of product launchingSome of the techniques of Paraconsistent Annotated Logic have been applied in Artificial Intelligence, Robotics, Information Technolgy (Computer Sciences), etc

4 citations

Proceedings Article
01 Jan 2007
TL;DR: It is demonstrated that the modular approach of Nmatrices provides new insights into the semantic role of the studied axioms and the dependencies between them, and it is shown that all of the nondeterministic semantics provided in this paper are effective.
Abstract: A paraconsistent logic is a logic which allows non-trivial inconsistent theories. One of the best-known approaches to designing useful paraconsistent logics is da Costa’s approach, which has led to the family of Logics of Formal Inconsistency (LFIs), where the notion of inconsistency is expressed at the object level. In this paper we use non-deterministic matrices, a generalization of standard multi-valued matrices, to provide simple and modular finite-valued semantics for a large family of first-order LFIs. We demonstrate that the modular approach of Nmatrices provides new insights into the semantic role of the studied axioms and the dependencies between them. Furthermore, we study the issue of effectiveness in Nmatrices, a property which is crucial for the usefulness of semantics. We show that all of the nondeterministic semantics provided in this paper are effective.

4 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202313
202255
202131
202036
201935
201847