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About this topic
Summary Any connective defined in any logic which does not correspond to a conjunction, disjunction, conditionals, or negation which is under discussion in the work belongs here.  However, I wish to distinguish between "Logical Connectives, Misc" and "Connectives, Misc" in two ways.  (1) The latter is more appropriate when the connective is not one of the above but nonetheless has a clear linguistic equivalent.  The former is more appropriate in the absence of such an equivalent.  (2) Even in the presence of such an equivalent, if the discussion concerns the purely formal properties of the connective, it fits in both categories.
Key works For logical connectives in group (1) in the summary, there is rarely a key work; for those in group (2) in the summary, there may well be, but this will vary with the connective of which there are far too many to enumerate.
Introductions For logical connectives in group (1) in the summary, there is almost never an introductory work; for those in group (2) in the summary, there may well be, but this will vary with the connective of which there are far too many to enumerate.
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175 found
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1 — 50 / 175
  1. Consequence Operations Based on Hypergraph Satisfiability.Adam Kolany - 1997 - Studia Logica 58 (2):261-272.
    Four consequence operators based on hypergraph satisfiability are defined. Their properties are explored and interconnections are displayed. Finally their relation to the case of the Classical Propositional Calculus is shown.
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  2. Concepts as Operators.Joe Adams - 1953 - Psychological Review 60 (4):241-251.
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  3. A New Theory of Quantifiers and Term Connectives.Ken Akiba - 2009 - Journal of Logic, Language and Information 18 (3):403-431.
    This paper sets forth a new theory of quantifiers and term connectives, called shadow theory , which should help simplify various semantic theories of natural language by greatly reducing the need of Montagovian proper names, type-shifting, and λ-conversion. According to shadow theory, conjunctive, disjunctive, and negative noun phrases such as John and Mary , John or Mary , and not both John and Mary , as well as determiner phrases such as every man , some woman , and the boys (...)
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  4. Maps Between Some Different Kinds of Contraction Function: The Finite Case.Carlos E. Alchourrón & David Makinson - 1986 - Studia Logica 45 (2):187 - 198.
    In some recent papers, the authors and Peter Gärdenfors have defined and studied two different kinds of formal operation, conceived as possible representations of the intuitive process of contracting a theory to eliminate a proposition. These are partial meet contraction (including as limiting cases full meet contraction and maxichoice contraction) and safe contraction. It is known, via the representation theorem for the former, that every safe contraction operation over a theory is a partial meet contraction over that theory. The purpose (...)
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  5. Epistemologic Controversy on Quantum Operators.Rafael-Andrés Alemañ-Berenguer - 2010 - Principia: An International Journal of Epistemology 14 (2):241-253.
    Since the very begining of quantum theory there started a debate on the proper role of space and time in it. Some authors assumed that space and time have their own algebraic operators. On that basis they supposed that quantum particles had “coordinates of position”, even though those coordinates were not possible to determine with infinite precision. Furthermore, time in quantum physics was taken to be on an equal foot, by means of a so-called “Heisenberg’s fourth relation of indeterminacy” concerning (...)
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  6. On First-Order Theories with Provability Operator.Sergei Artëmov & Franco Montagna - 1994 - Journal of Symbolic Logic 59 (4):1139-1153.
    In this paper the modal operator "x is provable in Peano Arithmetic" is incorporated into first-order theories. A provability extension of a theory is defined. Presburger Arithmetic of addition, Skolem Arithmetic of multiplication, and some first order theories of partial consistency statements are shown to remain decidable after natural provability extensions. It is also shown that natural provability extensions of a decidable theory may be undecidable.
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  7. Propositional Logic in the Sixteenth and Early Seventeenth Centuries.E. J. Ashworth - 1968 - Notre Dame Journal of Formal Logic 9 (2):179-192.
  8. Patrones inferenciales (Inferential Patterns).Axel Arturo Barceló Aspeitia - 2008 - Critica 40 (120):3 - 35.
    El objetivo de este artículo es proponer un método de traducción de tablas de verdad a reglas de inferencia, para la lógica proposicional, que sea tan directo como el tradicional método inverso (de reglas a tablas). Este método, además, permitirá resolver de manera elegante el viejo problema, formulado originalmente por Prior en 1960, de determinar qué reglas de inferencia definen un conectivo. /// This article aims at setting forth a method to translate truth tables into inference rules, in propositional logic, (...)
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  9. Multiplicative Conjunction and an Algebraic Meaning of Contraction and Weakening.A. Avron - 1998 - Journal of Symbolic Logic 63 (3):831-859.
    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, (...)
