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35
A Survey of Abstract Algebraic Logic
 TO APPEAR IN STUDIA LOGICA; (SPECIAL ISSUE ON ABSTRACT ALGEBRAIC LOGIC, PART II)
, 2003
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On negation: Pure local rules
, 2003
"... This is an initial systematic study of the properties of negation from the point of view of abstract deductive systems. A unifying framework of multipleconclusion consequence relations is adopted so as to allow us to explore symmetry in exposing and matching a great number of positive contextua ..."
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This is an initial systematic study of the properties of negation from the point of view of abstract deductive systems. A unifying framework of multipleconclusion consequence relations is adopted so as to allow us to explore symmetry in exposing and matching a great number of positive contextual subclassical rules involving this logical constant among others, wellknown forms of proof by cases, consequentia mirabilis and reductio ad absurdum. Finer definitions of paraconsistency and the dual paracompleteness can thus be formulated, allowing for pseudoscotus and ex contradictione to be di#erentiated and for a comprehensive version of the Principle of NonTriviality to be presented. A final proposal is made to the e#ect that pure positive rules involving negation being often fallible a characterization of what most negations in the literature have in common should rather involve, in fact, a reduced set of negative rules.
A classical linear lambdacalculus
, 1996
"... This paper proposes and studies a typed calculus for classical linear logic. I shall give an explanation of a multipleconclusion formulation for classical logic due to Parigot and compare it to more traditional treatments by Prawitz and others. I shall use Parigot's method to devise a natural ..."
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This paper proposes and studies a typed calculus for classical linear logic. I shall give an explanation of a multipleconclusion formulation for classical logic due to Parigot and compare it to more traditional treatments by Prawitz and others. I shall use Parigot's method to devise a natural deduction formulation of classical linear logic. This formulation is compared in detail to the sequent calculus formulation. In an appendix I shall also demonstrate a somewhat hidden connexion with the paradigm of control operators for functional languages which gives a new computational interpretation of Parigot's techniques.
Suszko's Thesis and dyadic semantics
 Department of Mathematics, Instituto Superior Técnico
"... A wellknown result by W\'ojcickiLindenbaum shows that any tarskian logic is manyvalued, and another result by Suszko shows how to provide 2valued semantics to these very same logics. This paper investigates the question of obtaining 2valued semantics for manyvalued logics, including parac ..."
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Cited by 8 (6 self)
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A wellknown result by W\'ojcickiLindenbaum shows that any tarskian logic is manyvalued, and another result by Suszko shows how to provide 2valued semantics to these very same logics. This paper investigates the question of obtaining 2valued semantics for manyvalued logics, including paraconsistent logics, in the lines of the socalled ``Suszko's Thesis". We set up the bases for developing a general algorithmic method to transform any truthfunctional finitevalued semantics satisfying reasonable conditions into a computable quasi tabular 2valued semantics, that we call dyadic. We also discuss how ``Suszko's Thesis" relates to such a method, in the light of truthfunctionality, while at the same time we reject an endorsement of Suszko's philosophical views about the misconception of manyvalued logics.
Conservatively extending classical logic with transparent truth
 Review of Symbolic Logic
, 2012
"... Abstract. This paper shows how to conservatively extend a classical logic with a transparent truth predicate, in the face of the paradoxes that arise as a consequence. All classical inferences are preserved, and indeed extended to the full (truthinvolving) vocabulary. However, not all classical met ..."
