Paraconsistent logic

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

R-Mingle is Nice, and so is Arnon Avron

Abstract: Arnon Avron has written: “Dunn-McCall logic RM is by far the best understood and the most well-behaved in the family of logics developed by the school of Anderson and Belnap.” I agree. There is the famous saying: “Do not let the perfect become the enemy of the good.” I might say: “good enough.” In this spirit, I will examine the logic R-Mingle, exploring how (in the terminology of Avron) it is only a “semi-relevant logic” but still a paraconsistent logic. I shall discuss the history of RM, and compare RM to Anderson and Belnap’s system R of relevant implication and to classical two-valued logic. There is a “consumer’s guide,” evaluating these logics as “tools,” in the light of my recent work on “Humans as Rational Toolmaking Animals.”

The Paraconsistent Annotated Logic with annotation of two values (PAL2v) in the context of the Industry 4.0 - An Approach for the Cyber-Physical Systems (CPS)

Abstract: Regarding the global productive systems such as manufacturing industry (automotive, electronics, etc), they always have problems of contradictory ∕ inconsistent data information on their control systems. Even in service sector such as health care (eg. devices for health control), always there exist contradictory ∕ inconsistent data information to be considered for decision making. Therefore, in the context of the Industry 4.0, the contradictory ∕ inconsistent data information problem, certainly, happen into the Cyber-Physical Systems (CPSs). Inserted into the group of Non-Classical Logics, the Paraconsistent Annotated Logic with annotation of two values (PAL2v) presents conditions to compute contradictory signals without the conflict of information that invalidates the conclusions. Thus, this paper proposes a PAL2v to solve the contradictory ∕ inconsistent data information problem in the context of the Industry 4.0 as a decision learning approach for the CPSs. The findings of the two examples demonstrated that the experiments are really promising and the developed control systems based on PAL2v are suitable for the Industry 4.0 environment. Key words: Paraconsistent Logic Controller, Paraconsistent Logic with annotation of two values (PAL2v), Industry 4.0, Cyber-Physical Systems (CPS).

Paraconsistent Logic: The View from the Right

Abstract: "The best known approaches to "reasoning with inconsistent data" require a logical framework which is decidedly non-classical. An alternative is presented here, beginning with some motivation which has been surprised in the work of C.I. Lewis, which does not require ripping great swatches from the fabric of classical logic. In effect, the position taken in this essay is representative of an approach in which one assumes the correctness of classical methods excepting only the cases in which the premise set is (classically) inconsistent.

Goal-Directed Proof Search in Multiple-Conclusions Intuitionistic Logic

Abstract: A key property in the definition of logic programming languages is the completeness of goal-directed proofs. This concept originated in the study of logic programming languages for intuitionistic logic in the (single-conclusioned) sequent calculus LJ, but has subsequently been adapted to multiple-conclusioned systems such as those for linear logic. Given these developments, it seems interesting to investigate the notion of goal-directed proofs for a multiple-conclusioned sequent calculus for intuitionistic logic, in that this is a logic for which there are both single-conclusioned and multiple-conclusioned systems (although the latter are less well known). In this paper we show that the language obtained for the multiple-conclusioned system differs from that for the single-conclusioned case, show how hereditary Harrop formulae can be recovered, and investigate contraction-free fragments of the logic.