Paraconsistent logic

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

A Paraconsistent Logic Program Based Control for a Discrete Event Cat and Mouse

Abstract: We have developed a paraconsistent logic program called an Extended Vector Annotated Logic Program with Strong Negation (abbr. EVALPSN), which can deal with defeasible deontic reasoning and contradiction, and applied it to safety verification and control such as railway interlocking safety verification, traffic signal control etc.. In this paper, we introduce how to apply EVALPSN to discrete event control with taking an example called Cat and Mouse. Generally, event control can be represented as deontic rules such as it is forbidden for both the cat and the mouse to occupy the same room simultaneously, and the control must deal with contradiction to avoid unexpected system states. We show that such a discrete event control can be easily formalized in EVALPSN and implemented.

Embedding-based approaches to paraconsistent and temporal description logics*

Abstract: In this article, some paraconsistent and temporal description logics are studied based on an embedding-based proof method. A new paraconsistent description logic, PALC, is obtained from the description logic ALC by adding a paraconsistent negation. Two temporal description logics, XALC and BALCl, are introduced by combining and modifying ALC and Prior’s tomorrow tense logic. XALC has the next-time operator, and BALCl has some restricted versions of the next-time, any-time and some-time operators, in which the time domain is bounded by a positive integer l. Some theorems for embedding PALC, XALC and BALCl into ALC are proved in a uniform way, and PALC, XALC and BALCl are shown to be decidable. Three tableau calculi for PALC, XALC and BALCl are introduced, and the completeness theorems for these calculi are proved.

None of the Above: The Catuṣkoṭi in Indian Buddhist Logic

Abstract: The catuṣkoṭi (Greek: tetralemma; English: four corners) is a venerable principle of Indian logic, which has been central to important aspects of reasoning in the Buddhist tradition. What, exactly, it is, and how it is applied, are, however, moot—though one thing that does seem clear is that it has been applied in different ways at different times and by different people. Of course, Indian logicians did not incorporate the various interpretations of the principle in anything like a theory of validity in the modern Western sense; but the tools of modern non-classical logic show exactly how to do this. The tools are those of the paraconsistent logic of First Degree Entailment and some of its modifications.

Discursive logic towards a logic of rational discourse

Abstract: Both logic and philosophy of science investigate formal aspects of scientific discourse, i.e. properties of (non-monotonic) consequence operations for discursive logic. In the present paper we handle two of them: paraconsistency and enthymematycity.