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  1. Translating a Fragment of Natural Deduction System for Natural Language Into Modern Type Theory.Ivo Pezlar - 2019 - In Rainer Osswald, Christian Retoré & Peter Sutton (eds.), Proceedings of the IWCS 2019 Workshop on Computing Semantics with Types, Frames and Related Structures. Stroudsburg, PA: Association for Computational Linguistics. pp. 10-18.
    In this paper, we investigate the possibility of translating a fragment of natural deduction system (NDS) for natural language semantics into modern type theory (MTT), originally suggested by Luo (2014). Our main goal will be to examine and translate the basic rules of NDS (namely, meta-rules, structural rules, identity rules, noun rules and rules for intersective and subsective adjectives) to MTT. Additionally, we will also consider some of their general features.
     
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  • Proof-Theoretic Reconstruction of Generalized Quantifiers.Nissim Francez & Gilad Ben-Avi - 2015 - Journal of Semantics 32 (3):313-371.
  • What is Inferentialism?Jaroslav Peregrin - unknown
    Inferentialism is the conviction that to be meaningful in the distinctively human way, or to have a 'conceptual content', is to be governed by a certain kind of inferential rules. The term was coined by Robert Brandom as a label for his theory of language; however, it is also naturally applicable (and is growing increasingly common) within the philosophy of logic.
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  • In Defence of Axiomatic Semantics.Chris Fox & Raymond Turner - 2012 - In Piotr Stalmaszcyzk (ed.), Philosophical and Formal Approaches to Linguistic Analysis. Ontos Verlag. pp. 145.
    We may wonder about the status of logical accounts of the meaning of language. When does a particular proposal count as a theory? How do we judge a theory to be correct? What criteria can we use to decide whether one theory is “better” than another? Implicitly, many accounts attribute a foundational status to set theory, and set-theoretic characterisations of possible worlds in particular. The goal of a semantic theory is then to find a translation of the phenomena of interest (...)
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  • Proof-Theoretic Semantics.Peter Schroeder-Heister - forthcoming - Stanford Encyclopedia of Philosophy.
  • Compositionality and the Prospect of a Pluralistic Semantic Theory.Adam C. Podlaskowski - 2019 - Australasian Journal of Philosophy 97 (2):325-339.
    A semantic theory is committed to semantic monism just in case every particular semantic property posited by the theory is a member of the same kind. The commitment to semantic monism appears to draw some support from the need to provide a compositional semantics, since taking a single kind of semantic property as key to a semantic theory affords a uniform pattern on the basis of which the meaning of any given sentence can be compositionally determined. This line of support (...)
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  • The Philosophy of Linguistics: Scientific Underpinnings and Methodological Disputes.Ryan M. Nefdt - 2019 - Philosophy Compass 14 (12).
    This article surveys the philosophical literature on theoretical linguistics. The focus of the paper is centred around the major debates in the philosophy of linguistics, past and present, with specific relation to how they connect to the philosophy of science. Specific issues such as scientific realism in linguistics, the scientific status of grammars, the methodological underpinnings of formal semantics, and the integration of linguistics into the larger cognitive sciences form the crux of the discussion.
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  • Constructive Belief Reports.Bartosz Więckowski - 2015 - Synthese 192 (3):603-633.
    The paper develops a proof-theoretic semantics for belief reports by extending the constructive type-theoretical formalism presented in Więckowski with a specific kind of set-forming operator suited for the representation of belief attitudes. The extended formalism allows us to interpret constructions which involve, e.g., iteration of belief, quantifying into belief contexts, and anaphora in belief reports. Moreover, constructive solutions to canonical instances of the problem of hyperintensionality are suggested. The paper includes a discussion of Ranta’s constructive account of belief reports.
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  • A Constructive Type-Theoretical Formalism for the Interpretation of Subatomically Sensitive Natural Language Constructions.Bartosz Więckowski - 2012 - Studia Logica 100 (4):815-853.
    The analysis of atomic sentences and their subatomic components poses a special problem for proof-theoretic approaches to natural language semantics, as it is far from clear how their semantics could be explained by means of proofs rather than denotations. The paper develops a proof-theoretic semantics for a fragment of English within a type-theoretical formalism that combines subatomic systems for natural deduction [20] with constructive (or Martin-Löf) type theory [8, 9] by stating rules for the formation, introduction, elimination and equality of (...)
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  • A Note on Harmony.Nissim Francez & Roy Dyckhoff - 2012 - Journal of Philosophical Logic 41 (3):613-628.
    In the proof-theoretic semantics approach to meaning, harmony , requiring a balance between introduction-rules (I-rules) and elimination rules (E-rules) within a meaning conferring natural-deduction proof-system, is a central notion. In this paper, we consider two notions of harmony that were proposed in the literature: 1. GE-harmony , requiring a certain form of the E-rules, given the form of the I-rules. 2. Local intrinsic harmony : imposes the existence of certain transformations of derivations, known as reduction and expansion . We propose (...)
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  • Bilateralism in Proof-Theoretic Semantics.Nissim Francez - 2014 - Journal of Philosophical Logic 43 (2-3):239-259.
    The paper suggests a revision of the notion of harmony, a major necessary condition in proof-theoretic semantics for a natural-deduction proof-system to qualify as meaning conferring, when moving to a bilateral proof-system. The latter considers both forces of assertion and denial as primitive, and is applied here to positive logics, lacking negation altogether. It is suggested that in addition to the balance between introduction and elimination rules traditionally imposed by harmony, a balance should be imposed also on: negative introduction and (...)
