Paraconsistent logic

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

The nature of logic

Abstract: Introduction 1. What is logic about? Wider still and wider ... resetting the bounds of logic 2. The institutionistic conception of logic: logic and analiticity 3. The implicational nature of logic: a structuralist account 4. The ontological commitment of logical theories 5. Validity 6. Is logic a theory of the obvious?

A Reply to Beall and Colyvan

Abstract: Beall and Colyvan (2001) extend the debate over paraconsistent approaches to the Sorites Paradox, offering additional argument for and additional argument against pursuing such an approach. Additional argument for a paraconsistent approach comes from considerations of simplicity which stress, amongst other things, uniformity of approach. This, coupled with the assumption that the paradoxes of self-reference are best dealt with by a paraconsistent approach, gives weight to the thought that, all other things being equal, one should pursue paraconsistent solutions to Sorites paradoxes as well. However, as Beall and Colyvan themselves note (see their footnote 5), all other things may not be equal. One does not need to look far to find independent arguments for paracompleteness -presupposition failure, reference failure, future contingents, etc. If any such argument is found compelling then similar considerations to those adduced by Beall and Colyvan will push in the opposite direction to paraconsistency, namely towards paracompleteness. On this plausible view paraconsistent logics are simply not able to 'do it all' and so the question re-arises as to whether a paraconsistent approach to the Sorites is superior. (Interestingly, if the Sorites Paradox could be shown to be 'of a kind' with the paradoxes of self-reference, then a more specific uniformity argument could be mounted in favour of a paraconsistent approach to paradoxes 'of this kind'.) In the end, considerations of uniformity may simply amount to an argument in favour of an even weaker paralogical approach-that is, one that is both paraconsistent and paracomplete.1

Paraconsistent Belief Revision based on a formal consistency operator

Abstract: In this paper two systems of AGM-like Paraconsistent Belief Revision are overviewed, both defined over Logics of Formal Inconsistency (LFIs) due to the possibility of defining a formal consistency operator within these logics. The AGM◦ system is strongly based on this operator and internalize the notion of formal consistency in the explicit constructions and postulates. Alternatively, the AGMp system uses the AGM-compliance of LFIs and thus assumes a wider notion of paraconsistency – not necessarily related to the notion of formal consistency. key-words Paraconsistent Belief Revision, paraconsistency, logics of formal inconsistency, contradiction, AGM-compliance.

Extending the Realm of Logic: The Adaptive-Logic Programme

Abstract: This paper reports on a development that involves a drastic broadening of the scope of symbolic logic. The central idea concerns dynamic proofs that explicate forms of reasoning for which no positive test is available. Two other forms of the dynamics of reasoning are briefly spelled out.

Decision tree-based paraconsistent learning

Abstract: It is possible to apply machine learning, uncertainty management and paraconsistent logic concepts to the design of a paraconsistent learning system, able to extract useful knowledge even in the presence of inconsistent information in a database. This paper presents a decision tree-based machine learning technique capable of handling inconsistent examples. The intention is to define a model able to handle databases with a large quantity of inconsistent examples. The model obtained is evaluated and compared with the C4.5 algorithm in terms of classification accuracy and size of the trees generated. As will be observed, in most situations where high rates of inconsistent examples were found, this presented better results when compared to the C4.5 algorithm.