# Logical Consequence and Entailment

Edited by Salvatore Florio (University of Birmingham)
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1. Analysis of the Talmudic Argumentum A Fortiori Inference Rule Using Matrix Abduction.M. Abraham, Dov M. Gabbay & U. Schild - 2009 - Studia Logica 92 (3):281-364.
We motivate and introduce a new method of abduction, Matrix Abduction, and apply it to modelling the use of non-deductive inferences in the Talmud such as Analogy and the rule of Argumentum A Fortiori. Given a matrix with entries in {0,1}, we allow for one or more blank squares in the matrix, say \$a_{i,j} =?.\$ The method allows us to decide whether to declare \$a_{i,j} = 0\$ or \$a_{i,j} = 1\$ or \$a_{i,j} =?\$ undecided. This algorithmic method is then applied (...)

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2. On Decidable Consequence Operators.Jaros?aw Achinger & Andrzej W. Jankowski - 1986 - Studia Logica 45 (4):415 - 424.
The main theorem says that a consequence operator is an effective part of the consequence operator for the classical prepositional calculus iff it is a consequence operator for a logic satisfying the compactness theorem, and in which every finitely axiomatizable theory is decidable.

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3. Begründung Einer Strengen Implikation.Wilhelm Ackermann - 1956 - Journal of Symbolic Logic 21 (2):113-128.

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4. Consequence Operations Based on Hypergraph Satisfiability.Kolany Adam - 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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5. Four Probability-Preserving Properties of Inferences.Ernest W. Adams - 1996 - Journal of Philosophical Logic 25 (1):1 - 24.
Different inferences in probabilistic logics of conditionals 'preserve' the probabilities of their premisses to different degrees. Some preserve certainty, some high probability, some positive probability, and some minimum probability. In the first case conclusions must have probability I when premisses have probability 1, though they might have probability 0 when their premisses have any lower probability. In the second case, roughly speaking, if premisses are highly probable though not certain then conclusions must also be highly probable. In the third case (...)

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6. Remarks on a Theorem of McGee.Ernest W. Adams - 1995 - Journal of Philosophical Logic 24 (4):343 - 348.

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7. Meeting of the Association for Symbolic Logic.J. W. Addison & H. B. Enderton - 1984 - Journal of Symbolic Logic 49 (1):322-326.

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8. Inductive Inference and Unsolvability.Leonard M. Adleman & M. Blum - 1991 - Journal of Symbolic Logic 56 (3):891-900.
It is shown that many different problems have the same degree of unsolvability. Among these problems are: THE INDUCTIVE INFERENCE PROBLEM. Infer in the limit an index for a recursive function f presented as f(0), f(1), f(2),.... THE RECURSIVE INDEX PROBLEM. Decide in the limit if i is the index of a total recursive function. THE ZERO NONVARIANT PROBLEM. Decide in the limit if a recursive function f presented as f(0), f(1), f(2),... has value unequal to zero for infinitely many (...)

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9. Conditional Sentence and Material Implication.Kazimierz Ajdukiewicz - 1956 - Studia Logica 4 (1):135-153.

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10. Logic and Truth.Ken Akiba - 2000 - Journal of Philosophical Research 25:101-123.
It is usually held that what distinguishes a good inference from a bad one is that a good inference is truth-preserving. Against this view, this paper argues that a logical inference is good or bad depending not on whether it is truth-preserving or not, but whether it belongs to a logical system the addition of which makes a deductively conservative extension of the derivation relations among the atomic statements. To so argue, the paper first contends that the meaning of the (...)

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11. Generalized Quantification as Substructural Logic.Natasha Alechina & Michiel van Lambalgen - 1996 - Journal of Symbolic Logic 61 (3):1006-1044.
We show how sequent calculi for some generalized quantifiers can be obtained by generalizing the Herbrand approach to ordinary first order proof theory. Typical of the Herbrand approach, as compared to plain sequent calculus, is increased control over relations of dependence between variables. In the case of generalized quantifiers, explicit attention to relations of dependence becomes indispensible for setting up proof systems. It is shown that this can be done by turning variables into structured objects, governed by various types of (...)

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12. Informational Semantics as a Third Alternative?Patrick Allo & Edwin Mares - 2012 - Erkenntnis 77 (2):167-185.
Informational semantics were first developed as an interpretation of the model-theory of substructural (and especially relevant) logics. In this paper we argue that such a semantics is of independent value and that it should be considered as a genuine alternative explication of the notion of logical consequence alongside the traditional model-theoretical and the proof-theoretical accounts. Our starting point is the content-nonexpansion platitude which stipulates that an argument is valid iff the content of the conclusion does not exceed the combined content (...)

