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46 found
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  1. Copredication in homotopy type theory.Hamidreza Bahramian - manuscript
    This paper applies homotopy type theory to formal semantics of natural languages and proposes a new model for the linguistic phenomenon of copredication. Copredication refers to sentences where two predicates which assume different requirements for their arguments are asserted for one single entity, e.g., "the lunch was delicious but took forever". This paper is particularly concerned with copredication sentences with quantification, i.e., cases where the two predicates impose distinct criteria of quantification and individuation, e.g., "Fred picked up and mastered three (...)
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  2. Analyticity and Syntheticity in Type Theory Revisited.Bruno Bentzen - forthcoming - Review of Symbolic Logic.
    I discuss problems with Martin-Löf's distinction between analytic and synthetic judgments in constructive type theory and propose a revision of his views. I maintain that a judgment is analytic when its correctness follows exclusively from the evaluation of the expressions occurring in it. I argue that Martin-Löf's claim that all judgments of the forms a : A and a = b : A are analytic is unfounded. As I shall show, when A evaluates to a dependent function type (x : (...)
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  3. Review of Properties and Propositions: The Metaphysics of Higher-Order Logic by Robert Trueman. [REVIEW]Nicholas K. Jones - forthcoming - Mind.
    This is a review of "Properties and Propositions: The Metaphysics of Higher-Order Logic" by Robert Trueman. Following an overview of the main themes of the book, I discuss the metaphysical presuppositions of Trueman's Fregean notation for predicate abstraction and evaluate his argument for strict typing.
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  4. Propositions as types.Ansten Klev - forthcoming - In Hilary Nesi & Petar Milin (eds.), International Encyclopedia of Language and Linguistics. Elsevier.
    Treating propositions as types allows for a unified presentation of logic and type theory. Both fields thereby gain in expressive and deductive power. This chapter introduces the reader to a system of type theory where propositions are types. The system will be presented as an extension of the simple theory of types. Philosophical and historical observations are made along the way. A linguistic example is given at the end.
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  5. Engineering Existence?Lukas Skiba - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy.
    This paper investigates the connection between two recent trends in philosophy: higher-orderism and conceptual engineering. Higher-orderists use higher-order quantifiers (in particular quantifiers binding variables that occupy the syntactic positions of predicates) to express certain key metaphysical doctrines, such as the claim that there are properties. I argue that, on a natural construal, the higher-orderist approach involves an engineering project concerning, among others, the concept of existence. I distinguish between a modest construal of this project, on which it aims at engineering (...)
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  6. A fictionalist theory of universals.Tim Button & Robert Trueman - 2024 - In Peter Fritz & Nicholas K. Jones (eds.), Higher-Order Metaphysics. Oxford University Press.
    Universals are putative objects like wisdom, morality, redness, etc. Although we believe in properties (which, we argue, are not a kind of object), we do not believe in universals. However, a number of ordinary, natural language constructions seem to commit us to their existence. In this paper, we provide a fictionalist theory of universals, which allows us to speak as if universals existed, whilst denying that any really do.
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  7. Operands and Instances.Peter Fritz - 2023 - Review of Symbolic Logic 16 (1):188-209.
    Can conjunctive propositions be identical without their conjuncts being identical? Can universally quantified propositions be identical without their instances being identical? On a common conception of propositions, on which they inherit the logical structure of the sentences which express them, the answer is negative both times. Here, it will be shown that such a negative answer to both questions is inconsistent, assuming a standard type-theoretic formalization of theorizing about propositions. The result is not specific to conjunction and universal quantification, but (...)
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  8. Type Polymorphism, Natural Language Semantics, and TIL.Ivo Pezlar - 2023 - Journal of Logic, Language and Information 32 (2):275-295.
    Transparent intensional logic (TIL) is a well-explored type-theoretical framework for semantics of natural language. However, its treatment of polymorphic functions, which are essential for the analysis of various natural language phenomena, is still underdeveloped. In this paper, we address this issue and propose an extension of TIL that introduces polymorphism via type variables ranging over types and generalized variables ranging over constructions and types. Furthermore, we offer an analysis of sentences involving non-specific notional attitudes of the general form ‘_A_ considers (...)
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  9. Against Cumulative Type Theory.Tim Button & Robert Trueman - 2022 - Review of Symbolic Logic 15 (4):907-49.