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  10. On an Implication Connective of RM.Arnon Avron - 1986 - Notre Dame Journal of Formal Logic 27 (2):201-209.
  11. Some Jump-Like Operations in $\Mathbf \Beta $-Recursion Theory.Colin G. Bailey - 2013 - Journal of Symbolic Logic 78 (1):57-71.
    In this paper we show that there are various pseudo-jump operators definable over inadmissible $J_{\beta}$ that relate to the failure of admissiblity and to non-regularity. We will use these ideas to construct some intermediate degrees.
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  12. Tableaux sin refutación.Tomás Barrero & Walter Carnielli - 2005 - Matemáticas: Enseñanza Universitaria 13 (2):81-99.
    Motivated by H. Curry’s well-known objection and by a proposal of L. Henkin, this article introduces the positive tableaux, a form of tableau calculus without refutation based upon the idea of implicational triviality. The completeness of the method is proven, which establishes a new decision procedure for the (classical) positive propositional logic. We also introduce the concept of paratriviality in order to contribute to the question of paradoxes and limitations imposed by the behavior of classical implication.
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  13. A Characterization of Jump Operators.Howard Becker - 1988 - Journal of Symbolic Logic 53 (3):708-728.
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  14. Hilbert's Ɛ-Operator and Classical Logic.J. L. Bell - 1993 - Journal of Philosophical Logic 22 (1):1 - 18.
  15. A New Modal Language with the Λ Operator.Ermanno Bencivenga & Peter W. Woodruff - 1981 - Studia Logica 40 (4):383 - 389.
    A system of modal logic with the operator is proposed, and proved complete. In contrast with a previous one by Stalnaker and Thomason, this system does not require two categories of singular terms.
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  16. Dividing in the Algebra of Compact Operators.Alexander Berenstein - 2004 - Journal of Symbolic Logic 69 (3):817-829.
    We interpret the algebra of finite rank operators as imaginaries inside a Hilbert space. We prove that the Hilbert space enlarged with these imaginaries has built-in canonical bases.
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  17. Schönfinkel-Type Operators for Classical Logic.Katalin Bimbó - 2010 - Studia Logica 95 (3):355-378.
    We briefly overview some of the historical landmarks on the path leading to the reduction of the number of logical connectives in classical logic. Relying on the duality inherent in Boolean algebras, we introduce a new operator ( Nallor ) that is the dual of Schönfinkel’s operator. We outline the proof that this operator by itself is sufficient to define all the connectives and operators of classical first-order logic ( Fol ). Having scrutinized the proof, we pinpoint the theorems of (...)
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  18. Remarks on Gregory's “Actually” Operator.Patrick Blackburn & Maarten Marx - 2002 - Journal of Philosophical Logic 31 (3):281-288.
    In this note we show that the classical modal technology of Sahlqvist formulas gives quick proofs of the completeness theorems in [8] (D. Gregory, Completeness and decidability results for some propositional modal logics containing "actually" operators, Journal of Philosophical Logic 30(1): 57-78, 2001) and vastly generalizes them. Moreover, as a corollary, interpolation theorems for the logics considered in [8] are obtained. We then compare Gregory's modal language enriched with an "actually" operator with the work of Arthur Prior now known under (...)
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  19. Propositional Connectives, Supposition, and Consequence in Paul of Pergola.Ivan Boh - 1966 - Notre Dame Journal of Formal Logic 7 (1):109-128.
  20. A Binary Sheffer Operator Which Does the Work of Quantifiers and Sentential Connectives.Robert B. Brandom - 1979 - Notre Dame Journal of Formal Logic 20 (2):262-264.
  21. Constructive Mathematics and Unbounded Operators — a Reply to Hellman.Douglas S. Bridges - 1995 - Journal of Philosophical Logic 24 (5):549 - 561.
    It is argued that Hellman's arguments purporting to demonstrate that constructive mathematics cannot cope with unbounded operators on a Hilbert space are seriously flawed, and that there is no evidence that his thesis is correct.
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  22. A Carnapian Approach to Counterexamples to Modus Ponens.Constantin C. Brîncuș & Iulian D. Toader - 2013 - Romanian Journal of Analytic Philosophy 7:78-85.
    This paper defends a Carnapian approach to known counterexamples to Modus Ponens (MP). More specifically, it proposes that instead of rejecting MP as invalid in certain interpretations, one should regard the interpretations themselves as non-normal, in Carnap’s sense.
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  23. Span Operators.B. Brogaard - 2007 - Analysis 67 (1):72-79.
