69 found
Order:
See also:
Profile: Arnon Avron (Tel Aviv University)
Profile: Arnon Avron (Tel Aviv University)
  1. Arnon Avron, Simple Consequence Relations.
    We provide a general investigation of Logic in which the notion of a simple consequence relation is taken to be fundamental. Our notion is more general than the usual one since we give up monotonicity and use multisets rather than sets. We use our notion for characterizing several known logics (including Linear Logic and non-monotonic logics) and for a general, semantics-independent classi cation of standard connectives via equations on consequence relations (these include Girard's \multiplicatives" and \additives"). We next investigate the (...)
     
    Export citation  
     
    My bibliography   12 citations  
  2.  18
    Ofer Arieli & Arnon Avron (1996). Reasoning with Logical Bilattices. Journal of Logic, Language and Information 5 (1):25--63.
    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. (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   29 citations  
  3. Anna Zamansky & Arnon Avron (2006). Cut-Elimination and Quantification in Canonical Systems. Studia Logica 82 (1):157 - 176.
    Canonical Propositional Gentzen-type systems are systems which in addition to the standard axioms and structural rules have only pure logical rules with the sub-formula property, in which exactly one occurrence of a connective is introduced in the conclusion, and no other occurrence of any connective is mentioned anywhere else. In this paper we considerably generalize the notion of a “canonical system” to first-order languages and beyond. We extend the Propositional coherence criterion for the non-triviality of such systems to rules with (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  4.  24
    Arnon Avron (1991). Natural 3-Valued Logics--Characterization and Proof Theory. Journal of Symbolic Logic 56 (1):276-294.
  5.  39
    Arnon Avron (1988). The Semantics and Proof Theory of Linear Logic. Theoretical Computer Science 57:161-184.
    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 investigate (...)
    Direct download  
     
    Export citation  
     
    My bibliography   23 citations  
  6. Arnon Avron, Non-Deterministic Matrices and Modular Semantics of Rules.
    We show by way of example how one can provide in a lot of cases simple modular semantics for rules of inference, so that the semantics of a system is obtained by joining the semantics of its rules in the most straightforward way. Our main tool for this task is the use of finite Nmatrices, which are multi-valued structures in which the value assigned by a valuation to a complex formula can be chosen non-deterministically out of a certain nonempty set (...)
     
    Export citation  
     
    My bibliography   6 citations  
  7.  3
    Arnon Avron & Beata Konikowska (2005). Multi-Valued Calculi for Logics Based on Non-Determinism. Logic Journal of the Igpl 13 (4):365-387.
    Non-deterministic matrices are multiple-valued structures in which the value assigned by a valuation to a complex formula can be chosen non-deterministically out of a certain nonempty set of options. We consider two different types of semantics which are based on Nmatrices: the dynamic one and the static one . We use the Rasiowa-Sikorski decomposition methodology to get sound and complete proof systems employing finite sets of mv-signed formulas for all propositional logics based on such structures with either of the above (...)
    Direct download  
     
    Export citation  
     
    My bibliography   9 citations  
  8. Arnon Avron (1987). A Constructive Analysis of RM. Journal of Symbolic Logic 52 (4):939 - 951.
  9. Arnon Avron, Logical Non-Determinism as a Tool for Logical Modularity: An Introduction.
    It is well known that every propositional logic which satisfies certain very natural conditions can be characterized semantically using a multi-valued matrix ([Los and Suszko, 1958; W´ ojcicki, 1988; Urquhart, 2001]). However, there are many important decidable logics whose characteristic matrices necessarily consist of an infinite number of truth values. In such a case it might be quite difficult to find any of these matrices, or to use one when it is found. Even in case a logic does have a (...)
    Translate
     
     
    Export citation  
     
    My bibliography   4 citations  
  10. Arnon Avron, Many-Valued Non-Deterministic Semantics for First-Order Logics of Formal (In)Consistency.
    A paraconsistent logic is a logic which allows non-trivial 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 non-deterministic semantics for a very large family (...)
    Translate
     
     
    Export citation  
     
    My bibliography   1 citation  
  11.  16
    Arnon Avron (2014). What is Relevance Logic? Annals of Pure and Applied Logic 165 (1):26-48.
    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.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  12.  5
    Ofer Arieli, Arnon Avron & Anna Zamansky (2011). Maximal and Premaximal Paraconsistency in the Framework of Three-Valued Semantics. Studia Logica 97 (1):31 - 60.
    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 non-deterministic three-valued matrices. We show that all reasonable paraconsistent logics based on three-valued deterministic matrices are maximal in our strong sense. This applies to practically all three-valued (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  13. Arnon Avron, Non-Deterministic Semantics for Logics with a Consistency Operator.
    In order to handle inconsistent knowledge bases in a reasonable way, one needs a logic which allows nontrivial inconsistent theories. Logics of this sort are called paraconsistent. 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 (...)
    Translate
     
     
    Export citation  
     
    My bibliography   3 citations  
  14. Arnon Avron, The Method of Hypersequents in the Proof Theory of Propositional Non-Classical Logics.
    Until not too many years ago, all logics except classical logic (and, perhaps, intuitionistic logic too) were considered to be things esoteric. Today this state of a airs seems to have completely been changed. There is a growing interest in many types of nonclassical logics: modal and temporal logics, substructural logics, paraconsistent logics, non-monotonic logics { the list is long. The diversity of systems that have been proposed and studied is so great that a need is felt by many researchers (...)
     
