PARACONSISTENT CIRCUMSCRIPTION: PRELIMINARY REPORT

1996 ◽  
Vol 10 (06) ◽  
pp. 679-686 ◽  
Author(s):  
ZUOQUAN LIN
Keyword(s):  
Classical Logic ◽  
Preliminary Report ◽  
Paraconsistent Logic ◽  
Nonmonotonic Logic ◽  
Logic Of Paradox

In this paper we describe the paraconsistent circumscription by the application of predicate circumscription in a paraconsistent logic, the logic of paradox LP. In addition to circumscribing the predicates, we also circumscribe the inconsistency. The paraconsistent circumscription can be well characterized by the minimal semantics which is both nonmonotonic and paraconsistent. It brings us advantages in two respects: nonmonotonic logic would be nontrivial while there was a contradiction, and paraconsistent logic would be equivalent to classical logic while there was no effect of a contradiction.

Subprevarieties versus extensions. Application to the logic of paradox

2000 ◽  
Vol 65 (2) ◽  
pp. 756-766 ◽  
Author(s):  
Alexej P. Pynko
Keyword(s):  
General Result ◽  
Classical Logic ◽  
Modus Ponens ◽  
Galois Connection ◽  
Normal Extension ◽  
Material Implication ◽  
Element Chain ◽  
Class Of Matrices ◽  
The One ◽  
Logic Of Paradox

AbstractIn the present paper we prove that the poset of all extensions of the logic defined by a class of matrices whose sets of distinguished values are equationally definable by their algebra reducts is the retract, under a Galois connection, of the poset of all subprevarieties of the prevariety generated by the class of the algebra reducts of the matrices involved. We apply this general result to the problem of finding and studying all extensions of the logic of paradox (viz., the implication-free fragment of any non-classical normal extension of the relevance-mingle logic). In order to solve this problem, we first study the structure of prevarieties of Kleene lattices. Then, we show that the poset of extensions of the logic of paradox forms a four-element chain, all the extensions being finitely many-valued and finitely-axiomatizable logics. There are just two proper consistent extensions of the logic of paradox. The first is the classical logic that is relatively axiomatized by the Modus ponens rule for the material implication. The second extension, being intermediate between the logic of paradox and the classical logic, is the one relatively axiomatized by the Ex Contradictione Quodlibet rule.

Extensions of paraconsistent weak Kleene logic

2020 ◽  
Author(s):  
Francesco Paoli ◽  
Michele Pra Baldi
Keyword(s):  
General Result ◽  
Classical Logic ◽  
Order Ideal ◽  
Consequence Relation ◽  
Reduced Models ◽  
Logic Of Paradox

Abstract Paraconsistent weak Kleene ($\textrm{PWK}$) logic is the $3$-valued logic based on the weak Kleene matrices and with two designated values. In this paper, we investigate the poset of prevarieties of generalized involutive bisemilattices, focussing in particular on the order ideal generated by Α$\textrm{lg} (\textrm{PWK})$. Applying to this poset a general result by Alexej Pynko, we prove that, exactly like Priest’s logic of paradox, $\textrm{PWK}$ has only one proper nontrivial extension apart from classical logic: $\textrm{PWK}_{\textrm{E}}\textrm{,}$ PWK logic plus explosion. This $6$-valued logic, unlike $\textrm{PWK} $, fails to be paraconsistent. We describe its consequence relation via a variable inclusion criterion and identify its Suszko-reduced models.

scholarly journals Paraconsistent Annotated Logic Algorithms Applied in Management and Control of Communication Network Routes

Sensors ◽  
2021 ◽  
Vol 21 (12) ◽  
pp. 4219
Author(s):  
João Inácio Da Silva Filho ◽  
Jair Minoro Abe ◽  
Alessandro de Lima Marreiro ◽  
Angel Antonio Gonzalez Martinez ◽  
Cláudio Rodrigo Torres ◽  
...  
Keyword(s):  
Communication Network ◽  
Communication Networks ◽  
Classical Logic ◽  
Paraconsistent Logic ◽  
Logic Gates ◽  
Main Property ◽  
Computational Method ◽  
Stream Control ◽  
Routing Management ◽  
And Control

This paper presents a computational method based on non-classical logic dedicated to routing management and information stream control in communication networks. Paraconsistent logic (PL) was used to create an algorithmic structure whose main property is to accept contradiction. Moreover, a computational structure, the denominated paraconsistent data analyzer (PDAPAL2v), was constructed to perform routing management in communication networks. Direct comparisons of PDAPAL2v with a classical logic system that simulates routing conditions were made in the laboratory. In the conventional system, the paraconsistent algorithms were considered as binary logic gates, and in the tests, the same adjustment limits of PDAPAL2v were applied. Using a database with controlled insertion of noise, we obtained an efficacy of 97% in the detection of deteriorated packets with PDAPAL2v and 72% with the conventional simulation system. Functional tests were carried out, showing that PDAPAL2v is able to assess the conditions and degradation of links and perform the analysis and correlation of various inputs and variables, even if the signals have contradictory values. From practical tests in the laboratory, the proposed method represents a new way of managing and controlling communication network routes with good performance.