    I. Tensed Plural Quantifiers Presentists typically assent to a range of tensed statements, for instance, that there were dinosaurs, that there was a president named Lincoln, and that my future grandchildren will be on their way to school.1 Past- and future-tensed claims are dealt with by introducing primitive, intensional tense operators, for instance, it has been 12 years ago that, it was the case when I was born that, and it will be the case that (Prior 1968). For example, ‘there (...)
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  24. Variable Binding Term Operators in $\Lambda $-Calculus.M. W. Bunder - 1979 - Notre Dame Journal of Formal Logic 20 (4):876-878.
  25. Operators in Nature.M. Burgin & J. E. Brenner - forthcoming - Mind and Society.
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  26. Knot and Tonk: Nasty Connectives on Many-Valued Truth-Tables for Classical Sentential Logic.Tim Button - 2016 - Analysis 76 (1):7-19.
    Prior’s Tonk is a famously horrible connective. It is defined by its inference rules. My aim in this article is to compare Tonk with some hitherto unnoticed nasty connectives, which are defined in semantic terms. I first use many-valued truth-tables for classical sentential logic to define a nasty connective, Knot. I then argue that we should refuse to add Knot to our language. And I show that this reverses the standard dialectic surrounding Tonk, and yields a novel solution to the (...)
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  27. An Algebraic Approach to Intuitionistic Connectives.Xavier Caicedo & Roberto Cignoli - 2001 - Journal of Symbolic Logic 66 (4):1620-1636.
    It is shown that axiomatic extensions of intuitionistic propositional calculus defining univocally new connectives, including those proposed by Gabbay, are strongly complete with respect to valuations in Heyting algebras with additional operations. In all cases, the double negation of such a connective is equivalent to a formula of intuitionistic calculus. Thus, under the excluded third law it collapses to a classical formula, showing that this condition in Gabbay's definition is redundant. Moreover, such connectives can not be interpreted in all Heyting (...)
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  28. On the Mosaic Method for Many-Dimensional Modal Logics: A Case Study Combining Tense and Modal Operators. [REVIEW]Carlos Caleiro, Luca Viganò & Marco Volpe - 2013 - Logica Universalis 7 (1):33-69.
    We present an extension of the mosaic method aimed at capturing many-dimensional modal logics. As a proof-of-concept, we define the method for logics arising from the combination of linear tense operators with an “orthogonal” S5-like modality. We show that the existence of a model for a given set of formulas is equivalent to the existence of a suitable set of partial models, called mosaics, and apply the technique not only in obtaining a proof of decidability and a proof of completeness (...)
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  29. The Collapse of Logical Pluralism has Been Greatly Exaggerated.Colin R. Caret - 2017 - Erkenntnis 82 (4):739-760.
    According to the logical pluralism of Beall and Restall, there are several distinct relations of logical consequence. Some critics argue that logical pluralism suffers from what I call the collapse problem: that despite its intention to articulate a radically pluralistic doctrine about logic, the view unintentionally collapses into logical monism. In this paper, I propose a contextualist resolution of the collapse problem. This clarifies the mechanism responsible for a plurality of logics and handles the motivating data better than the original (...)
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  30. Logical Operations and Invariance.Enrique Casanovas - 2006 - Journal of Philosophical Logic 36 (1):33 - 60.
    I present a notion of invariance under arbitrary surjective mappings for operators on a relational finite type hierarchy generalizing the so-called Tarski-Sher criterion for logicality and I characterize the invariant operators as definable in a fragment of the first-order language. These results are compared with those obtained by Feferman and it is argued that further clarification of the notion of invariance is needed if one wants to use it to characterize logicality.
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  31. Frontal Operators in Weak Heyting Algebras.Sergio A. Celani & Hernán J. San Martín - 2012 - Studia Logica 100 (1-2):91-114.
    In this paper we shall introduce the variety FWHA of frontal weak Heyting algebras as a generalization of the frontal Heyting algebras introduced by Leo Esakia in [ 10 ]. A frontal operator in a weak Heyting algebra A is an expansive operator τ preserving finite meets which also satisfies the equation $${\tau(a) \leq b \vee (b \rightarrow a)}$$, for all $${a, b \in A}$$. These operators were studied from an algebraic, logical and topological point of view by Leo Esakia (...)
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  32. Discontinuities of Provably Correct Operators on the Provably Recursive Real Numbers.William J. Collins & Paul Young - 1983 - Journal of Symbolic Logic 48 (4):913-920.
    In this paper we continue, from [2], the development of provably recursive analysis, that is, the study of real numbers defined by programs which can be proven to be correct in some fixed axiom system S. In particular we develop the provable analogue of an effective operator on the set C of recursive real numbers, namely, a provably correct operator on the set P of provably recursive real numbers. In Theorems 1 and 2 we exhibit a provably correct operator on (...)