    Export citation  
     
    My bibliography   3 citations  
  15.  14
    Arnon Avron (2005). A Non-Deterministic View on Non-Classical Negations. Studia Logica 80 (2-3):159 - 194.
    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 Gentzen-type 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 which is (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   4 citations  
  16.  21
    Arnon Avron (1986). On an Implication Connective of RM. Notre Dame Journal of Formal Logic 27 (2):201-209.
  17. Arnon Avron, On Negation, Completeness and Consistency.
    We have avoided here the term \false", since we do not want to commit ourselves to the view that A is false precisely when it is not true. Our formulation of the intuition is therefore obviously circular, but this is unavoidable in intuitive informal characterizations of basic connectives and quanti ers.
    Translate
     
     
    Export citation  
     
    My bibliography   2 citations  
  18. Arnon Avron, 5-Valued Non-Deterministic Semantics for The Basic Paraconsistent Logic mCi.
    One of the most important paraconsistent logics is the logic mCi, which is one of the two basic logics of formal inconsistency. In this paper we present a 5-valued characteristic nondeterministic matrix for mCi. This provides a quite non-trivial example for the utility and effectiveness of the use of non-deterministic many-valued semantics.
     
    Export citation  
     
    My bibliography   2 citations  
  19.  35
    Arnon Avron (1992). Whither Relevance Logic? Journal of Philosophical Logic 21 (3):243 - 281.
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography   4 citations  
  20.  21
    Arnon Avron (1984). Relevant Entailment--Semantics and Formal Systems. Journal of Symbolic Logic 49 (2):334-342.
  21.  21
    Arnon Avron (1984). On Modal Systems Having Arithmetical Interpretations. Journal of Symbolic Logic 49 (3):935-942.
  22. Arnon Avron (1997). Multiplicative Conjunction as an Extensional Conjunction. Logic Journal of the Igpl 5 (2):181-208.
    We show that the rule that allows the inference of A from A ⊗ B is admissible in many of the basic multiplicative systems. By adding this rule to these systems we get, therefore, conservative extensions in which the tensor behaves as classical conjunction. Among the systems obtained in this way the one derived from RMIm has a particular interest. We show that this system has a simple infinite-valued semantics, relative to which it is strongly complete, and a nice cut-free (...)
    Direct download  
     
    Export citation  
     
    My bibliography   4 citations  
  23.  25
    Arnon Avron, Jonathan Ben-Naim & Beata Konikowska (2007). Cut-Free Ordinary Sequent Calculi for Logics Having Generalized Finite-Valued Semantics. Logica Universalis 1 (1):41-70.
    . The paper presents a method for transforming a given sound and complete n-sequent proof system into an equivalent sound and complete system of ordinary sequents. The method is applicable to a large, central class of (generalized) finite-valued logics with the language satisfying a certain minimal expressiveness condition. The expressiveness condition decrees that the truth-value of any formula φ must be identifiable by determining whether certain formulas uniformly constructed from φ have designated values or not. The transformation preserves the general (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography  
  24. Arnon Avron, Gentzen-Type Systems, Resolution and Tableaux.
    In advanced books and courses on logic (e.g. Sm], BM]) Gentzen-type systems or their dual, tableaux, are described as techniques for showing validity of formulae which are more practical than the usual Hilbert-type formalisms. People who have learnt these methods often wonder why the Automated Reasoning community seems to ignore them and prefers instead the resolution method. Some of the classical books on AD (such as CL], Lo]) do not mention these methods at all. Others (such as Ro]) do, but (...)
    Translate
     
     
    Export citation  
     
    My bibliography   1 citation  
  25. Arnon Avron, A Framework for Formalizing Set Theories Based on the Use of Static Set Terms.
    We present a new unified framework for formalizations of axiomatic set theories of different strength, from rudimentary set theory to full ZF . It allows the use of set terms, but provides a static check of their validity. Like the inconsistent “ideal calculus” for set theory, it is essentially based on just two set-theoretical principles: extensionality and comprehension (to which we add ∈-induction and optionally the axiom of choice). Comprehension is formulated as: x ∈ {x | ϕ} ↔ ϕ, where (...)
    No categories
     
