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  1. Intuitionistic epistemic logic.Sergei Artemov & Tudor Protopopescu - 2016 - Review of Symbolic Logic 9 (2):266-298.
    We outline an intuitionistic view of knowledge which maintains the original Brouwer–Heyting–Kolmogorov semantics for intuitionism and is consistent with the well-known approach that intuitionistic knowledge be regarded as the result of verification. We argue that on this view coreflectionA→KAis valid and the factivity of knowledge holds in the formKA→ ¬¬A‘known propositions cannot be false’.We show that the traditional form of factivityKA→Ais a distinctly classical principle which, liketertium non datur A∨ ¬A, does not hold intuitionistically, but, along with the whole of (...)
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  • Dialogue structure and logical expressivism.Paul Piwek - 2011 - Synthese 183 (S1):33-58.
    This paper aims to develop the implications of logical expressivism for a theory of dialogue coherence. I proceed in three steps. Firstly, certain structural properties of cooperative dialogue are identified. Secondly, I describe a variant of the multi-agent natural deduction calculus that I introduced in Piwek (J Logic Lang Inf 16(4):403–421, 2007 ) and demonstrate how it accounts for the aforementioned structures. Thirdly, I examine how the aforementioned system can be used to formalise an expressivist account of logical vocabulary that (...)
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  • Natural Semantics: Why Natural Deduction is Intuitionistic.James W. Garson - 2001 - Theoria 67 (2):114-139.
    In this paper investigates how natural deduction rules define connective meaning by presenting a new method for reading semantical conditions from rules called natural semantics. Natural semantics explains why the natural deduction rules are profoundly intuitionistic. Rules for conjunction, implication, disjunction and equivalence all express intuitionistic rather than classical truth conditions. Furthermore, standard rules for negation violate essential conservation requirements for having a natural semantics. The standard rules simply do not assign a meaning to the negation sign. Intuitionistic negation fares (...)
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  • Semantics and the Justification of Deductive Inference.Ebba Gullberg & Sten Lindström - 2007 - Hommage À Wlodek: Philosophical Papers Dedicated to Wlodek Rabinowicz.
    Is it possible to give a justification of our own practice of deductive inference? The purpose of this paper is to explain what such a justification might consist in and what its purpose could be. On the conception that we are going to pursue, to give a justification for a deductive practice means to explain in terms of an intuitively satisfactory notion of validity why the inferences that conform to the practice coincide with the valid ones. That is, a justification (...)
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  • Situations as indices and as denotations.Tim Fernando - 2009 - Linguistics and Philosophy 32 (2):185-206.
    A distinction is drawn between situations as indices required for semantically evaluating sentences and situations as denotations resulting from such evaluation. For atomic sentences, possible worlds may serve as indices, and events as denotations. The distinction is extended beyond atomic sentences according to formulae-as-types and applied to implicit quantifier domain restrictions, intensionality and conditionals.
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  • On Dialogues, Predication and Elementary sentences.Shahid Rahman & Nicolas Clerbout - 2013 - Revista de Humanidades de Valparaíso 2:7-46.
    In its origins Dialogical logic constituted the logical foundations of an overall new movement called the Erlangen School or Erlangen Constructivism that should provide a new start to a general theory of language and of science. In relation to the theory of language, according to the Erlangen-School, language is not just a fact that we discover, but a human cultural accomplishment whose construction reason can and should control. The constructive development of a scientific language was called the Orthosprache-project. Unfortunately, the (...)
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  • Natural Language Inference in Coq.Stergios Chatzikyriakidis & Zhaohui Luo - 2014 - Journal of Logic, Language and Information 23 (4):441-480.
    In this paper we propose a way to deal with natural language inference by implementing Modern Type Theoretical Semantics in the proof assistant Coq. The paper is a first attempt to deal with NLI and natural language reasoning in general by using the proof assistant technology. Valid NLIs are treated as theorems and as such the adequacy of our account is tested by trying to prove them. We use Luo’s Modern Type Theory with coercive subtyping as the formal language into (...)
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  • Figures of dialogue: a view from Ludics.Alain Lecomte & Myriam Quatrini - 2011 - Synthese 183 (S1):59-85.
    In this paper, we study dialogue as a game, but not only in the sense in which there would exist winning strategies and a priori rules. Dialogue is not governed by game rules like for chess or other games, since even if we start from a priori rules, it is always possible to play with them, provided that some invariant properties are preserved. An important discovery of Ludics is that such properties may be expressed in geometrical terms. The main feature (...)
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  • Meaning and dialogue coherence: A proof-theoretic investigation.Paul Piwek - 2007 - Journal of Logic, Language and Information 16 (4):403-421.
    This paper presents a novel proof-theoretic account of dialogue coherence. It focuses on an abstract class of cooperative information-oriented dialogues and describes how their structure can be accounted for in terms of a multi-agent hybrid inference system that combines natural deduction with information transfer and observation. We show how certain dialogue structures arise out of the interplay between the inferential roles of logical connectives (i.e., sentence semantics), a rule for transferring information between agents, and a rule for information flow between (...)
