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  1. Tarek Sayed Ahmed (2002). Martin's Axiom, Omitting Types, and Complete Representations in Algebraic Logic. 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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  2. Jesús Alcolea Banegas (1988). Intuitionistic type theory. Theoria 4 (1):235-238.
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  3. P. B. Andrews (2002). An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof. 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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  4. George Bealer (1994). Property Theory: The Type-Free Approach V. The Church Approach. 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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  5. Maria Bittner (1999). Concealed Causatives. 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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  6. Maria Bittner (1994). Cross-Linguistic Semantics. 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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  7. Irving M. Copi (1971). The Theory of Logical Types. London,Routledge and K. Paul.
    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 ...
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  8. Duilio D'Alfonso (2011). Generalized Quantifiers: Logic and Language. 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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  9. Chris Fox & Shalom Lappin, A Type-Theoretic Approach to Anaphora and Ellipsis Resolution.
    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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  10. André Fuhrmann (2010). Russell´s Early Type Theory and the Paradox of Propositions. Principia 5 (1-2):19-42.
    The paradox of propositiOns, presented in Appenclix B of Russell's The Principies of Mathernatics (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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  11. Daniel Gallin (1972). Intensional and Higher-Order Modal Logic. [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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  12. Giorgio Lando (2012). Russell's Relations, Wittgenstein's Objects, and the Theory of Types. 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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  13. Shalom Lappin, Intensional First-Order Logic with Types.
    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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  14. David Liebesman (2015). Predication as Ascription. 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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  15. Ofra Magidor (2009). Category Mistakes Are Meaningful. 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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  16. Ofra Magidor (2009). The Last Dogma of Type Confusions. 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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  17. Richard Montague (1970). English as a Formal Language. In Bruno Visentini (ed.), Linguaggi nella societa e nella tecnica. Edizioni di Communita 188-221.
    I reject the contention that an important theoretical difference exists between formal and natural languages.
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  18. Dilip Ninan (2010). De Se Attitudes: Ascription and Communication. 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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  19. Giuseppe Primiero & Mariarosiaria Taddeo (2012). A Modal Type Theory for Formalizing Trusted Communications. 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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  20. Bartosz Więckowski (2012). A Constructive Type-Theoretical Formalism for the Interpretation of Subatomically Sensitive Natural Language Constructions. 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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  21. Juhani Yli-Vakkuri & James McGilvray (2010). Reference and Extension. In P. C. Horgan (ed.), The Cambridge Encyclopaedia of the Language Sciences. Cambridge University Press