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  • A Logic Inspired by Natural Language: Quantifiers As Subnectors.Nissim Francez - 2014 - Journal of Philosophical Logic 43 (6):1153-1172.
    Inspired by the grammar of natural language, the paper presents a variant of first-order logic, in which quantifiers are not sentential operators, but are used as subnectors . A quantified term formed by a subnector is an argument of a predicate. The logic is defined by means of a meaning-conferring natural-deduction proof-system, according to the proof-theoretic semantics program. The harmony of the I/E-rules is shown. The paper then presents a translation, called the Frege translation, from the defined logic to standard (...)
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  • Proof-Theoretic Semantics for Subsentential Phrases.Nissim Francez, Roy Dyckhoff & Gilad Ben-Avi - 2010 - Studia Logica 94 (3):381-401.
    The paper briefly surveys the sentential proof-theoretic semantics for fragment of English. Then, appealing to a version of Frege’s context-principle (specified to fit type-logical grammar), a method is presented for deriving proof-theoretic meanings for sub-sentential phrases, down to lexical units (words). The sentential meaning is decomposed according to the function-argument structure as determined by the type-logical grammar. In doing so, the paper presents a novel proof-theoretic interpretation of simple type, replacing Montague’s model-theoretic type interpretation (in arbitrary Henkin models). The domains (...)
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  • Bilateralism in Proof-Theoretic Semantics.Nissim Francez - 2013 - Journal of Philosophical Logic (2-3):1-21.
    The paper suggests a revision of the notion of harmony, a major necessary condition in proof-theoretic semantics for a natural-deduction proof-system to qualify as meaning conferring, when moving to a bilateral proof-system. The latter considers both forces of assertion and denial as primitive, and is applied here to positive logics, lacking negation altogether. It is suggested that in addition to the balance between (positive) introduction and elimination rules traditionally imposed by harmony, a balance should be imposed also on: (i) negative (...)
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  • Characterizing Generics Are Material Inference Tickets: A Proof-Theoretic Analysis.Preston Stovall - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy:1-37.
    ABSTRACTAn adequate semantics for generic sentences must stake out positions across a range of contested territory in philosophy and linguistics. For this reason the study of generic sentences is a venue for investigating different frameworks for understanding human rationality as manifested in linguistic phenomena such as quantification, classification of individuals under kinds, defeasible reasoning, and intensionality. Despite the wide variety of semantic theories developed for generic sentences, to date these theories have been almost universally model-theoretic and representational. This essay outlines (...)
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  • Proof-Theoretic Semantics for Natural Language.Nissim Francez - forthcoming - Topoi:1-15.
    The paper has two parts: 1. A brief exposition of proof-theoretic semantics, not necessarily in connection to natural language. 2. A review, with a contrastive flavour, of some of the applications of PTS to NL with an indication of advantages of PTS as a theory of meaning for NL.
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  • Truth-Conditional Cognitivism and the Lexical Problem.Fabrizio Calzavarini - forthcoming - Topoi:1-12.
    When dealing with ‘meaning’ or related notions, one cannot ignore what for a long time was the dominant paradigm in semantics. According to such paradigm, truth-conditional formal semantics for natural language is a theory of semantic competence. In this article, I shall discuss a foundational problem for such semantic program. I shall first be following authors who claim that truth-conditional formal semantics is unable to provide a complete account of lexical competence, and, therefore, it suffers from incompleteness. Moreover, as a (...)
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  • Harmonious Rules for Identity.Owen Griffiths - 2014 - Review of Symbolic Logic 7 (3):499-510.
  • Subatomic Natural Deduction for a Naturalistic First-Order Language with Non-Primitive Identity.Bartosz Więckowski - 2016 - Journal of Logic, Language and Information 25 (2):215-268.
    A first-order language with a defined identity predicate is proposed whose apparatus for atomic predication is sensitive to grammatical categories of natural language. Subatomic natural deduction systems are defined for this naturalistic first-order language. These systems contain subatomic systems which govern the inferential relations which obtain between naturalistic atomic sentences and between their possibly composite components. As a main result it is shown that normal derivations in the defined systems enjoy the subexpression property which subsumes the subformula property with respect (...)
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  • On a Distinction of Two Facets of Meaning and its Role in Proof-Theoretic Semantics.Nissim Francez - 2015 - Logica Universalis 9 (1):121-127.
    I show that in the context of proof-theoretic semantics, Dummett’s distinction between the assertoric meaning of a sentence and its ingredient sense can be seen as a distinction between two proof-theoretic meanings of a sentence: 1.Meaning as a conclusion of an introduction rule in a meaning-conferring natural-deduction proof system. 2.Meaning as a premise of an introduction rule in a meaning-conferring natural-deduction proof system. The effect of this distinction on compositionality of proof-theoretic meaning is discussed.
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  • Harmony in Multiple-Conclusion Natural-Deduction.Nissim Francez - 2014 - Logica Universalis 8 (2):215-259.
    The paper studies the extension of harmony and stability, major themes in proof-theoretic semantics, from single-conclusion natural-deduction systems to multiple -conclusions natural-deduction, independently of classical logic. An extension of the method of obtaining harmoniously-induced general elimination rules from given introduction rules is suggested, taking into account sub-structurality. Finally, the reductions and expansions of the multiple -conclusions natural-deduction representation of classical logic are formulated.
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  • A Proof-Theoretic Universal Property of Determiners.Nissim Francez - 2015 - Journal of Applied Logic 13 (4):799-808.
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