    Standard Type Theory, STT, tells us that b^n(a^m) is well-formed iff n=m+1. However, Linnebo and Rayo have advocated the use of Cumulative Type Theory, CTT, has more relaxed type-restrictions: according to CTT, b^β(a^α) is well-formed iff β > α. In this paper, we set ourselves against CTT. We begin our case by arguing against Linnebo and Rayo’s claim that CTT sheds new philosophical light on set theory. We then argue that, while CTT ’s type-restrictions are unjustifiable, the type-restrictions imposed by (...)
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  10. Going Nowhere and Back: Is Trivialization the Same as Zero Execution?Ivo Pezlar - 2022 - In Pavel Materna & Bjørn Jespersen (eds.), Logically Speaking. A Festschrift for Marie Duží. College Publications. pp. 187-202.
    In this paper I will explore the question whether the Trivialization construction of transparent intensional logic (TIL) can be understood in terms of the Execution construction, specifically, in terms of its degenerate case known as the 0-Execution. My answer will be positive and the apparent contrast between the intuitive understanding of Trivialization and 0-Execution will be explained as a matter of distinct yet related informal perspectives, not as a matter of technical or conceptual differences.
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  11. (1 other version)Overgeneration in the higher infinite.Salvatore Florio & Luca Incurvati - 2021 - In Gil Sagi & Jack Woods (eds.), The Semantic Conception of Logic : Essays on Consequence, Invariance, and Meaning. New York, NY: Cambridge University Press.
    The Overgeneration Argument is a prominent objection against the model-theoretic account of logical consequence for second-order languages. In previous work we have offered a reconstruction of this argument which locates its source in the conflict between the neutrality of second-order logic and its alleged entanglement with mathematics. Some cases of this conflict concern small large cardinals. In this article, we show that in these cases the conflict can be resolved by moving from a set-theoretic implementation of the model-theoretic account to (...)
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  12. Unrestricted Quantification and the Structure of Type Theory.Salvatore Florio & Nicholas K. Jones - 2021 - Philosophy and Phenomenological Research 102 (1):44-64.
    Semantic theories based on a hierarchy of types have prominently been used to defend the possibility of unrestricted quantification. However, they also pose a prima facie problem for it: each quantifier ranges over at most one level of the hierarchy and is therefore not unrestricted. It is difficult to evaluate this problem without a principled account of what it is for a quantifier to be unrestricted. Drawing on an insight of Russell’s about the relationship between quantification and the structure of (...)
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  13. (1 other version)Overgeneration in the higher infinite.Luca Incurvarti & Salvatore Florio - 2021 - In Gil Sagi & Jack Woods (eds.), The Semantic Conception of Logic : Essays on Consequence, Invariance, and Meaning. New York, NY: Cambridge University Press.
    The Overgeneration Argument is a prominent objection against the model-theoretic account of logical consequence for second-order languages. In previous work we have offered a reconstruction of this argument which locates its source in the conflict between the neutrality of second-order logic and its alleged entanglement with mathematics. Some cases of this conflict concern small large cardinals. In this article, we show that in these cases the conflict can be resolved by moving from a set-theoretic implementation of the model-theoretic account to (...)
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  14. On Different Ways of Being Equal.Bruno Bentzen - 2020 - Erkenntnis 87 (4):1809-1830.
    The aim of this paper is to present a constructive solution to Frege's puzzle (largely limited to the mathematical context) based on type theory. Two ways in which an equality statement may be said to have cognitive significance are distinguished. One concerns the mode of presentation of the equality, the other its mode of proof. Frege's distinction between sense and reference, which emphasizes the former aspect, cannot adequately explain the cognitive significance of equality statements unless a clear identity criterion for (...)
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  15. Sense, reference, and computation.Bruno Bentzen - 2020 - Perspectiva Filosófica 47 (2):179-203.
    In this paper, I revisit Frege's theory of sense and reference in the constructive setting of the meaning explanations of type theory, extending and sharpening a program–value analysis of sense and reference proposed by Martin-Löf building on previous work of Dummett. I propose a computational identity criterion for senses and argue that it validates what I see as the most plausible interpretation of Frege's equipollence principle for both sentences and singular terms. Before doing so, I examine Frege's implementation of his (...)
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  16. What Types Should Not Be.Bruno Bentzen - 2020 - Philosophia Mathematica 28 (1):60-76.
    In a series of papers Ladyman and Presnell raise an interesting challenge of providing a pre-mathematical justification for homotopy type theory. In response, they propose what they claim to be an informal semantics for homotopy type theory where types and terms are regarded as mathematical concepts. The aim of this paper is to raise some issues which need to be resolved for the successful development of their types-as-concepts interpretation.