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Abstract. This paper shows how to conservatively extend a classical logic with a transparent truth predicate, in the face of the paradoxes that arise as a consequence. All classical inferences are preserved, and indeed extended to the full (truthinvolving) vocabulary. However, not all classical metainferences are preserved; in particular, the resulting logical system is nontransitive. Some limits on this nontransitivity are adumbrated, and two proof systems are presented and shown to be sound and complete. (One proof system features admissible Cut, but the other does not.) §1. Introduction. Adding a truth predicate to a language governed by classical logic is not easy. It is particularly tricky when the truth predicate is intended to be transparent— such that T 〈A 〉 and A are everywhere intersubstitutable. The trouble, as is wellknown, comes from such paradoxes as the liar; because of them, theories of truth typically either use a nontransparent truth predicate (Halbach, 2011; Maudlin, 2004) or a logic weaker than
Ineffable Inconsistencies
 Paraconsistency with no Frontiers
"... For any given consistent tarskian logic it is possible to find another nontrivial logic that allows for an inconsistent model yet completely coincides with the initial given logic from the point of view of their associated singleconclusion consequence relations. A paradox? This short note... ..."
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For any given consistent tarskian logic it is possible to find another nontrivial logic that allows for an inconsistent model yet completely coincides with the initial given logic from the point of view of their associated singleconclusion consequence relations. A paradox? This short note...
On Theorems Equivalent with Kotzig's Result on Graphs with Unique 1Factors
, 2001
"... We show that several known theorems on graphs and digraphs are equivalent. The list of equivalent theorems include Kotzig's result on graphs with unique 1factors, a lemma by Seymour and Giles, theorems on alternating cycles in edgecolored graphs, and a theorem on semicycles in digraphs. ..."
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We show that several known theorems on graphs and digraphs are equivalent. The list of equivalent theorems include Kotzig's result on graphs with unique 1factors, a lemma by Seymour and Giles, theorems on alternating cycles in edgecolored graphs, and a theorem on semicycles in digraphs. We consider computational problems related to the quoted results; all these problems ask whether a given (di)graph contains a cycle satisfying certain properties which runs through p prescribed vertices. We show that all considered problems can be solved in polynomial time for p < 2 but are NPcomplete for p # 2. 1
Reasoned Use of Expertise in Argumentation
"... ABSTRACT: This article evaluates the strengths and weaknesses of arguments based on appeals to expertise. The intersection of two areas is explored: (i) the traditional argumentum ad verecundiam (literally, "appeal to modesty; " but characteristically the appeal to the authority of expert ..."
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ABSTRACT: This article evaluates the strengths and weaknesses of arguments based on appeals to expertise. The intersection of two areas is explored: (i) the traditional argumentum ad verecundiam (literally, "appeal to modesty; " but characteristically the appeal to the authority of expert judgment) in informal logic, and (ii) the uses of expert systems in artificial intelligence. The article identifies a model of practical reasoning that underlies the logic of expert systems and the model of argument appropriate for the informal logic of the argumentum ad verecundiam.
Possibletranslations semantics (Extended Abstract)
 COMBLOG’04 — PROCEEDINGS OF THE WORKSHOP ON COMBINATION OF LOGICS: THEORY AND APPLICATIONS, HELD IN LISBON, PT
, 2004
"... This text aims at providing a bird’s eye view of possibletranslations semantics ([10, 24]), defined, developed and illustrated as a very comprehensive formalism for obtaining or for representing semantics for all sorts of logics. With that tool, a wide class of complex logics will very naturally tu ..."
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This text aims at providing a bird’s eye view of possibletranslations semantics ([10, 24]), defined, developed and illustrated as a very comprehensive formalism for obtaining or for representing semantics for all sorts of logics. With that tool, a wide class of complex logics will very naturally turn out to be (de)composable by way of some suitable combination of simpler logics. Several examples will be mentioned, and some related special cases of possibletranslations semantics, among which are society semantics and nondeterministic semantics, will also be surveyed.
Bases of admissible rules of Łukasiewicz logic
, 2009
"... We construct explicit bases of singleconclusion and multipleconclusion admissible rules of propositional Łukasiewicz logic, and we prove that every formula has an admissibly saturated approximation. We also show that Łukasiewicz logic has no finite basis of admissible rules. ..."
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We construct explicit bases of singleconclusion and multipleconclusion admissible rules of propositional Łukasiewicz logic, and we prove that every formula has an admissibly saturated approximation. We also show that Łukasiewicz logic has no finite basis of admissible rules.