Topic
Paraconsistent logic
About: Paraconsistent logic is a research topic. Over the lifetime, 1610 publications have been published within this topic receiving 28842 citations.
Papers published on a yearly basis
Papers
More filters
01 Jan 2002
TL;DR: It is shown how definite extended logic programs can be used for defining and reasoning with rough sets and a link between rough set theory and logic programming is established, making possible transfer of expertise between both fields.
Abstract: We show how definite extended logic programs can be used for defining and reasoning with rough sets Moreover, a rough-set-specific query language is presented and an answering algorithm is outlined Thus, we not only show a possible application of a paraconsistent logic to the field of rough sets as we also establish a link between rough set theory and logic programming, making possible transfer of expertise between both fields
5 citations
••
TL;DR: Paraconsistent logics are characterized by rejection of ex falso quodlibet, the principle of explosion, which states that from a contradiction, anything can be derived as discussed by the authors.
Abstract: Paraconsistent logics are characterized by rejection of ex falso quodlibet, the principle of explosion, which states that from a contradiction, anything can be derived. Strikingly these logics have found a wide range of application, despite the misgivings of philosophers as prominent as Lewis and Putnam. Such applications, I will argue, are of significant philosophical interest. They suggest ways to employ these logics in philosophical and scientific theories. To this end I will sketch out a ‘naturalized semantic dialetheism’ following Priest’s early suggestion that the principles governing human natural language may well be inconsistent. There will be a significant deviation from Priest’s work, namely, the assumption of a broadly Chomskyan picture of semantics. This allows us to explain natural language inconsistency tolerance without commitment to contentious views in formal logic.
5 citations
••
06 Aug 2020TL;DR: The Dialetheic approach to the paradoxes of self-reference has been discussed in this paper, with the focus on the use of a paraconsistent logic to quarantine the contradictions delivered by these notions.
Abstract: Given a formal language, a metalanguage is a language which can express — amongst other things — statements about it and its properties. And a metatheory is a theory couched in that language concerning how some of those notions behave. Two such notions that have been of particular interest to modern logicians — for obvious reasons — are truth and validity. These notions are, however, notoriously deeply entangled in paradox. A standard move is to take the metalanguage to be distinct from the language in question, and so avoid the paradoxes. One of the attractions of a dialetheic approach to the paradoxes of self-reference is that this move may be avoided. One may have a language with the expressive power to talk about — among other things — itself, and a theory in that language about how notions such as truth and validity for that language behave. The contradictions delivered by these notions are forthcoming, but they are quarantined by the use of a paraconsistent logic. The point of this paper is to discuss this project, the extent to which it has been successful, and the places where issues still remain.
5 citations
01 Jan 2004
TL;DR: In this article, it was shown that asking questions and giving answers are just as much logical core activities as drawing conclusions, and that the natural dynamic counterpart of static epistemic logic is the theory of arbitrary individual or social learning mechanisms.
Abstract: Classical logic is about propositions which we can know or believe, and unchanging inferential relationships between them. But inference is first and foremost an activity, for which propositions are merely the input, and the result. In recent years, there has been a growing awareness that various activities of reasoning, evaluation, belief revision, or communication, are themselves typical themes for logical investigation, and that their dynamic structure can be studied explicitly by logical means. 1 For instance, it seems strange to study only the statics of what it means to 'know' a proposition, when knowledge usually results from basic actions of learning that we perform all the time, such as asking a question and getting an answer. Indeed, asking questions and giving answers are just as much logical core activities as drawing conclusions! This line can be extended: the natural dynamic counterpart of static epistemic logic is the theory of arbitrary individual or social learning mechanisms. Similar trajectories from static to dynamic arise when we look at inference in such stages, first as a zero-agent mathematical relationship between static propositions, then as a one-agent activity of drawing conclusions, and finally as a many-agent interactive process of argumentation. This broadening of perspective, sometimes called the 'Dynamic Turn', started around 1980 with work on interpretation procedures for natural language, as well as belief revision in artificial intelligence. But how should logic incorporate actions as first-class citizens into its scope? Plausible formal frameworks to this effect come from the philosophy of action, temporal
5 citations