Paraconsistent logic

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

In Defense of the Law of Noncontradiction

Abstract: An important philosophical puzzle arises whenever we find a group of philosophically interesting sentences which individually appear to be true but jointly imply a contradiction. It is traditional to suppose that since the sentences in the group are jointly inconsistent, we cannot accept them all. This refusal to accept all the sentences in the group is not just grounded in (a) the problem of accepting the derivable contradiction, but also in (b) the problem that classical logic gives us the means to derive every sentence whatsoever once we have derived a contradiction. But with certain really hard puzzles of this kind, it is difficult to identify even one sentence in the puzzling group to reject. In such cases, there seems to be no good reason or argument for rejecting one of the sentences rather than another. We often find ourselves in the uncomfortable position of having to reject statements that have a strong claim to truth. Paraconsistent logic and dialetheism constitute a fascinating body of doctrines for critically analyzing this kind of philosophical puzzle. Paraconsistent logic removes problem (b), noted above, concerning the presence of contradictions in classical logic. In contrast to classical logic, paraconsistent logic tolerates the derivation of a contradiction without thereby yielding a proof of every sentence. Dialetheism goes one step further, however, and addresses problem (a). It is the doctrine that, in some of these really hard cases, there are indeed true contradictions. Di-

Rule-Based Reasoning with Belief Structures

Abstract: This paper introduces \(\text {4QL}^{\!\text {Bel}}\), a four-valued rule language designed for reasoning with paraconsistent and paracomplete belief bases as well as belief structures. Belief bases consist of finite sets of ground literals providing (partial and possibly inconsistent) complementary or alternative views of the world. As introduced earlier, belief structures consist of constituents, epistemic profiles and consequents. Constituents and consequents are belief bases playing different roles. Agents perceive the world forming their constituents, which are further transformed into consequents via the agents’ or groups’ epistemic profile.

Quasi-matrix logic as a paraconsistent logic for dubitable information

Abstract: We distinguish three types of statements — indubitably true statements (the value “n”), indubitably false statements (the value “i”) and statements of dubitable information (the value “c”).

Logic modeling with partially ordered preferences

Abstract: Logic modeling is the use of formal logic as a modeling tool for problems of interest to management science. Based on a review of the logic of preference literature this paper presents five axioms for reasoning about a decision maker's preferences. A semantics of situations is adopted for the symbols used. Both logical deduction and a modification of dynamic programming are proposed for the problem of selecting preferred states of affairs over time. Finally, a sketch of an implementation in Prolog is presented.

A paraconsistent system of autonomous agents for Brazilian bank check treatment

Abstract: This work is part of the Multicheck Project that defines the architecture of autonomous agents for the automatic treatment of handwritten Brazilian bank checks. The competence of these agents is implemented in two layers. The first corresponds to pattern recognition algorithms directly applied to image segments. The second one corresponds to reasoning mechanisms applied to the information from the first layer, either to validate or to interpret it. The interpretation process also involves information obtained from other agents. This information can present inconsistencies. This problem is treated properly and naturally through the concepts and operators of paraconsistent logic. This paper focuses on the second layer, on task distribution problems and on communication between agents. The first layer information was obtained through a simulated database.