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  17. Formal Semantics and Applied Mathematics: An Inferential Account.Ryan M. Nefdt - 2020 - Journal of Logic, Language and Information 29 (2):221-253.
    In this paper, I utilise the growing literature on scientific modelling to investigate the nature of formal semantics from the perspective of the philosophy of science. Specifically, I incorporate the inferential framework proposed by Bueno and Colyvan : 345–374, 2011) in the philosophy of applied mathematics to offer an account of how formal semantics explains and models its data. This view produces a picture of formal semantic models as involving an embedded process of inference and representation applying indirectly to linguistic (...)
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  18. 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. 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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  19. Montague's treatment of determiner phrases: A philosophical introduction.Ken Akiba - 2018 - Philosophy Compass 13 (6):e12496.
    This paper introduces Richard Montague's theory of determiner phrases to the philosophically oriented readers who are familiar with Russell's traditional treatment. Determiner phrases include not only quantifier phrases in the narrow sense, such as every man, some woman, and nothing, but also DP conjunctions such as Adam and Betty and Adam or Betty, and even proper names such as Adam and Betty. Montague treats all determiner phrases as belonging to type t, i.e., the type of functions from properties of individuals (...)
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  20. Static and dynamic vector semantics for lambda calculus models of natural language.Mehrnoosh Sadrzadeh & Reinhard Muskens - 2018 - Journal of Language Modelling 6 (2):319-351.
    Vector models of language are based on the contextual aspects of language, the distributions of words and how they co-occur in text. Truth conditional models focus on the logical aspects of language, compositional properties of words and how they compose to form sentences. In the truth conditional approach, the denotation of a sentence determines its truth conditions, which can be taken to be a truth value, a set of possible worlds, a context change potential, or similar. In the vector models, (...)
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  21. Predication as Ascription.David Liebesman - 2015 - Mind 124 (494):517-569.
    I articulate and defend a necessary and sufficient condition for predication. The condition is that a term or term-occurrence stands in the relation of ascription to its designatum, ascription being a fundamental semantic relation that differs from reference. This view has dramatically different semantic consequences from its alternatives. After outlining the alternatives, I draw out these consequences and show how they favour the ascription view. I then develop the view and elicit a number of its virtues.
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  22. Category Mistakes.Ofra Magidor - 2013 - Oxford, GB: Oxford University Press.
    Category mistakes are sentences such as 'Green ideas sleep furiously' or 'Saturday is in bed'. They strike us as highly infelicitous but it is hard to explain precisely why this is so. Ofra Magidor explores four approaches to category mistakes in philosophy of language and linguistics, and develops and defends an original, presuppositional account.
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  23. Russell's Relations, Wittgenstein's Objects, and the Theory of Types.Giorgio Lando - 2012 - Teorema: International Journal of Philosophy (2):21-35.
    We discuss a previously unnoticed resemblance between the theory of relations and predicates in The Philosophy of Logical Atomism [TPLA] by Russell and the theory of objects and names in the Tractatus Logico-Philosophicus [TLP] by Wittgenstein. Points of likeness are detected on three levels: ontology, syntax, and semantics. This analogy explains the prima facie similarities between the informal presentation of the theory of types in TPLA and the sections of the TLP devoted to this same topic. Eventually, we draw some (...)
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  24. A modal type theory for formalizing trusted communications.Giuseppe Primiero & Mariarosaria Taddeo - 2012 - Journal of Applied Logic 10 (1):92-114.
    This paper introduces a multi-modal polymorphic type theory to model epistemic processes characterized by trust, defined as a second-order relation affecting the communication process between sources and a receiver. In this language, a set of senders is expressed by a modal prioritized context, whereas the receiver is formulated in terms of a contextually derived modal judgement. Introduction and elimination rules for modalities are based on the polymorphism of terms in the language. This leads to a multi-modal non-homogeneous version of a (...)
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  25. 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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  26. Generalized Quantifiers: Logic and Language.Duilio D'Alfonso - 2011 - Logic and Philosophy of Science 9 (No. 1):85-94.
    The Generalized Quantifiers Theory, I will argue, in the second half of last Century has led to an important rapprochement, relevant both in logic and in linguistics, between logical quantification theories and the semantic analysis of quantification in natural languages. In this paper I concisely illustrate the formal aspects and the theoretical implications of this rapprochement.