    Export citation  
     
    My bibliography   1 citation  
  26.  5
    Liron Cohen & Arnon Avron (forthcoming). The Middle Ground-Ancestral Logic. Synthese:1-23.
    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 first-order logic . However, there are good reasons to avoid using full second-order 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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  27. Arnon Avron, Canonical Calculi with (N,K)-Ary Quantifiers.
    Propositional canonical Gentzen-type systems, introduced in [2], are systems which in addition to the standard axioms and structural rules have only logical rules in which exactly one occurrence of a connective is introduced and no other connective is mentioned. [2] provides a constructive coherence criterion for the non-triviality of such systems and shows that a system of this kind admits cut-elimination iff it is coherent. The semantics of such systems is provided using two-valued non-deterministic matrices (2Nmatrices). [23] extends these results (...)
     
    Export citation  
     
    My bibliography   1 citation  
  28.  6
    Arnon Avron (1990). Relevance and Paraconsistency---A New Approach. II. The Formal Systems. Notre Dame Journal of Formal Logic 31 (2):169-202.
  29.  24
    Arnon Avron (1990). Relevance and Paraconsistency--A New Approach. Journal of Symbolic Logic 55 (2):707-732.
  30.  12
    Arnon Avron (1989). Gentzenizing Schroeder-Heister's Natural Extension of Natural Deduction. Notre Dame Journal of Formal Logic 31 (1):127-135.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  31. Arnon Avron (1987). A Constructive Analysis of $Mathbf{RM}$. Journal of Symbolic Logic 52 (4):939-951.
  32.  10
    Arnon Avron & Beata Konikowska (2001). Decomposition Proof Systems for Gödel-Dummett Logics. Studia Logica 69 (2):197-219.
    The main goal of the paper is to suggest some analytic proof systems for LC and its finite-valued counterparts which are suitable for proof-search. This goal is achieved through following the general Rasiowa-Sikorski methodology for constructing analytic proof systems for semantically-defined logics. All the systems presented here are terminating, contraction-free, and based on invertible rules, which have a local character and at most two premises.
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  33.  28
    Arnon Avron, Furio Honsell, Marino Miculan & Cristian Paravano (1998). Encoding Modal Logics in Logical Frameworks. Studia Logica 60 (1):161-208.
    We present and discuss various formalizations of Modal Logics in Logical Frameworks based on Type Theories. We consider both Hilbert- and Natural Deduction-style 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 proof-editors for Modal Logics when implemented in Proof Development Environments, such as Coq or LEGO.
    Direct download (8 more)  
     
    Export citation  
     
    My bibliography  
  34. Arnon Avron, Tonk- A Full Mathematical Solution.
    There is a long tradition (See e.g. [9, 10]) starting from [12], according to which the meaning of a connective is determined by the introduction and elimination rules which are associated with it. The supporters of this thesis usually have in mind natural deduction systems of a certain ideal type (explained in Section 3 below). Unfortunately, already the handling of classical negation requires rules which are not of that type. This problem can be solved in the framework of multiple-conclusion Gentzen-type (...)
     
    Export citation  
     
    My bibliography  
  35.  5
    Arnon Avron (1986). On Purely Relevant Logics. Notre Dame Journal of Formal Logic 27 (2):180-194.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  36.  5
    Arnon Avron (2014). Paraconsistency, Paracompleteness, Gentzen Systems, and Trivalent Semantics. Journal of Applied Non-Classical Logics 24 (1-2):12-34.
    A quasi-canonical Gentzen-type system is a Gentzen-type 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 quasi-canonical 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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  37.  4
    Arnon Avron, Oskar Becker, Johan van Benthem, Andreas Blass, Robert Brandom, L. E. J. Brouwer, Donald Davidson, Michael Dummett & Walter Felscher (2009). Jagadeesan, Radha, 306 Japaridze, Giorgi, Xi. In Ondrej Majer, Ahti-Veikko Pietarinen & Tero Tulenheimo (eds.), Games: Unifying Logic, Language, and Philosophy. Springer Verlag 377.
    No categories
    Translate
      Direct download  
     
    Export citation  
     
    My bibliography  
  38.  4
    Arnon Avron (1994). What is a Logical System? In Dov M. Gabbay (ed.), What is a Logical System? Oxford University Press
    Direct download  
     
