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### Paraconsistent Reasoning via Quantified Boolean Formulas,I: Axiomatising Signed Systems [article]

Philippe Besnard, Stefan Woltran Institut für Informationssysteme, Technische Universität Wien)
2002 arXiv   pre-print
In this paper, we show how the family of corresponding paraconsistent consequence relations can be axiomatised by means of quantified Boolean formulas. This approach has several benefits.  ...  First, it furnishes an axiomatic specification of paraconsistent reasoning within the framework of signed systems.  ...  Discussion We have shown how paraconsistent inference problems within the framework of signed systems can be axiomatised by means of quantified Boolean formulas.  ...

### Paraconsistent Reasoning via Quantified Boolean Formulas, I: Axiomatising Signed Systems [chapter]

Philippe Besnard, Torsten Schaub, Hans Tompits, Stefan Woltran
2002 Lecture Notes in Computer Science
We alternatively provide a translation of these two paraconsistent logics into quantified Boolean formulas representing circumscription, the well-known system for logical minimization.  ...  Here, we address this and specifically provide a translation of two such paraconsistent logics into the language of quantified Boolean formulas (QBFs).  ...  Quantified Boolean formulas.  ...

### Representing Paraconsistent Reasoning via Quantified Propositional Logic [chapter]

Philippe Besnard, Torsten Schaub, Hans Tompits, Stefan Woltran
2005 Lecture Notes in Computer Science
To this end, we show how certain paraconsistent reasoning principles can be naturally formulated or reformulated by means of quantified Boolean formulas.  ...  As such, quantified propositional logic is a fragment of secondorder logic, and its sentences are usually referred to as quantified Boolean formulas (QBFs).  ...  The basic contribution of this chapter is to illustrate how paraconsistent reasoning principles can be naturally formulated or reformulated by means of quantified Boolean formulas.  ...

### Page 8151 of Mathematical Reviews Vol. , Issue 2004j [page]

2004 Mathematical Reviews
rea- soning via quantified Boolean formulas.  ...  Axiomatising signed systems (320-331); Sébastien Konieczny and Pierre Marquis, Three-valued logics for inconsistency handling (332-344); Joao Alcantara, Carlos Viegas Damasio and Luis Moniz Pereira, Para  ...

### Relevance Logic [chapter]

J. Michael Dunn, Greg Restall
2002 Handbook of Philosophical Logic
Meyer, and of course Alan Ross Anderson, to whose memory I dedicate this essay.  ...  ACKNOWLEDGEMENTS Dunn's acknowledgements from the first edition: I wish to express my thanks and deep indebtedness to a number of fellow toilers in the relevant vineyards, for information and discussion  ...  Brady [1991] constructs out of signed formulae T A and F A instead of formulae alone, and this is enough to include negation without spoiling the decidability property.  ...

### Denial and Disagreement

Julien Murzi, Massimiliano Carrara
2014 Topoi
Hence, it can't be expressed in the glut theorist's language, essentially for the same reasons why Boolean negation can't be expressed in such a language either.  ...  We represent them by means of signed formulae: þA for assertion and ÀA for denial, where þ and À are non-embeddable force signs (Rumfitt 2000) .  ...  They essentially comprise (i) what Rumfitt calls signed positive analogues of the standard rules for intuitionistic logic, i.e. standard rules such as _-I, written in a yes-or-no format (ii) rules for  ...

### Page 2356 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews
(English summary) 2004m:68219 Besnard, Philippe (with Schaub, Torsten; Tompits, Hans; Woltran, Stefan) Paraconsistent reasoning via quantified Boolean formulas. I. Axiomatising signed systems.  ...  (English summary) 2004c:68016 Tompits, Hans Expressing default abduction problems as quantified Boolean formulas.  ...

### An Old Discipline with a New Twist: The Course "Logic in Action"

Johan van Benthem
2017 IfColog journal of logics and their applications (FLAP)
Liau [9] introduced Boolean matrix operations for multiple agents' belief reasoning, revision, and fusion.  ...  Critical Thinking I'll start by discussing a course in critical thinking that I first taught in 2013. I do so for two reasons.  ...  The answer may seem obvious: surely we can just represent it using the simple atomic formula ate(john)? Well, no.  ...

### Algebraic logic and topoi; a philosophical holistic approach

Tarek Sayed Ahmed
2020 International Journal of Algebra
Rich theories occuring in Henkin's completeness proof eliminate existential quantifiers in existential formulas via individual constants more commonly referred to as witnesses.  ...  He proved that his system of geometry admits elimination of quantifiers, the theory is complete and decidable.  ...

### Relevant and substructural logics [chapter]

Greg Restall
2006 Handbook of the History of Logic
Brady's technique involved extending the Gentzen system with signed formulas, to give straightforward rules for negation without resorting to a multiple consequent calculus.  ...  ¡ £ ¡ £ § § ¡ ££ ¥ ¡ § ¡ £ ¥ ¡ £ § § will do instead of contraction in any of these axiomatisations. 25 Martin's proof proceeds via a result showing that the logic given by prefixing and suffixing (without  ...

### Some Concerns Regarding Ternary-relation Semantics and Truth-theoretic Semantics in General

2017 IfColog journal of logics and their applications (FLAP)
Finally, we also acknowledge the support by the Austrian Science Fund (FWF): project I 1923-N25 (New perspectives on residuated posets).  ...  My thanks go to Kata, for her kind invitation and to the participants of the workshop for their positive reception of the research work I presented.  ...  As part of this process, we use signed formulae T A and F A instead of a formula A, and structure them inductively as follows. (1) If S is a sign T or F , and A is a formula then SA is a structure. (2)  ...

### Page 2515 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews
(see 2004k:68003) 03B60 (03B45, 68T27) — (with Besnard, Philippe; Schaub, Torsten; Woltran, Stefan) Paraconsistent reasoning via quantified Boolean formulas. I. Axiomatising signed systems.  ...  (Mirostaw Truszczynski) 2004e:68012 68N17 (03B60) — Expressing default abduction problems as quantified Boolean formulas. (English summary) AI Commun. 16 (2003), no. 2, 89-105.  ...

### Paraconsistent Logics and Paraconsistency: Technical and Philosophical Developments *

Newton Da Costa, Décio Krause, Otávio Bueno
2004 unpublished
Béziau for sending us updated information on their works on paraconsistency.  ...  Boolean algebra.  ...  The structure of the paraconsistent Boolean algebra clearly is richer than the classical one.  ...

### Page 211 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews
(Summary) 2004f:74091 74S15 (65N38, 74G15) Besnard, Philippe (with Schaub, Torsten; Tompits, Hans; Woltran, Stefan) Paraconsistent reasoning via quantified Boolean formulas. I.  ...  Axiomatising signed systems. (English summary) Logics in artificial intelligence, 320-331, Lecture Notes in Comput. Sci., 2424, Springer, Berlin, 2002.  ...

### Sequent Calculi with Context Restrictions and Applications to Conditional Logic

Björn Lellmann, Marek Sergot, Dirk Pattison, Engineering And Physical Sciences Research Council
2014
We also explore the expressivity of such systems with the cut rule in terms of axioms in a Hilbert-style system by exhibiting a corresponding syntactically defined class of axioms along with automatic  ...  With certain limitations this allows the automatic construction of a cut free and tractable sequent system from a finite number of rules.  ...  , 150, 157, 167 rules for weak systems, 138 strong systems, 143 weak systems, 121, 124, 136 congruence, 27, 54, 69 congruence rule, 34 ConL(., ., .), 44 connective, 25 boolean, 25 modal  ...
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