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 explicitly shows that after combining the standard (classical) values in {>,⊥} to get a space of four values, as FDE demands, the given process of combining values ‘all the way up’ to α many values, for any ordinal α, results in the same account of logical consequence (viz., FDE).
Abstract: A very natural and philosophically important subclassical logic is FDE (for first-degree entailment). This account of logical consequence can be seen as going beyond the standard two-valued account (of “just true” and “just false”) to a four-valued account (adding the additional values of “both true and false” and “neither true nor false”). A natural question arises: What account of logical consequence arises from considering further (positive) combinations of such values? A partial answer was given by Priest in 2014; Shramko and Wansing had also given a partial result some years earlier, although in a different (more algebraic) context. In this note we generalize Priest’s (and indirectly Shramko and Wansing’s) result to show that even if one considers ordinal-many (positive) combinations of the previous values, for any ordinal, the resulting consequence relation (the resulting logic) remains FDE.
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01 Jan 1990TL;DR: In this paper, the authors discuss De Morgan's central contribution to the logic of relations, which he published in 1860 under the title, “On the Syllogism: IV and on the Logic of Relations.
Abstract: We have now examined the philosophical framework surrounding De Morgan’s views on relations, and we have also seen how these views show the need for a logic of relations. In this chapter, we will discuss De Morgan’s central contribution to the logic of relations, which he published in 1860 under the title, “On the Syllogism: IV and on the Logic of Relations.” In this classic memoir, De Morgan moves beyond his relational analysis of the syllogism and the bicopular syllogism to something that may justifiably be called a logic of relations: that is, the specification and systematization of previously unrecognized valid forms of relational inference.
1 citations
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TL;DR: In this paper , the authors discuss how to adapt these postulates when the underlying logic is Priest's LP logic, in order to model a rational change, while being a conservative extension of AGM/KM belief revision.
Abstract: Belief revision aims at incorporating, in a rational way, a new piece of information into the beliefs of an agent. Most works in belief revision suppose a classical logic setting, where the beliefs of the agent are consistent. Moreover, the consistency postulate states that the result of the revision should be consistent if the new piece of information is consistent. But in real applications it may easily happen that (some parts of) the beliefs of the agent are not consistent. In this case then it seems reasonable to use paraconsistent logics to derive sensible conclusions from these inconsistent beliefs. However, in this context, the standard belief revision postulates trivialize the revision process. In this work we discuss how to adapt these postulates when the underlying logic is Priest's LP logic, in order to model a rational change, while being a conservative extension of AGM/KM belief revision. This implies, in particular, to adequately adapt the notion of expansion. We provide a representation theorem and some examples of belief revision operators in this setting.
1 citations
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TL;DR: In this article , negation-free paraconsistency is defined and characterized as the failure of a principle of explosion, and negation operator is not essential for describing it.
Abstract: Paraconsistency is commonly defined and/or characterized as the failure of a principle of explosion. The various standard forms of explosion involve one or more logical operators or connectives, among which the negation operator is the most frequent. In this article, we ask whether a negation operator is essential for describing paraconsistency. In other words, is it possible to describe a notion of paraconsistency that is independent of connectives? We present two such notions of negation-free paraconsistency, one that is completely independent of connectives and another that uses a conjunction-like binary connective that we call 'fusion'. We also derive a notion of 'quasi-negation' from the former, and investigate its properties.
1 citations