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  27. De se attitudes: Ascription and communication.Dilip Ninan - 2010 - Philosophy Compass 5 (7):551-567.
    This paper concerns two points of intersection between de se attitudes and the study of natural language: attitude ascription and communication. I first survey some recent work on the semantics of de se attitude ascriptions, with particular attention to ascriptions that are true only if the subject of the ascription has the appropriate de se attitude. I then examine – and attempt to solve – some problems concerning the role of de se attitudes in linguistic communication.
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  28. Reference and Extension.Juhani Yli-Vakkuri & James McGilvray - 2010 - In Patrick Colm Hogan (ed.), The Cambridge Encyclopaedia of the Language Sciences. Cambridge, U.K: Cambridge University Press.
  29. Category mistakes are meaningful.Ofra Magidor - 2009 - Linguistics and Philosophy 32 (6):553-581.
    Category mistakes are sentences such as ‘Colourless green ideas sleep furiously’ or ‘The theory of relativity is eating breakfast’. Such sentences are highly anomalous, and this has led a large number of linguists and philosophers to conclude that they are meaningless (call this ‘the meaninglessness view’). In this paper I argue that the meaninglessness view is incorrect and category mistakes are meaningful. I provide four arguments against the meaninglessness view: in Sect. 2, an argument concerning compositionality with respect to category (...)
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  30. The last dogma of type confusions.Ofra Magidor - 2009 - Proceedings of the Aristotelian Society 109 (1pt1):1-29.
    In this paper I discuss a certain kind of 'type confusion' which involves use of expressions of the wrong grammatical category, as in the string 'runs eats'. It is (nearly) universally accepted that such strings are meaningless. My purpose in this paper is to question this widespread assumption (or as I call it, 'the last dogma'). I discuss a range of putative reasons for accepting the last dogma: in §II, semantic and metaphysical reasons; in §III, logical reasons; and in §IV, (...)
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  31. Language, Lambdas, and Logic.Reinhard Muskens - 2003 - In R. Oehrle & J. Kruijff (eds.), resource sensitivity, binding, and anaphora. kluwer. pp. 23--54.
    The paper develops Lambda Grammars, a form of categorial grammar that, unlike other categorial formalisms, is non-directional. Linguistic signs are represented as sequences of lambda terms and are combined with the help of linear combinators.
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  32. Martin's axiom, omitting types, and complete representations in algebraic logic.Tarek Sayed Ahmed - 2002 - Studia Logica 72 (2):285 - 309.
    We give a new characterization of the class of completely representable cylindric algebras of dimension 2 #lt; n w via special neat embeddings. We prove an independence result connecting cylindric algebra to Martin''s axiom. Finally we apply our results to finite-variable first order logic showing that Henkin and Orey''s omitting types theorem fails for L n, the first order logic restricted to the first n variables when 2 #lt; n#lt;w. L n has been recently (and quite extensively) studied as a (...)
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  33. (1 other version)An introduction to mathematical logic and type theory: to truth through proof.Peter Bruce Andrews - 2002 - Boston: Kluwer Academic Publishers.
    This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs (...)
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  34. Russell´s Early Type Theory and the Paradox of Propositions.André Fuhrmann - 2001 - Principia: An International Journal of Epistemology 5 (1-2):19–42.
    The paradox of propositions, presented in Appendix B of Russell's The Principles of Mathematics (1903), is usually taken as Russell's principal motive, at the time, for moving from a simple to a ramified theory of types. I argue that this view is mistaken. A closer study of Russell's correspondence with Frege reveals that Russell carne to adopt a very different resolution of the paradox, calling into question not the simplicity of his early type theory but the simplicity of his early (...)
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  35. Concealed causatives.Maria Bittner - 1999 - Natural Language Semantics 7 (1):1-78.
    Crosslinguistically, causative constructions conform to the following generalization: If the causal relation is syntactically concealed, then it is semantically direct. Concealed causatives span a wide syntactic spectrum, ranging from resultative complements in English to causative subjects in Miskitu. A unified type-driven theory is proposed which attributes the understood causal relation—and other elements of constructional meaning—to type lifting operations predictably licensed by type mismatch at LF. The proposal has far-reaching theoretical implications not only for the theory of compositionality and causation, but (...)
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  36. (1 other version)Meaning and Partiality.Reinhard Muskens - 1995 - Stanford, CA: CSLI Publications.
