
250A paraconsistent logic is a logic which allows nontrivial inconsistent theories. One of the oldest and best known approaches to the problem of designing useful paraconsistent logics is da Costa’s approach, which seeks to allow the use of classical logic whenever it is safe to do so, but behaves completely diﬀerently when contradictions are involved. da Costa’s approach has led to the family of Logics of Formal (In)consistency (LFIs). In this paper we provide nondeterministic semantics for a ve…Read more

119Ideal Paraconsistent LogicsStudia Logica 99 (13): 3160. 2011.We define in precise terms the basic properties that an ‘ideal propositional paraconsistent logic’ is expected to have, and investigate the relations between them. This leads to a precise characterization of ideal propositional paraconsistent logics. We show that every threevalued paraconsistent logic which is contained in classical logic, and has a proper implication connective, is ideal. Then we show that for every n > 2 there exists an extensive family of ideal n valued logics, each one of …Read more

100Cutfree ordinary sequent calculi for logics having generalized finitevalued semanticsLogica Universalis 1 (1): 4170. 2007.. The paper presents a method for transforming a given sound and complete nsequent proof system into an equivalent sound and complete system of ordinary sequents. The method is applicable to a large, central class of (generalized) finitevalued logics with the language satisfying a certain minimal expressiveness condition. The expressiveness condition decrees that the truthvalue of any formula φ must be identifiable by determining whether certain formulas uniformly constructed from φ have des…Read more

97What is relevance logic?Annals of Pure and Applied Logic 165 (1): 2648. 2014.We suggest two precise abstract definitions of the notion of ‘relevance logic’ which are both independent of any proof system or semantics. We show that according to the simpler one, R → source is the minimal relevance logic, but R itself is not. In contrast, R and many other logics are relevance logics according to the second definition, while all fragments of linear logic are not

87Natural 3valued logics—characterization and proof theoryJournal of Symbolic Logic 56 (1): 276294. 1991.

82Encoding modal logics in logical frameworksStudia Logica 60 (1): 161208. 1998.We present and discuss various formalizations of Modal Logics in Logical Frameworks based on Type Theories. We consider both Hilbert and Natural Deductionstyle proof systems for representing both truth (local) and validity (global) consequence relations for various Modal Logics. We introduce several techniques for encoding the structural peculiarities of necessitation rules, in the typed calculus metalanguage of the Logical Frameworks. These formalizations yield readily proofeditors for Moda…Read more

82The Semantics and Proof Theory of Linear LogicTheoretical Computer Science 57 (2): 161184. 1988.Linear logic is a new logic which was recently developed by Girard in order to provide a logical basis for the study of parallelism. It is described and investigated in Gi]. Girard's presentation of his logic is not so standard. In this paper we shall provide more standard proof systems and semantics. We shall also extend part of Girard's results by investigating the consequence relations associated with Linear Logic and by proving corresponding str ong completeness theorems. Finally, we shall i…Read more

68Relevant entailmentsemantics and formal systemsJournal of Symbolic Logic 49 (2): 334342. 1984.

62On modal systems having arithmetical interpretationsJournal of Symbolic Logic 49 (3): 935942. 1984.

60Reasoning with logical bilatticesJournal of Logic, Language and Information 5 (1): 2563. 1996.The notion of bilattice was introduced by Ginsberg, and further examined by Fitting, as a general framework for many applications. In the present paper we develop proof systems, which correspond to bilattices in an essential way. For this goal we introduce the notion of logical bilattices. We also show how they can be used for efficient inferences from possibly inconsistent data. For this we incorporate certain ideas of Kifer and Lozinskii, which happen to suit well the context of our work. The …Read more

59Implicational fstructures and implicational relevance logicsJournal of Symbolic Logic 65 (2): 788802. 2000.We describe a method for obtaining classical logic from intuitionistic logic which does not depend on any proof system, and show that by applying it to the most important implicational relevance logics we get relevance logics with nice semantical and prooftheoretical properties. Semantically all these logics are sound and strongly complete relative to classes of structures in which all elements except one are designated. Prooftheoretically they correspond to cutfree hypersequential Gentzenty…Read more

54A Nondeterministic View on Nonclassical NegationsStudia Logica 80 (23): 159194. 2005.We investigate two large families of logics, differing from each other by the treatment of negation. The logics in one of them are obtained from the positive fragment of classical logic (with or without a propositional constant ff for “the false”) by adding various standard Gentzentype rules for negation. The logics in the other family are similarly obtained from LJ+, the positive fragment of intuitionistic logic (again, with or without ff). For all the systems, we provide simple semantics whic…Read more

52Multiplicative conjunction and an algebraic meaning of contraction and weakeningJournal of Symbolic Logic 63 (3): 831859. 1998.We show that the elimination rule for the multiplicative (or intensional) conjunction $\wedge$ is admissible in many important multiplicative substructural logics. These include LL m (the multiplicative fragment of Linear Logic) and RMI m (the system obtained from LL m by adding the contraction axiom and its converse, the mingle axiom.) An exception is R m (the intensional fragment of the relevance logic R, which is LL m together with the contraction axiom). Let SLL m and SR m be, respectively, …Read more

51Rough Sets and 3Valued LogicsStudia Logica 90 (1): 6992. 2008.In the paper we explore the idea of describing Pawlak’s rough sets using threevalued logic, whereby the value t corresponds to the positive region of a set, the value f — to the negative region, and the undefined value u — to the border of the set. Due to the properties of the above regions in rough set theory, the semantics of the logic is described using a nondeterministic matrix (Nmatrix). With the strong semantics, where only the value t is treated as designated, the above logic is a “comm…Read more

46What is a logical system?In Dov M. Gabbay (ed.), What is a logical system?, Oxford University Press. 1994.

