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 2007
6 citations
11 Sep 2017
TL;DR: The aim of this paper is to fill in the gap by presenting a semantics for P \(^1\) a la Jaśkowski which sheds some light on the intuitive understanding of Sette’s logic.
Abstract: One of the simple approaches to paraconsistent logic is in terms of three-valued logics. Assuming the standard behavior with respect to the “classical"values, there are only two possibilities for paraconsistent negation, namely the negation of the Logic of Paradox and the negation of Sette’s logic P \(^1\). From a philosophical perspective, the paraconsistent negation of P \(^1\) is less discussed due to the lack of an intuitive reading of the third value. Based on these, the aim of this paper is to fill in the gap by presenting a semantics for P \(^1\) a la Jaśkowski which sheds some light on the intuitive understanding of Sette’s logic. A variant of P \(^1\) known as I \(^1\) will be also discussed.
6 citations
TL;DR: A unifying framework is provided that allows to better understand the relationship between different Q-worlds, and a general method for transferring concepts and results between TQT and QST is defined, thereby significantly increasing the expressive power of both approaches.
Abstract: Quantum set theory (QST) and topos quantum theory (TQT) are two long running projects in the mathematical foundations of quantum mechanics that share a great deal of conceptual and technical affinity. Most pertinently, both approaches attempt to resolve some of the conceptual difficulties surrounding quantum mechanics by reformulating parts of the theory inside of non-classical mathematical universes, albeit with very different internal logics. We call such mathematical universes, together with those mathematical and logical structures within them that are pertinent to the physical interpretation, `Q-worlds'. Here, we provide a unifying framework that allows us to (i) better understand the relationship between different Q-worlds, and (ii) define a general method for transferring concepts and results between TQT and QST, thereby significantly increasing the expressive power of both approaches. Along the way, we develop a novel connection to paraconsistent logic and introduce a new class of structures that have significant implications for recent work on paraconsistent set theory.
6 citations
TL;DR: A comparison is performed from the standpoint of agreement with experience between traditional logic and chain-set logic to show that the chain- set treatment of the if then connective is nearer to a scientifically true theory than traditional logic.
6 citations
01 Jan 1990
TL;DR: This paper removes the restriction that programs be well-behaved and extends the soundness and completeness results to apply to arbitrary existential queries and to arbitrary GHPs, resulting in the strongest possible completeness result for GHPs.
Abstract: In [6], we introduced a means of allowing logic programs to contain negations in both the head and the body of a clause. Such programs were called generally Horn programs (GHPs, for short). The model-theoretic semantics of GHPs were defined in terms of four-valued Belnap lattices [5]. For a class of programs called well-behaved programs, an SLD-resolution like proof procedure was introduced. This procedure was proven (under certain restrictions) to be sound (for existential queries) and complete (for ground queries). In this paper, we remove the restriction that programs be well-behaved and extend our soundness and completeness results to apply to arbitrary existential queries and to arbitrary GHPs. This is the strongest possible completeness result for GHPs. The results reported llere apply to tIle design of very large knowledge bases and in processing queries to kno\vledge bases that possibly contain erroneous information.
6 citations