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13. A Naive Variety Of Logical Consequence.Enrique Alonso - 1995 - Sorites 3:12-26.
The semantic analysis of logical consequence must obey a set of requisites which nowadays have acquired a dogmatic status. This situation prevents the development of other varieties of this fundamental relation. In this issue we try to define what we call a naive variety of logical consequence. The main feature of this relation is the way it depends on formulas in premises and conclusion: every sentence must contribute to the acceptability of an argument in a significative way. This circumstance can (...)
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14. The Logical Enterprise.J. E. J. Altham - 1979 - Philosophical Books 20 (3):134-136.

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15. A Quantitative-Informational Approach to Logical Consequence.Marcos Antonio Alves & Ítala M. Loffredo D'Otaviano - 2015 - In Jean-Yves Beziau (ed.), The Road to Universal Logic (Studies in Universal Logic). Switzerland: Springer International Publishing. pp. 105-24.
In this work, we propose a definition of logical consequence based on the relation between the quantity of information present in a particular set of formulae and a particular formula. As a starting point, we use Shannon‟s quantitative notion of information, founded on the concepts of logarithmic function and probability value. We first consider some of the basic elements of an axiomatic probability theory, and then construct a probabilistic semantics for languages of classical propositional logic. We define the quantity of (...)

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16. Studies in Indian Logic.K. K. Ambikadevi - 2010 - Sukrtindra Oriental Research Institute.
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17. Entailment: The Logic of Relevance and Necessity.Alan Ross Anderson - 1975 - Princeton University Press.
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18. The Pure Calculus of Entailment.Alan Ross Anderson & Nuel D. Belnap Jr - 1962 - Journal of Symbolic Logic 27 (1):19-52.

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19. Modalities in Ackermann's "Rigorous Implication".Alan Ross Anderson & Nuel D. Belnap Jr - 1959 - Journal of Symbolic Logic 24 (2):107-111.

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20. Independent Axiom Schemata for the Pure Theory of Entailment.Alan Ross Anderson, Nuel D. Belnap & John R. Wallace - 1960 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 6 (1-6):93-95.

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21. Deducibility, Entailment and Analytic Containment.Richard B. Angell - 1989 - In Jean Norman & Richard Sylvan (eds.), Directions in Relevant Logic. Kluwer Academic Publishers. pp. 119-143.
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22. Grounded Consequence for Defeasible Logic.Aldo Antonelli - 2005 - Cambridge University Press.
This is a title on the foundations of defeasible logic, which explores the formal properties of everyday reasoning patterns whereby people jump to conclusions, reserving the right to retract them in the light of further information. Although technical in nature the book contains sections that outline basic issues by means of intuitive and simple examples. This book is primarily targeted at philosophers interested in the foundations of defeasible logic, logicians, and specialists in artificial intelligence and theoretical computer science.

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23. A Simple Defense of Material Implication.Lee C. Archie - 1979 - Notre Dame Journal of Formal Logic 20 (2):412-414.

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24. A Note on the Truth-Table for ``If \$P\$ Then \$Q\$''.Lee C. Archie, B. G. Hurdle & William Stewart Thomblison - 1977 - Notre Dame Journal of Formal Logic 18 (4):596-598.

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25. Strict and Material Implication in the Early Sixteenth Century.E. J. Ashworth - 1972 - Notre Dame Journal of Formal Logic 13 (4):556-560.

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26. Petrus Fonseca and Material Implication.E. J. Ashworth - 1968 - Notre Dame Journal of Formal Logic 9 (3):227-228.

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27. What Does '&' Mean?Axel Arturo Barceló Aspeitia - 2007 - The Proceedings of the Twenty-First World Congress of Philosophy 5:45-50.
Using conjunction as an example, I show a technical and philosophical problem when trying to conciliate the currently prevailing views on the meaning of logical connectives: the inferientialist (also called 'syntactic') one based on introduction and elimination rules, and the representationalist (also called 'semantic') one given through truth tables. Mostly I show that the widespread strategy of using the truth theoretical definition of logical consequence to collapse both definitions must be rejected by inferentialists. An important consequence of my argument is (...)