    Export citation  
     
    My bibliography  
  39.  5
    Arnon Avron (2014). The Classical Constraint on Relevance. Logica Universalis 8 (1):1-15.
    We show that as long as the propositional constants t and f are not included in the language, any language-preserving extension of any important fragment of the relevance logics R and RMI can have only classical tautologies as theorems . This property is not preserved, though, if either t or f is added to the language, or if the contraction axiom is deleted.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  40.  14
    Arnon Avron (1991). A Note of Provability, Truth and Existence. Journal of Philosophical Logic 20 (4):403 - 409.
  41.  11
    Arnon Avron & Beata Konikowska (2009). Proof Systems for Reasoning About Computation Errors. Studia Logica 91 (2):273-293.
    In the paper we examine the use of non-classical truth values for dealing with computation errors in program specification and validation. In that context, 3-valued McCarthy logic is suitable for handling lazy sequential computation, while 3-valued Kleene logic can be used for reasoning about parallel computation. If we want to be able to deal with both strategies without distinguishing between them, we combine Kleene and McCarthy logics into a logic based on a non-deterministic, 3-valued matrix, incorporating both (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  42.  8
    Arnon Avron (1990). Relevance and Paraconsistency---A New Approach. II. The Formal Systems. Notre Dame Journal of Formal Logic 31 (2):169-202.
  43. Arnon Avron, A Model-Theoretic Approach for Recovering Consistent Data From Inconsistent Knowledge-Bases.
    One of the most signi cant drawbacks of classical logic is its being useless in the presence of an inconsistency. Nevertheless, the classical calculus is a very convenient framework to work with. In this work we propose means for drawing conclusions from systems that are based on classical logic, although the informationmightbe inconsistent. The idea is to detect those parts of the knowledge-base that \cause" the inconsistency, and isolate the parts that are \recoverable". We do this by temporarily switching (...)
     
    Export citation  
     
    My bibliography  
  44. Arnon Avron, LFIs with Marco's Schema.
    We construct a modular semantic frameworks for LFIs (logics of formal (in)consistency) which extends the framework developed in [1; 3], but includes Marco’s schema too (and so practically all the axioms considered in [11] plus a few more). In addition, the paper provides another demonstration of the power of the idea of nondeterministic semantics, especially when it is combined with the idea of using truth-values to encode relevant data concerning propositions.
    Translate
     
     
    Export citation  
     
    My bibliography  
  45. Arnon Avron, A New Approach to Predicative Set Theory.
    We suggest a new framework for the Weyl-Feferman predicativist program by constructing a formal predicative set theory P ZF which resembles ZF , and is suitable for mechanization. The basic idea is that the predicatively acceptable instances of the comprehension schema are those which determine the collections they define in an absolute way, independent of the extension of the “surrounding universe”. The language of P ZF is type-free, and it reflects real mathematical practice in making an extensive use of statically (...)
    Translate
     
     
    Export citation  
     
    My bibliography  
  46. Arnon Avron, Constructibility and Decidability Versus Domain Independence and Absoluteness.
    We develop a unified framework for dealing with constructibility and absoluteness in set theory, decidability of relations in effective structures (like the natural numbers), and domain independence of queries in database theory. Our framework and results suggest that domain-independence and absoluteness might be the key notions in a general theory of constructibility, predicativity, and computability.
    Translate
     
     
    Export citation  
     
    My bibliography  
  47. Arnon Avron, A Simple Proof of Completeness and Cut-Elimination for Propositional G¨ Odel Logic.
    We provide a constructive, direct, and simple proof of the completeness of the cut-free part of the hypersequential calculus for G¨odel logic (thereby proving both completeness of the calculus for its standard semantics, and the admissibility of the cut rule in the full calculus). We then extend the results and proofs to derivations from assumptions, showing that such derivations can be confined to those in which cuts are made only on formulas which occur in the assumptions.
     
    Export citation  
     
    My bibliography  
  48. Arnon Avron, A Note on the Structure of Bilattices.
    The notion of a bilattice was rst introduced by Ginsburg (see Gin]) as a general framework for a diversity of applications (such as truth maintenance systems, default inferences and others). The notion was further investigated and applied for various purposes by Fitting (see Fi1]- Fi6]). The main idea behind bilattices is to use structures in which there are two (partial) order relations, having di erent interpretations. The two relations should, of course, be connected somehow in order for the mathematical structure (...)
    No categories
     
    Export citation  
     
    My bibliography  
  49. Arnon Avron, Many-Valued Non-Deterministic Semantics for First-Order Logics of Formal (in)Consistency.
    A paraconsistent logic is a logic which allows non-trivial 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 non-deterministic semantics for a very large family (...)
     
    Export citation  
     
    My bibliography  
  50. Arnon Avron, What Reasonable First-Order Queries Are Permitted by Trakhtenbrot's Theorem?
    Around 1950, B.A. Trakhtenbrot proved an important undecidability result (known, by a pure accident, as \Trakhtenbrot's theorem"): there is no algorithm to decide, given a rst-order sentence, whether the sentence is satis able in some nite model. The result is in fact true even if we restrict ourselves to languages that has only one binary relation Tra63]. It is hardly conceivable that at that time Prof. Trakhtenbrot expected his result to in uence the development of the theory of relational databases (...)
    Translate
     
     
    Export citation  
     
    My bibliography  
1 — 50 / 69