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Weak consistency and strong paraconsistency

Gemma Robles
2009 tripleC: Communication, Capitalism & Critique  
In a standard sense, consistency and paraconsistency are understood as, respectively, the absence of any contradiction and as the absence of the ECQ ("E contradictione quodlibet") rule that allows us to  ...  The aim of this paper is to explain the concepts of weak consistency alternative to the standard one, the concepts of paraconsistency related to them and the concept of strong paraconsistency, all of which  ...  Standard concepts of consistency and paraconsistency Consistency is generally defined as the absence of any contradiction, that is, the conjunction of an affirmation and its negation.  ... 
doi:10.31269/vol7iss2pp185-193 fatcat:gs3i477wnfg4lhdxwrgcs4vcga

Weak consistency and strong paraconsistency

Gemma Robles
2009 tripleC: Communication, Capitalism & Critique  
In a standard sense, consistency and paraconsistency are understood as, respectively, the absence of any contradiction and as the absence of the ECQ ("E contradictione quodlibet") rule that allows us to  ...  The aim of this paper is to explain the concepts of weak consistency alternative to the standard one, the concepts of paraconsistency related to them and the concept of strong paraconsistency, all of which  ...  Standard concepts of consistency and paraconsistency Consistency is generally defined as the absence of any contradiction, that is, the conjunction of an affirmation and its negation.  ... 
doi:10.31269/triplec.v7i2.99 fatcat:6a4rl4wrt5fi3ijtywsrptpefq

Logics of Formal Inconsistency [chapter]

Walter Carnielli, Marcelo E. Coniglio, João Marcos
2007 Handbook of Philosophical Logic  
Acknowledgements 74 Acknowledgements The first author acknowledges support by CNPq, Brazil, and by a senior scientist research grant from the Center for Logic and Computation (CLC), IST, Portugal.  ...  The third author was supported by the Fundação para a Ciência e  ...  [Mendelson, 1997] ), any logic having (Ax1) and (Ax2) as axioms, and modus ponens (MP) as the only inference rule has a deductive implication. 6 In any logic endowed with a deductive implication, the  ... 
doi:10.1007/978-1-4020-6324-4_1 fatcat:5pzf3pzqqbcrlhb34y6vh2oxzi

An epistemic approach to paraconsistency: a logic of evidence and truth

Walter Carnielli, Abilio Rodrigues
2017 Synthese  
The paper defines a paraconsistent and paracomplete natural deduction system, called the  ...  The purpose of this paper is to present a paraconsistent formal system and a corresponding intended interpretation according to which true contradictions are not tolerated.  ...  A proof of this follows. Let A be any theorem. Since A A ∨ ¬A, if for any A and B, A ∨ ¬A B ∨ ¬B, by transitivity it follows that A B ∨ ¬B. As A is a theorem, we conclude B ∨ ¬B.  ... 
doi:10.1007/s11229-017-1621-7 fatcat:5cmsnk2jt5fb3picce7bfav75y

A Taxonomy of C-systems [article]

W.A. Carnielli RUG, Belgium)
2001 arXiv   pre-print
Relations between logical principles are formally studied, a novel notion of consistency is introduced, the logics of formal inconsistency, and the subclasses of C-systems and dC-systems are defined and  ...  A thorough investigation of the foundations of paraconsistent logics.  ...  The connectives '' and '' have a good behavior inside of Ci, and we show that any formula having them as the main operator is consistently provable, and that consistency propagates through negation (and  ... 
arXiv:math/0108036v1 fatcat:7rrurvfsszgjvk5hs7auoz4xwq

Anti-intuitionism and paraconsistency

Andreas B.M. Brunner, Walter A. Carnielli
2005 Journal of Applied Logic  
Fundamental properties of our method are investigated, and we also discuss some questions on the duality between the intuitionistic and the paraconsistent paradigms, including the problem of self-duality  ...  Comparing these anti-intuitionistic logics with well-known paraconsistent calculi, we prove that they do not coincide with any of these.  ...  We also extend our thanks to two anonymous referees who will recognize the effects of their criticisms, suggestions and objections in the above pages.  ... 
doi:10.1016/j.jal.2004.07.016 fatcat:rcpmpiwsknhq5co466i26a7wua

The Basic Constructive Logic for Negation-Consistency

Gemma Robles
2007 Journal of Logic, Language and Information  
In this paper, consistency is understood in the standard way, i.e. as the absence of a contradiction.  ...  The basic constructive logic B Kc4 , which is adequate to this sense of consistency in the ternary relational semantics without a set of designated points, is defined.  ...  Acknowledgements Work supported by the research project HUM2005-05707 of the Spanish Ministry of Education and Science.  ... 
doi:10.1007/s10849-007-9056-z fatcat:odflpxj7ybfcnj6hyff2jpmdum

Dialetheism, Game Theoretic Semantics, and Paraconsistent Team Semantics [article]