45General patterns for nonmonotonic reasoning: from basic entailments to plausible relationsLogic Journal of the IGPL 8 (2): 119148. 2000.This paper has two goals. First, we develop frameworks for logical systems which are able to reflect not only nonmonotonic patterns of reasoning, but also paraconsistent reasoning. Our second goal is to have a better understanding of the conditions that a useful relation for nonmonotonic reasoning should satisfy. For this we consider a sequence of generalizations of the pioneering works of Gabbay, Kraus, Lehmann, Magidor and Makinson. These generalizations allow the use of monotonic nonclassica…Read more

45Maximal and Premaximal Paraconsistency in the Framework of ThreeValued SemanticsStudia Logica 97 (1). 2011.Maximality is a desirable property of paraconsistent logics, motivated by the aspiration to tolerate inconsistencies, but at the same time retain from classical logic as much as possible. In this paper we introduce the strongest possible notion of maximal paraconsistency, and investigate it in the context of logics that are based on deterministic or nondeterministic threevalued matrices. We show that all reasonable paraconsistent logics based on threevalued deterministic matrices are maximal …Read more

44Gentzenizing SchroederHeister's natural extension of natural deductionNotre Dame Journal of Formal Logic 31 (1): 127135. 1989.

43Paraconsistency, paracompleteness, Gentzen systems, and trivalent semanticsJournal of Applied NonClassical Logics 24 (12): 1234. 2014.A quasicanonical Gentzentype system is a Gentzentype system in which each logical rule introduces either a formula of the form , or of the form , and all the active formulas of its premises belong to the set . In this paper we investigate quasicanonical systems in which exactly one of the two classical rules for negation is included, turning the induced logic into either a paraconsistent logic or a paracomplete logic, but not both. We provide a constructive coherence criterion for such syste…Read more

42Multivalued Semantics: Why and HowStudia Logica 92 (2): 163182. 2009.According to Suszko's Thesis,any multivalued semantics for a logical system can be replaced by an equivalent bivalent one. Moreover: bivalent semantics for families of logics can frequently be developed in a modular way. On the other hand bivalent semantics usually lacks the crucial property of analycity, a property which is guaranteed for the semantics of multivalued matrices. We show that one can get both modularity and analycity by using the semantic framework of multivalued nondeterminis…Read more

41Relevance and paraconsistencya new approach. II. The formal systemsNotre Dame Journal of Formal Logic 31 (2): 169202. 1990.

40The middle groundancestral logicSynthese 196 (7): 26712693. 2019.Many efforts have been made in recent years to construct formal systems for mechanizing general mathematical reasoning. Most of these systems are based on logics which are stronger than firstorder logic. However, there are good reasons to avoid using full secondorder logic for this task. In this work we investigate a logic which is intermediate between FOL and SOL, and seems to be a particularly attractive alternative to both: ancestral logic. This is the logic which is obtained from FOL by au…Read more

37FourValued Paradefinite LogicsStudia Logica 105 (6): 10871122. 2017.Paradefinite logics are logics that can be used for handling contradictory or partial information. As such, paradefinite logics should be both paraconsistent and paracomplete. In this paper we consider the simplest semantic framework for introducing paradefinite logics. It consists of the fourvalued matrices that expand the minimal matrix which is characteristic for first degree entailments: Dunn–Belnap matrix. We survey and study the expressive power and proof theory of the most important logi…Read more

34Decomposition proof systems for gödelDummett logicsStudia Logica 69 (2): 197219. 2001.The main goal of the paper is to suggest some analytic proof systems for LC and its finitevalued counterparts which are suitable for proofsearch. This goal is achieved through following the general RasiowaSikorski methodology for constructing analytic proof systems for semanticallydefined logics. All the systems presented here are terminating, contractionfree, and based on invertible rules, which have a local character and at most two premises

33Two types of multipleconclusion systemsLogic Journal of the IGPL 6 (5): 695718. 1998.Hypersequents are finite sets of ordinary sequents. We show that multipleconclusion sequents and singleconclusion hypersequents represent two different natural methods of switching from a singleconclusion calculus to a multipleconclusion one. The use of multipleconclusion sequents corresponds to using a multiplicative disjunction, while the use of singleconclusion hypersequents corresponds to using an additive one. Moreover: each of the two methods is usually based on a different natural s…Read more

Tel Aviv UniversityResearcher

Tel Aviv UniversityRegular Faculty
Tel Aviv, Israel
Areas of Interest
Logic and Philosophy of Logic 
Philosophy of Mathematics 