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28. Logical Consequences. Theory and Applications: An Introduction.M. Augusto Luis - forthcoming - London: College Publications..
The theory of logical consequence is central in modern logic and its applications. However, it is mostly dispersed in an abundance of often difficultly accessible papers, and rarely treated with applications in mind. This book collects the most fundamental aspects of this theory and offers the reader the basics of its applications in computer science, artificial intelligence, and cognitive science, to name but the most important fields where this notion finds its many applications.
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29. Logical Consequences. Theory and Applications: An Introduction.M. Augusto Luis - forthcoming - London: College Publications..
The theory of logical consequence is central in modern logic and its applications. However, it is mostly dispersed in an abundance of often difficultly accessible papers, and rarely treated with applications in mind. This book collects the most fundamental aspects of this theory and offers the reader the basics of its applications in computer science, artificial intelligence, and cognitive science, to name but the most important fields where this notion finds its many applications.
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30. Logical Consequences. Theory and Applications: An Introduction.Luis M. Augusto - forthcoming - London: College Publications..
The theory of logical consequence is central in modern logic and its applications. However, it is mostly dispersed in an abundance of often difficultly accessible papers, and rarely treated with applications in mind. This book collects the most fundamental aspects of this theory and offers the reader the basics of its applications in computer science, artificial intelligence, and cognitive science, to name but the most important fields where this notion finds its many applications.
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31. Logical Consequences. Theory and Applications: An Introduction.Luis M. Augusto - forthcoming - London: College Publications..
The theory of logical consequence is central in modern logic and its applications. However, it is mostly dispersed in an abundance of often difficultly accessible papers, and rarely treated with applications in mind. This book collects the most fundamental aspects of this theory and offers the reader the basics of its applications in computer science, artificial intelligence, and cognitive science, to name but the most important fields where this notion finds its many applications.
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32. Logical Consequences. Theory and Applications: An Introduction.Luis M. Augusto - forthcoming - London: College Publications..
The theory of logical consequence is central in modern logic and its applications. However, it is mostly dispersed in an abundance of often difficultly accessible papers, and rarely treated with applications in mind. This book collects the most fundamental aspects of this theory and offers the reader the basics of its applications in computer science, artificial intelligence, and cognitive science, to name but the most important fields where this notion finds its many applications.
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33. Logical Consequences. Theory and Applications: An Introduction.Luis M. Augusto - forthcoming - London: College Publications..
The theory of logical consequence is central in modern logic and its applications. However, it is mostly dispersed in an abundance of often difficultly accessible papers, and rarely treated with applications in mind. This book collects the most fundamental aspects of this theory and offers the reader the basics of its applications in computer science, artificial intelligence, and cognitive science, to name but the most important fields where this notion finds its many applications.
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34. Logical Consequences. Theory and Applications: An Introduction.Luis M. Augusto - 2017 - London: College Publications.
The theory of logical consequence is central in modern logic and its applications. However, it is mostly dispersed in an abundance of often difficultly accessible papers, and rarely treated with applications in mind. This book collects the most fundamental aspects of this theory and offers the reader the basics of its applications in computer science, artificial intelligence, and cognitive science, to name but the most important fields where this notion finds its many applications.

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35. On an Implication Connective of RM.Arnon Avron - 1986 - Notre Dame Journal of Formal Logic 27 (2):201-209.

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36. Relevant Entailment--Semantics and Formal Systems.Arnon Avron - 1984 - Journal of Symbolic Logic 49 (2):334-342.

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37. Non-Classical Metatheory for Non-Classical Logics.Andrew Bacon - 2013 - Journal of Philosophical Logic 42 (2):335-355.
A number of authors have objected to the application of non-classical logic to problems in philosophy on the basis that these non-classical logics are usually characterised by a classical metatheory. In many cases the problem amounts to more than just a discrepancy; the very phenomena responsible for non-classicality occur in the field of semantics as much as they do elsewhere. The phenomena of higher order vagueness and the revenge liar are just two such examples. The aim of this paper is (...)

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38. A Lindström-Style Theorem for Finitary Propositional Weak Entailment Languages with Absurdity.Guillermo Badia - 2016 - Logic Journal of the IGPL 24 (2):115-137.
Following a result by De Rijke for modal logic, it is shown that the basic weak entailment model-theoretic language with absurdity is the maximal model-theoretic language having the finite occurrence property, preservation under relevant directed bisimulations and the finite depth property. This can be seen as a generalized preservation theorem characterizing propositional weak entailment formulas among formulas of other model-theoretic languages.

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39. On Two Immediate Inferences by Limitation.John Robert Baker - 1975 - Notre Dame Journal of Formal Logic 16 (4):496-500.