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  33. The Representation of Takeuti's *20c ||_ -Operator.Roger M. Cooke & Michiel Lambalgen - 1983 - Studia Logica 42 (4):407 - 415.
    Gaisi Takeuti has recently proposed a new operation on orthomodular lattices L, ⫫: $\scr{P}(L)\rightarrow L$ . The properties of ⫫ suggest that the value of ⫫ $(A)(A\subseteq L)$ corresponds to the degree in which the elements of A behave classically. To make this idea precise, we investigate the connection between structural properties of orthomodular lattices L and the existence of two-valued homomorphisms on L.
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  34. Minimal Degrees and the Jump Operator.S. B. Cooper - 1973 - Journal of Symbolic Logic 38 (2):249-271.
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  35. Conversely: Extrapropositional and Prosentential.John Corcoran & Sriram Nambiar - 2014 - Bulletin of Symbolic Logic 20:404-5.
    This self-contained lecture examines uses and misuses of the adverb conversely with special attention to logic and logic-related fields. Sometimes adding conversely after a conjunction such as and signals redundantly that a converse of what preceded will follow. -/- (1) Tarski read Church and, conversely, Church read Tarski. -/- In such cases, conversely serves as an extrapropositional constituent of the sentence in which it occurs: deleting conversely doesn’t change the proposition expressed. Nevertheless it does introduce new implicatures: a speaker would (...)
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  36. Modality, Quantification, and Many Vlach-Operators.Fabrice Correia - 2007 - Journal of Philosophical Logic 36 (4):473-488.
    Consider two standard quantified modal languages A and P whose vocabularies comprise the identity predicate and the existence predicate, each endowed with a standard S5 Kripke semantics where the models have a distinguished actual world, which differ only in that the quantifiers of A are actualist while those of P are possibilist. Is it possible to enrich these languages in the same manner, in a non-trivial way, so that the two resulting languages are equally expressive-i.e., so that for each sentence (...)
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  37. The Suszko Operator. Part I.Janusz Czelakowski - 2003 - Studia Logica 74 (1-2):181 - 231.
    The paper is conceived as a first study on the Suszko operator. The purpose of this paper is to indicate the existence of close relations holding between the properties of the Suszko operator and the structural properties of the model class for various sentential logics. The emphasis is put on generality both of the results and methods of tackling the problems that arise in the theory of this operator. The attempt is made here to develop the theory for non-protoalgebraic logics.
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  38. Storage Operators and Directed Lambda-Calculus.René David & Karim Nour - 1995 - Journal of Symbolic Logic 60 (4):1054-1086.
    Storage operators have been introduced by J. L. Krivine in [5] they are closed λ-terms which, for a data type, allow one to simulate a "call by value" while using the "call by name" strategy. In this paper, we introduce the directed λ-calculus and show that it has the usual properties of the ordinary λ-calculus. With this calculus we get an equivalent--and simple--definition of the storage operators that allows to show some of their properties: $\bullet$ the stability of the set (...)
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  39. Determination, Uniformity, and Relevance: Normative Criteria for Generalization and Reasoning by Analogy.Todd R. Davies - 1988 - In David H. Helman (ed.), Analogical Reasoning. Kluwer Academic Publishers. pp. 227-250.
    This paper defines the form of prior knowledge that is required for sound inferences by analogy and single-instance generalizations, in both logical and probabilistic reasoning. In the logical case, the first order determination rule defined in Davies (1985) is shown to solve both the justification and non-redundancy problems for analogical inference. The statistical analogue of determination that is put forward is termed 'uniformity'. Based on the semantics of determination and uniformity, a third notion of "relevance" is defined, both logically and (...)
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  40. Sahlqvist's Theorem for Boolean Algebras with Operators with an Application to Cylindric Algebras.Maarten de Rijke & Yde Venema - 1995 - Studia Logica 54 (1):61-78.
    For an arbitrary similarity type of Boolean Algebras with Operators we define a class ofSahlqvist identities. Sahlqvist identities have two important properties. First, a Sahlqvist identity is valid in a complex algebra if and only if the underlying relational atom structure satisfies a first-order condition which can be effectively read off from the syntactic form of the identity. Second, and as a consequence of the first property, Sahlqvist identities arecanonical, that is, their validity is preserved under taking canonical embedding algebras. (...)
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  41. A Logic with Relative Knowledge Operators.Stéphane Demri - 1999 - Journal of Logic, Language and Information 8 (2):167-185.