Pietro Galliani
2014 arXiv   pre-print
Furthermore, we prove that a Paraconsistent Non-dependence Logic formula is consistent if and only if it is equivalent to some First Order Logic sentence; and we show that, on the other hand, all Paraconsistent  ...  We introduce a variant of Dependence Logic in which truth is defined not in terms of existence of winning strategies for the Proponent (Eloise) in a semantic game, but in terms of lack of winning strategies  ...  Paraconsistent Team Semantics) to any formula of Paraconsistent Dependence Logic (and, in particular, to any first order formula), since it is not upwards closed in the sense of Theorem 3.5.  ... 
arXiv:1206.6573v2 fatcat:umpnxey6s5a6ngkaeeiafzlmem

TOWARDS A PHILOSOPHICAL UNDERSTANDING OF THE LOGICS OF FORMAL INCONSISTENCY

WALTER CARNIELLI, ABÍLIO RODRIGUES
2015 Manuscrito  
of consistency within the object language in such a way that consistency may be logically independent of non-contradiction.  ...  In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion  ...  ACKNOWLEDGEMENTS The first author acknowledges the support of FAPESP (São Paulo Research Council) and CNPq, Brazil (The National Council for Scientific and Technological Development).  ... 
doi:10.1590/0100-6045.2015.v38n2.wcear fatcat:wkmbxomjavcefpi5j2pl44g3wu

The Prospects of a Paraconsistent Response to Vagueness [chapter]

Dominic Hyde
2010 Cuts and Clouds  
The view then is that SpV is superior to any paraconsistent theory both at the level of semantics and logic.  ...  Some have thought so but the majority view has been that a paracomplete response 1 -roughly, a truth-value gap response -is as radical a departure from classical semantics as is necessary (and, of course  ...  Keefe is ambivalent on the matter, suspecting they may amount to one and the same thing and viewing any resulting incoherence on what she sees as possible conflict arising from the absence of a clear-cut  ... 
doi:10.1093/acprof:oso/9780199570386.003.0023 fatcat:4waevyclyjaarlvt6arnjsjeva

Extensions of the basic constructive logic for weak consistency BKc1 defined with a falsity constant

Gemma Robles
2008 Logic and Logical Philosophy  
The logic B Kc1 is the basic constructive logic for weak consistency (i.e., absence of the negation of a theorem) in the ternary relational semantics without a set of designated points.  ...  the constructive negation of B Kc1 and the (constructive) contraposition axioms.  ...  Notes Work supported by the research projects HUM2005-05707 and HUM2005-03848/ FISIO and by Juan de la Cierva Program, financed by the Spanish Ministry of Education and Science.  ... 
doi:10.12775/llp.2007.010 fatcat:ickwwdw4zvh5fm5m4egz6f7eoa

Devising the set of abnormalities for a given defeasible rule

Diderik Batens
2020 Logical Investigations  
Where the adaptive logic is corrective, the deductive logic is the upper limit logic, the rules of which are valid in case the premises do not require any abnormalities to be true.  ...  In some cases, the idea for devising an adaptive logic does not relate to a set of abnormalities, but to one or more defeasible rules, and perhaps also to one of the deductive logics.  ...  I want to thank the referee and the editor for their careful work.  ... 
doi:10.21146/2074-1472-2020-26-1-9-35 fatcat:v4lbeoo4qfc3piktge3iovhpsm

Tolerating Inconsistencies: A Study of Logic of Moral Conflicts

Meha Mishra, A.V. Ravishankar Sarma
2022 Bulletin of the Section of Logic  
In this paper, we analyze Graham Priest's paraconsistent logic LP, and extending our examination to the deontic extension of LP known as DLP.  ...  Our analysis is expected to provide novel tools towards the logical representation of moral conflicts and to shed some light on the relationship between the actual world and the context-sensitive ideal  ...  Axiom Schemas: A1 O(A → B) → (OA → OB) A2 OF → F Rule of Inference: RL1 A is theorem ⇒ OA is a theorem The standard deduction theorem holds in DLP →,F as in LP → .  ... 
doi:10.18778/0138-0680.2022.06 fatcat:ioy6wakmn5cpdcv73dtxxy42py

Analytic Continuation of ζ(s) Violates the Law of Non-Contradiction (LNC) [article]

Ayal Sharon
2019 arXiv   pre-print
This result violates all three of Aristotle's "Laws of Thought": the Law of Identity (LOI), the Law of the Excluded Middle (LEM), and the Law of Non-Contradition (LNC).  ...  Riemann's ζ(s) is one of the L-functions, which are all invalid due to analytic continuation. This result renders unsound all theorems (e.g. Modularity, Fermat's last) and conjectures (e.g.  ...  Acknowledgments The author thanks the reviewer(s) and the editorial staff.  ... 
arXiv:1802.08062v7 fatcat:vavvaszmi5atfkjcfpr6dxxarm

Structuring Co-constructive Logic for Proofs and Refutations

James Trafford
2016 Logica Universalis  
This paper considers a topos-theoretic structure for the interpretation of co-constructive logic for proofs and refutations following [49] .  ...  By developing abstractions of elementary topoi, we consider an elementary topos as structure for proofs, and complement topos as structure for refutation.  ...  Acknowledgment This work has greatly benefited from conversations with Fabien Schang and Dave Ripley, comments from two anonymous reviewers, and the audience at Unilog 2015 in Istanbul.  ... 
doi:10.1007/s11787-016-0138-z fatcat:jsdroby2r5hrhiypycshuxnoja
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