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40. Modal Logics for Parallelism, Orthogonality, and Affine Geometries.Philippe Balbiani & Valentin Goranko - 2002 - Journal of Applied Non-Classical Logics 12 (3-4):365-397.
We introduce and study a variety of modal logics of parallelism, orthogonality, and affine geometries, for which we establish several completeness, decidability and complexity results and state a number of related open, and apparently difficult problems. We also demonstrate that lack of the finite model property of modal logics for sufficiently rich affine or projective geometries (incl. the real affine and projective planes) is a rather common phenomenon.

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41. Validity and Necessity.Roberta Ballarin - 2004 - Journal of Philosophical Logic 34 (3):275-303.
In this paper I argue against the commonly received view that Kripke's formal Possible World Semantics (PWS) reflects the adoption of a metaphysical interpretation of the modal operators. I consider in detail Kripke's three main innovations vis-à-vis Carnap's PWS: a new view of the worlds, variable domains of quantification, and the adoption of a notion of universal validity. I argue that all these changes are driven by the natural technical development of the model theory and its related notion of validity: (...)

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42. New Psychological Paradigm for Conditionals and General de Finetti Tables.J. Baratgin, D. Over & G. Politzer - 2014 - Mind and Language 29 (1):73-84.
The new Bayesian paradigm in the psychology of reasoning aims to integrate the study of human reasoning, decision making, and rationality. It is supported by two findings. One, most people judge the probability of the indicative conditional, P(if A then B), to be the conditional probability, P(B|A), as implied by the Ramsey test. Two, they judge if A then B to be void when A is false. Their three-valued response table used to be called ‘defective’, but should be termed the (...)

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43. Presupposition and Entailment.John A. Barker - 1976 - Notre Dame Journal of Formal Logic 17 (2):272-278.

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44. Barrio, EA" Consecuencia lógica, modalidad y generalidad irrestricta". [REVIEW]Tomás Barrero - 2008 - Ideas Y Valores 57 (138):177-180.
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45. Consecuencia lógica, modalidad y generalidad irrestricta.Eduardo Barrio - 2007 - Manuscrito 30 (1):35-63.
En este trabajo, me propongo discutir la plausibilidad de la tesis de que es posible captar las características modales del concepto intuitivo de consecuencia a través de un concepto de consecuencia definido generalizando sobre interpretaciones. Desde mi perspectiva, las argumentaciones que han ofrecido aquellos que, como Ray, quieren salvar el salto de lo general a lo modal, mostrando que hay suficientes interpretaciones como para representar las características modales de la noción preteórica de consecuencia, poseen un mismo tipo de limitación. La (...)
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46. Substructural Logics, Pluralism and Collapse.Eduardo Alejandro Barrio, Federico Pailos & Damian Szmuc - forthcoming - Synthese:1-17.
When discussing Logical Pluralism several critics argue that such an open-minded position is untenable. The key to this conclusion is that, given a number of widely accepted assumptions, the pluralist view collapses into Logical Monism. In this paper we show that the arguments usually employed to arrive at this conclusion do not work. The main reason for this is the existence of certain substructural logics which have the same set of valid inferences as Classical Logic—although they are, in a clear (...)

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47. A Recovery Operator for Nontransitive Approaches.Eduardo Alejandro Barrio, Federico Pailos & Damian Szmuc - forthcoming - Review of Symbolic Logic:1-25.
In some recent papers, Cobreros, Egré, Ripley and van Rooij have defended the idea that abandoning transitivity may lead to a solution to the trouble caused by semantic paradoxes. For that purpose, they develop the Strict-Tolerant approach, which leads them to entertain a non-transitive theory of truth, where the structural rule of Cut is not generally valid. However, that Cut fails in general in the target theory of truth does not mean that there are not certain safe instances of Cut (...)

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48. Notes on Ω-Inconsistent Theories of Truth in Second-Order Languages.Eduardo Barrio & Lavinia Picollo - 2013 - Review of Symbolic Logic 6 (4):733-741.
It is widely accepted that a theory of truth for arithmetic should be consistent, but -consistency is a highly desirable feature for such theories. The point has already been made for first-order languages, though the evidence is not entirely conclusive. We show that in the second-order case the consequence of adopting -inconsistent theories of truth are considered: the revision theory of nearly stable truth T # and the classical theory of symmetric truth FS. Briefly, we present some conceptual problems with (...)

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49. Consistency and Logical Consequence.Jon Barwise - 1990 - In J. Dunn & A. Gupta (eds.), Truth or Consequences. Kluwer Academic Publishers. pp. 111--122.