    We study a knowledge logic that assumes that to each set of agents, an indiscernibility relation is associated and the agents decide the membership of objects or states up to this indiscernibility relation. Its language contains a family of relative knowledge operators. We prove the decidability of the satisfiability problem, we show its EXPTIME-completeness and as a side-effect, we define a complete Hilbert-style axiomatization.
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  42. A Completeness Proof for a Logic with an Alternative Necessity Operator.Stéphane Demri - 1997 - Studia Logica 58 (1):99-112.
    We show the completeness of a Hilbert-style system LK defined by M. Valiev involving the knowledge operator K dedicated to the reasoning with incomplete information. The completeness proof uses a variant of Makinson's canonical model construction. Furthermore we prove that the theoremhood problem for LK is co-NP-complete, using techniques similar to those used to prove that the satisfiability problem for propositional S5 is NP-complete.
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  43. Diagonalization and Truth Functional Operators.Harry Deutsch - 2010 - Analysis 70 (2):215-217.
    (No abstract is available for this citation).
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  44. Weak Disharmony: Some Lessons for Proof-Theoretic Semantics.Bogdan Dicher - 2016 - Review of Symbolic Logic:1-20.
    A logical constant is weakly disharmonious if its elimination rules are weaker than its introduction rules. Substructural weak disharmony is the weak disharmony generated by structural restrictions on the eliminations. I argue that substructural weak disharmony is not a defect of the constants which exhibit it. To the extent that it is problematic, it calls into question the structural properties of the derivability relation. This prompts us to rethink the issue of controlling the structural properties of a logic by means (...)
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  45. The Relationship Between KLM and MAK Models for Nonmonotonic Inference Operations.Jürgen Dix & David Makinson - 1992 - Journal of Logic, Language and Information 1 (2):131-140.
    The purpose of this note is to make quite clear the relationship between two variants of the general notion of a preferential model for nonmonotonic inference: the models of Kraus, Lehmann and Magidor (KLM models) and those of Makinson (MAK models).On the one hand, we introduce the notion of the core of a KLM model, which suffices to fully determine the associated nonmonotonic inference relation. On the other hand, we slightly amplify MAK models with a monotonic consequence operation as additional (...)
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  46. ``Epistemic Operators".Fred I. Dretske - 1970 - Journal of Philosophy 67 (24):1007-1023.
  47. Deontic ‘Cocktail’ According to E. Mally’s Receipt.Lisanyuk Elena - 2013 - Logical Investigations 19:5-27.
    In 1926, Ernst Mally, an Austrian logician, has introduced a system of deontic logic in which he has proposed three fundamental distinctions which proved to be important in the context of the further development of the logic of norms. It is argued that in his philosophical considerations Mally has introduced a number of important distinctions concerning the very concept of norm, but by getting them confused in introducing the subsequent formalisms he failed to formally preserve them. In some of his (...)
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  48. Modal Operators with Probabilistic Interpretations, I.M. Fattorosi-Barnaba & G. Amati - 1987 - Studia Logica 46 (4):383-393.
    We present a class of normal modal calculi PFD, whose syntax is endowed with operators M r, one for each r [0,1] : if a is sentence, M r is to he read the probability that a is true is strictly greater than r and to he evaluated as true or false in every world of a F-restricted probabilistic kripkean model. Every such a model is a kripkean model, enriched by a family of regular probability evaluations with range in a (...)
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  49. Logic TK: Algebraic Notions From Tarski's Consequence Operator.Hércules A. Feitosa, Mauri C. Do Nascimento & Maria Claudia C. Grácio - 2010 - Principia: An International Journal of Epistemology 14 (1):47-70.
    Tarski apresentou sua definição de operador de consequência com a intenção de expor as concepções fundamentais da consequência lógica. Um espaço de Tarski é um par ordenado determinado por um conjunto não vazio e um operador de consequência sobre este conjunto. Esta estrutura matemática caracteriza um espaço quase topológico. Este artigo mostra uma visão algébrica dos espaços de Tarski e introduz uma lógica proposicional modal que interpreta o seu operador modal nos conjuntos fechados de algum espaço de Tarski. DOI:10.5007/1808-1711.2010v14n1p47.
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  50. Selective Revision.Eduardo L. Fermé & Sven Ove Hansson - 1999 - Studia Logica 63 (3):331-342.
    We introduce a constructive model of selective belief revision in which it is possible to accept only a part of the input information. A selective revision operator ο is defined by the equality K ο α = K * f(α), where * is an AGM revision operator and f a function, typically with the property ⊢ α → f(α). Axiomatic characterizations are provided for three variants of selective revision.
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