Paraconsistent logic

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

Potoses: Categorical Paraconsistent Universum for Paraconsistent Logic and Mathematic

Abstract: It is well-known that the concept of da Costa algebra [3] reflects most of the logical properties of paraconsistent propositional calculi Cn, 1 ≤ n ≤ ω introduced by N.C.A. da Costa. In [10] the construction of topos of functors from a small category to the category of sets was proposed which allows to yield the categorical semantics for da Costa’s paraconsistent logic. Another categorical semantics for Cn would be obtained by introducing the concept of potos – the categorical counterpart of da Costa algebra (the name “potos” is borrowed from W.Carnielli’s story of the idea of such kind of categories)

The Nature of Logic and the Concept of the Logic of Norms

Abstract: In a passage of the introduction to his book “Logical Studies” (1957) von Wright writes: “Deontic logic gets part of its philosophical significance from the fact that norms and valuations, though removed from the realm of truth, yet are subjected to logical law. This shows that logic, so to speak, has a wider reach than truth.” (p.III)

Interactive Learning from Contradictions in a Paraconsistent Logic

Abstract: In this paper, we describe a formal logical framework which we claim as essential to prove and to revise a model produced by combined ILP techniques. The dynamic process of proof embrace the supervision of the learning machine by a human, and this framework places the interpretation of contradictions in the heart of the interactive process which leads to a model which can be discussed, justified, and proven. We illustrate and validate this framework on an industrial application in the field of Drug Discovery, combining different learning processes to predict pharmaco-kinetic properties (ADME-T) and adverse side effects of therapeutic drug molecules.

A New Logic For Uncertainty

Abstract: Fuzziness and randomicity widespread exist in natural science, engineering, technology and social science. The purpose of this paper is to present a new logic - uncertain propositional logic which can deal with both fuzziness by taking truth value semantics and randomicity by taking probabilistic semantics or possibility semantics. As the first step for purpose of establishing a logic system which completely reflect the uncertainty of the objective world, this logic will lead to a set of logical foundations for uncertainty theory as what classical logic done in certain or definite situations or circumstances.

Paraconsistent Set Theory

Abstract: This chapter offers a new approach to paraconsistent set theory by means of employing LFIs and their powerful consistency operator into sets, as well as into sentences. By assuming that not only sentences, but sets themselves can be classified as consistent or inconsistent objects, the basis for new paraconsistent set-theories that resist certain paradoxes without falling into trivialism is established.