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Categories of First-Order Quantifiers

In Urszula Wybraniec-Skardowska & Ángel Garrido (eds.), The Lvov-Warsaw School. Past and Present. Basel, Switzerland: pp. 575-597 (2018)

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  1. On Language Adequacy.Urszula Wybraniec-Skardowska - 2015 - Studies in Logic, Grammar and Rhetoric 40 (1):257-292.
    The paper concentrates on the problem of adequate reflection of fragments of reality via expressions of language and inter-subjective knowledge about these fragments, called here, in brief, language adequacy. This problem is formulated in several aspects, the most being: the compatibility of language syntax with its bi-level semantics: intensional and extensional. In this paper, various aspects of language adequacy find their logical explication on the ground of the formal-logical theory T of any categorial language L generated by the so-called classical (...)
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  • Categories of First -Order Quantifiers.Urszula Wybraniec-Skardowska - 2018 - Lvov-Warsaw School. Past and Present.
    One well known problem regarding quantifiers, in particular the 1st order quantifiers, is connected with their syntactic categories and denotations.The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized first-order languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of language expressions. In the paper the principle is introduced for categorial languages generated (...)
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  • Logical and Philosophical Ideas in Certain Formal Approaches to Language.Urszula Wybraniec-Skardowska - 1998 - Synthese 116 (2):231-277.
    This paper reminds, puts in order, sketches and also initiates some researches from the field of logic and philosophy of language. It lays emphasis on the logical-linguistic and ontological developmental lines originated with Polish researchers. The author discusses two opposite orientations of the former line in the process of formalization of language, called here nominalistic and Platonistic. The paper mentions the author's result (1989; 1991) concerning theoretical equivalence of two axiomatic approaches to language syntax which take into consideration these two (...)
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  • Categorial Languages and Variable-Binding Operators.Adam Nowaczyk - 1978 - Studia Logica 37 (1):27 - 39.
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  • Über Sinn Und Bedeutung.G. Frege - 1892 - Philosophical Review 1:574.
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  • Combinatory Logic.CURRY & FEYS - 1958
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  • Theory of Language Syntax. Categorial Approach.Urszula Wybraniec-Skardowska - 1991 - Dordrecht/Boston/London: Kluwer Academic Publishers.
    This book presents a formal and philosophical analysis of language syntax. It refers to some ideas of E.Husserl and G. Frege, to S. Leśniewski's theory of syntactic categories and K. Ajdukiewicz's conception of formal grammar, also to Ch.S. Pierces's distinction between tokens (concrete linguistic entities) and types (ideal linguistic entities) and to A.A. Markov's theory of algorithms. The central aim of the book is - in the spirit of these ideas - to provide both strict yet comprehensive lectures on two (...)
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  • Universal Grammar.Richard Montague - 1970 - Theoria 36 (3):373--398.
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  • Combinators and Categorial Grammar.Peter Simons - 1989 - Notre Dame Journal of Formal Logic 30 (2):241-261.
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  • Die Grundlagen der Arithmetik. Eine logisch mathematische Untersuchung über den Begriff der Zahl.Gottlob Frege - 1996 - Wittgenstein-Studien 3 (2):993-999.
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  • On a Generalization of Quantifiers.Andrzej Mostowski - 1957 - Fundamenta Mathematicae 44 (2):12--36.
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  • The Semantic Conception of Truth and the Foundations of Semantics.Alfred Tarski - 1944 - Journal of Symbolic Logic 9 (3):68-68.
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  • Begriffschrift, eine der Arithmetischen nachgebildete Formelsprache des reinen Denkens.Gottlob Frege - 1879 - Revue Philosophique de la France Et de l'Etranger 8:108-109.
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  • Languages with Variable-Binding Operators: Categorial Syntax and Combinatorial Semantics.Peter Simons - 2006 - Poznan Studies in the Philosophy of the Sciences and the Humanities 89:239.
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  • Über Die Grundlagen der Ontologie.Stanisław Le'sniewski - 1930 - Sprawozdania Z Posiedze'n Towarzystwa Naukowego Warszawskiego, Wydział Nauk Matematyczno-Fizycznych 23:111-132.
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  • Essays in Logical Semantics.J. F. A. K. van Benthem - 1986
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  • Combinatory Logic.Haskell B. Curry - 1958 - Amsterdam: North-Holland Pub. Co..
    CHAPTER Addenda to Pure Combinatory Logic This chapter will treat various additions to, and modifications of, the subject matter of Chapters-7. ...
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  • First order predicate logic with generalized quantifiers.Per Lindström - 1966 - Theoria 32 (3):186--195.
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  • Ontology in the Tractatus of L. Wittgenstein.Roman Suszko - 1968 - Notre Dame Journal of Formal Logic 9 (1):7-33.
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