Paraconsistent logic

About: Paraconsistent logic is a research topic. Over the lifetime, 1610 publications have been published within this topic receiving 28842 citations.

Ways of understanding hugh Maccoll's concept of symbolic existence

Abstract: Hugh MacColl (1837-1909) proposed, in several papers, a non-standard way of understanding the ontology underlying what we today call quantified propositions. His ideas, mixed with reflections about the use of arbitrary objects, were not greatly successful and were ruthlessly criticised by Bertrand Russell especially. The aim of this paper is to show that a thorough reading of MacColl's general understanding of symbolic existence, a concept which is connected with his view of traditional hypotheticals, elucidates his proposals on the role of ontology in logics. The interpretation of MacColl's concept of symbolic existence put forward in this paper and embedded in a dialogical system of free logic can be expressed in a nutshell: in any argumentation, it sometimes makes sense to restrict the use and introduction of singular terms in the context of quantification to a formal use of those terms. That is, the Proponent is allowed to use a constant iff this constant has been explicitly conceded by the Opponent. The paper also offers a second way of reconstructing MacColl's ideas on contradictory objects by means of combining the concept of formal use of constants in free logics and that of the formal use of elementary negations in paraconsistent logics.

On the Methodology of Paraconsistent Logic

Abstract: The present note contains a critical discussion of the methodology of paraconsistent logic in general and “the central optimisation problem of paraconsistent logics” in particular. It is argued that there exist several reasons not to consider classical logic as the reference logic for developing systems of paraconsistent logic, and it is suggested to weaken a certain maximality condition that may be seen as essential for “optimisation”, which is a methodology in the tradition of Newton da Costa. It is argued that the guiding motivation for the development of paraconsistent logics should be neither epistemological nor ontological, but informational. Moreover, it is pointed out that there are other notions of maximality and other methodologies. A methodology due to Graham Priest and Richard Routley and another methodology that focuses on a minimal shrinkage of expressiveness relative to a given reference logic are considered in some detail.

Fuzzy Logic or Lukasiewicz Logic: A Clarification

Abstract: Pavelka [10] had shown in 1979 that the only natural way of formalizing fuzzy logic for truth-value in the unit interval [0,1] is by using Lukasiewicz's implication operator a→b = min{1, 1−a+b} or some isomorphic form of it A considerable number of other papers around the same time had attempted to formulate alternative definitions for a→b by giving intuitive justifications for them. There continues to be some confusion, however, even today about the right notion of fuzzy logic. Much of this has its origin in the use of improper “and” (“or”) and the “not” operations and a misunderstanding of some of the key differences between “proofs” or inferencing in fuzzy logic and those in Lukasiewicz's logic. We point out the need for defining the strong conjunction operator “⊗” in connection with fuzzy Modus-ponens rule and why we do not need the fuzzy Syllogism rule. We also point out the shortcomings of many of the alternative definitions of a→b, which indicate further support for Pavelka's result. We hope that these discussions help to clarify the misconceptions about fuzzy logic.

How Do Logics Explain

Abstract: Anti-exceptionalists about logic maintain that it is continuous with the empirical sciences. Taking anti-exceptionalism for granted, we argue that traditional approaches to explanation are inadequate in the case of logic. We argue that Andrea Woody's functional analysis of explanation is a better fit with logical practice and accounts better for the explanatory role of logical theories.