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  • Propositional Forms of Judgemental Interpretations.Tao Xue, Zhaohui Luo & Stergios Chatzikyriakidis - 2023 - Journal of Logic, Language and Information 32 (4):733-758.
    In formal semantics based on modern type theories, some sentences may be interpreted as judgements and some as logical propositions. When interpreting composite sentences, one may want to turn a judgemental interpretation or an ill-typed semantic interpretation into a proposition in order to obtain an intended semantics. For instance, an incorrect judgement $$a:A$$ may be turned into its propositional form $$\textsc {is}(A,a)$$ and an ill-typed application p(a) into $$\textsc {do}(p,a)$$, so that the propositional forms can take part in logical compositions (...)
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  • Dialogical Harmony: tonk, constructive type theory and rules for anonymous players.Juan Redmond & Shahid Rahman - unknown
    Recent literature on dialogical logic discusses the case of tonk and the notion harmony in the context of a rule-based theory of meaning. Now, since the publications of those papers, a dialogical version of constructive type theory has been developed. The aim of the present paper is to show that, from the dialogical point of view, the harmony of the CTT-rules is the consequence of a more fundamental level of meaning characterized by the independence of players. We hope that the (...)
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  • Meaning and Dialogue Coherence: A Proof-theoretic Investigation.Paul Piwek - 2008 - Journal of Logic, Language and Information 17 (3):383-383.
    This paper presents a novel proof-theoretic account of dialogue coherence. It focuses on an abstract class of cooperative information-oriented dialogues and describes how their structure can be accounted for in terms of a multi-agent hybrid inference system that combines natural deduction with information transfer and observation. We show how certain dialogue structures arise out of the interplay between the inferential roles of logical connectives (i.e., sentence semantics), a rule for transferring information between agents, and a rule for information flow between (...)
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  • Cut-Elimination and Quantification in Canonical Systems.Anna Zamansky & Arnon Avron - 2006 - 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 (...)
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  • Variable Handling and Compositionality: Comparing DRT and DTS.Yukiko Yana, Koji Mineshima & Daisuke Bekki - 2019 - Journal of Logic, Language and Information 28 (2):261-285.
    This paper provides a detailed comparison between discourse representation theory and dependent type semantics, two frameworks for discourse semantics. Although it is often stated that DRT and those frameworks based on dependent types are mutually exchangeable, we argue that they differ with respect to variable handling, more specifically, how substitution and other operations on variables are defined. This manifests itself in two recalcitrant problems posed for DRT; namely, the overwrite problem and the duplication problem. We will see that these problems (...)
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  • Implicit epistemic aspects of constructive logic.Göran Sundholm - 1997 - Journal of Logic, Language and Information 6 (2):191-212.
    In the present paper I wish to regard constructivelogic as a self-contained system for the treatment ofepistemological issues; the explanations of theconstructivist logical notions are cast in anepistemological mold already from the outset. Thediscussion offered here intends to make explicit thisimplicit epistemic character of constructivism.Particular attention will be given to the intendedinterpretation laid down by Heyting. This interpretation, especially as refined in the type-theoretical work of Per Martin-Löf, puts thesystem on par with the early efforts of Frege andWhitehead-Russell. This quite (...)
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  • Propositions as games as types.Aarne Ranta - 1988 - Synthese 76 (3):377 - 395.
    Without violating the spirit of Game-Theoretical semantics, its results can be re-worked in Martin-Löf''s Constructive Type Theory by interpreting games as types of Myself''s winning strategies. The philosophical ideas behind Game-Theoretical Semantics in fact highly recommend restricting strategies to effective ones, which is the only controversial step in our interpretation. What is gained, then, is a direct connection between linguistic semantics and computer programming.
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  • Handbook of philosophical logic. [REVIEW]Graham White - 2004 - History and Philosophy of Logic 25 (2):147-152.
    D. M. GABBAY and F. GUENTHER, Handbook of philosophical logic, 2nd edn, vol. 9. Dordrecht, Boston, London: Kluwer, 2002. xiv + 368 pp. €129.00, US$112.00, £79.00. ISBN1 402 00699 3. The philo...
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  • Constructing Situations and Time.Tim Fernando - 2011 - Journal of Philosophical Logic 40 (3):371 - 396.
    Situations serving as partial worlds as well as events in natural language semantics are constructed from a type-theoretic interpretation of firstorder formulae and (after a type reduction) temporal formulae. Limitations of the Russell-Wiener-Kamp derivation of time from events are discussed and overcome to give a more widely applicable account of temporal granularity. Finite situations are formulated as strings of observations, conceptualized to persist inertially (in the absence of forces).
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  • Expressing ‘the structure of’ in homotopy type theory.David Corfield - 2017 - Synthese 197 (2):681-700.
    As a new foundational language for mathematics with its very different idea as to the status of logic, we should expect homotopy type theory to shed new light on some of the problems of philosophy which have been treated by logic. In this article, definite description, and in particular its employment within mathematics, is formulated within the type theory. Homotopy type theory has been proposed as an inherently structuralist foundational language for mathematics. Using the new formulation of definite descriptions, opportunities (...)
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  • Antirealism and the Roles of Truth.B. G. Sundholm - unknown
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