    This book radically simplifies Montague Semantics and generalizes the theory by basing it on a partial higher order logic. The resulting theory is a synthesis of Montague Semantics and Situation Semantics. In the late sixties Richard Montague developed the revolutionary idea that we can understand the concept of meaning in ordinary languages much in the same way as we understand the semantics of logical languages. Unfortunately, however, he formalized his idea in an unnecessarily complex way - two outstanding researchers in (...)
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  37. Property theory: The Type-Free Approach v. the Church Approach.George Bealer - 1994 - Journal of Philosophical Logic 23 (2):139 - 171.
    In a lengthy review article, C. Anthony Anderson criticizes the approach to property theory developed in Quality and Concept (1982). That approach is first-order, type-free, and broadly Russellian. Anderson favors Alonzo Church’s higher-order, type-theoretic, broadly Fregean approach. His worries concern the way in which the theory of intensional entities is developed. It is shown that the worries can be handled within the approach developed in the book but they remain serious obstacles for the Church approach. The discussion focuses on: (1) (...)
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  38. Cross-linguistic semantics.Maria Bittner - 1994 - Linguistics and Philosophy 17 (1):53 - 108.
    Rooth & Partee (1982) and Rooth (1985) have shown that the English-specific rule-by-rule system of PTQ can be factored out into function application plus two transformations for resolving type mismatch (type lifting and variable binding). Building on these insights, this article proposes a universal system for type-driven translation, by adding two more innovations: local type determination for gaps (generalizing Montague 1973) and a set of semantic filters (extending Cooper 1983). This system, dubbed Cross-Linguistic Semantics (XLS), is shown to account for (...)
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  39. Categorial grammar and discourse representation theory.Reinhard Muskens - 1994 - In Yorick Wilks (ed.), Proceedings of COLING 94. Kyoto: pp. 508-514.
    In this paper it is shown how simple texts that can be parsed in a Lambek Categorial Grammar can also automatically be provided with a semantics in the form of a Discourse Representation Structure in the sense of Kamp [1981]. The assignment of meanings to texts uses the Curry-Howard-Van Benthem correspondence.
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  40. Tense and the logic of change.Reinhard Muskens - 1991 - In Talking about Trees and Truth-Conditions. Springer Verlag. pp. 147-183.
    In this paper it is shown how the DRT (Discourse Representation Theory) treatment of temporal anaphora can be formalized within a version of Montague Semantics that is based on classical type logic.
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  41. (1 other version)Intuitionistic type theory. [REVIEW]Jesús Alcolea Banegas - 1988 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 4 (1):235-238.
  42. Intensional and higher-order modal logic.Daniel Gallin - 1972 - [Berkeley,: [Berkeley.
    INTENSIONAL LOGIC §1. Natural Language and Intensional Logic When we speak of a theory of meaning for a natural language such as English, we have in mind an ...
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  43. The Theory of Logical Types.Irving Marmer Copi - 1971 - London: Routledge.
    This reissue, first published in 1971, provides a brief historical account of the Theory of Logical Types; and describes the problems that gave rise to it, its various different formulations, the difficulties connected with each, and the criticisms that have been directed against it. Professor Copi seeks to make the subject accessible to the non-specialist and yet provide a sufficiently rigorous exposition for the serious student to see exactly what the theory is and how it works.
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  44. English as a Formal Language.Richard Montague - 1970 - In B. Visentini (ed.), Linguaggi Nella Societ\'{a} e Nella Tecnica'. Edizioni di Communita. pp. 188-221.
    I reject the contention that an important theoretical difference exists between formal and natural languages.
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  45. A Type-Theoretic Approach to Anaphora and Ellipsis Resolution.Shalom Lappin & C. Fox - unknown
    We present an approach to anaphora and ellipsis resolution in which pronouns and elided structures are interpreted by the dynamic identification in discourse of type constraints on their semantic representations. The content of these conditions is recovered in context from an antecedent expression. The constraints define separation types in Property Theory with Curry Typing, an expressive first-order logic with Curry typing that we have proposed as a formal framework for natural language semantics.
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  46. Intensional first-order logic with types.Shalom Lappin - unknown
    The paper presents Property Theory with Curry Typing (PTCT) where the language of terms and well-formed formulæ are joined by a language of types. In addition to supporting fine-grained intensionality, the basic theory is essentially first-order, so that implementations using the theory can apply standard first-order theorem proving techniques. Some extensions to the type theory are discussed, type polymorphism, and enriching the system with sufficient number theory to account for quantifiers of proportion, such as “most.”.
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