FACING INCONSISTENCY: THEORIES AND OUR RELATIONS TO THEM

Episteme ◽  
2013 ◽  
Vol 10 (4) ◽  
pp. 351-367 ◽  
Author(s):  
Michaelis Michael
Keyword(s):  
Classical Logic ◽  
Paraconsistent Logic ◽  
Indispensability Argument ◽  
Mathematical Objects ◽  
The Face ◽  
Inconsistent Objects ◽  
Inconsistent Theories

AbstractClassical logic is explosive in the face of contradiction, yet we find ourselves using inconsistent theories. Mark Colyvan, one of the prominent advocates of the indispensability argument for realism about mathematical objects, suggests that such use can be garnered to develop an argument for commitment to inconsistent objects and, because of that, a paraconsistent underlying logic. I argue to the contrary that it is open to a classical logician to make distinctions, also needed by the paraconsistent logician, which allow a more nuanced ranking of theories in which inconsistent theories can have different degrees of usefulness and productivity. Facing inconsistency does not force us to adopt an underlying paraconsistent logic. Moreover we will see that the argument to best explanation deployed by Colyvan in this context is unsuccessful. I suggest that Quinean approach which Colyvan champions will not lead to the revolutionary doctrines Colyvan endorses.

scholarly journals Rewriting the History of Connexive Logic

2022 ◽  
Author(s):  
Wolfgang Lenzen
Keyword(s):  
Twentieth Century ◽  
Classical Logic ◽  
Paraconsistent Logic ◽  
Historical Analysis ◽  
Relevance Logic ◽  
Overwhelming Majority ◽  
Lewis Carroll ◽  
Self Consistent ◽  
History Of ◽  
Connexive Logic

AbstractThe “official” history of connexive logic was written in 2012 by Storrs McCall who argued that connexive logic was founded by ancient logicians like Aristotle, Chrysippus, and Boethius; that it was further developed by medieval logicians like Abelard, Kilwardby, and Paul of Venice; and that it was rediscovered in the 19th and twentieth century by Lewis Carroll, Hugh MacColl, Frank P. Ramsey, and Everett J. Nelson. From 1960 onwards, connexive logic was finally transformed into non-classical calculi which partly concur with systems of relevance logic and paraconsistent logic. In this paper it will be argued that McCall’s historical analysis is fundamentally mistaken since it doesn’t take into account two versions of connexivism. While “humble” connexivism maintains that connexive properties (like the condition that no proposition implies its own negation) only apply to “normal” (e.g., self-consistent) antecedents, “hardcore” connexivism insists that they also hold for “abnormal” propositions. It is shown that the overwhelming majority of the forerunners of connexive logic were only “humble” connexivists. Their ideas concerning (“humbly”) connexive implication don’t give rise, however, to anything like a non-classical logic.

scholarly journals The “Ontological Difference” Again. A Dialetheic Perspective on Heidegger’s Mainstay

2018 ◽  
Vol 1 (1) ◽  
pp. 143-154
Author(s):  
Francesco Gandellini
Keyword(s):  
Crucial Role ◽  
Paraconsistent Logic ◽  
Main Argument ◽  
Ontological Difference ◽  
The Third ◽  
Classical Notion ◽  
Late Works ◽  
Logic Of Paradox ◽  
Previous Paragraph

Abstract This paper intends to offer a new assessment of the “Ontological Difference” (OD), one of Martin Heidegger’s mainstays, in the light of the metaphysical view called “dialetheism”. In the first paragraph I briefly summarize the main argument of Heidegger’s contradiction of Being, where OD is present as a premise. In the second paragraph I introduce dialetheism, indicate two kinds of dialetheic solutions to the paradox and explain why they face comeback troubles from OD. The third paragraph is devoted to a review of Heidegger’s uses of OD and underlines the crucial role of negation in it. In the fourth paragraph I investigate the philosopher’s account of negation and show similarities with the account provided by the paraconsistent logic called “Logic of Paradox”. The fifth paragraph puts forward two possible readings of OD, the first based on the classical notion of negation and the second on the notion of negation pointed out in the previous paragraph. The second reading is proved suitable for dialetheists and in accordance with the exegesis of some textual passages from Heidegger’s late works.

scholarly journals What If? The Exploration of an Idea

2017 ◽  
Vol 14 (1) ◽  
Author(s):  
Graham Priest
Keyword(s):  
Paraconsistent Logic ◽  
The Other ◽  
Semantic Paradoxes ◽  
Crucial Question ◽  
The Third ◽  
Present Essay ◽  
Set Up ◽  
Logic Of Paradox

A crucial question here is what, exactly, the conditional in the naive truth/set comprehension principles is. In 'Logic of Paradox', I outlined two options. One is to take it to be the material conditional of the extensional paraconsistent logic LP. Call this "Strategy 1". LP is a relatively weak logic, however. In particular, the material conditional does not detach. The other strategy is to take it to be some detachable conditional. Call this "Strategy 2". The aim of the present essay is to investigate Stragey 1. It is not to advocate it. The work is simply an extended exploration of the strategy, its strengths, its weaknesses, and the various dierent ways in which it may be implemented. In the first part of the paper I will set up the appropriate background details. In the second, I will look at the strategy as it applies to the semantic paradoxes. In the third I will look at how it applies to the set-theoretic paradoxes.

MULTIPLE-CONCLUSION LP AND DEFAULT CLASSICALITY

2011 ◽  
Vol 4 (2) ◽  
pp. 326-336 ◽  
Author(s):  
JC BEALL
Keyword(s):  
Paraconsistent Logic ◽  
Nonmonotonic Logic ◽  
Paraconsistent Logics ◽  
Alternative Approach

Philosophical applications of familiar paracomplete and paraconsistent logics often rely on an idea of ‘default classicality’. With respect to the paraconsistent logic LP (the dual of Strong Kleene or K3), such ‘default classicality’ is standardly cashed out via an LP-based nonmonotonic logic due to Priest (1991, 2006a). In this paper, I offer an alternative approach via a monotonic multiple-conclusion version of LP.

Sign in / Sign up

Export Citation Format

Share Document