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Wider Still And Wider...  Resetting The Bounds Of Logic
, 1997
"... Modern logic is often defined in terms of specific formal languages, rules, and calculi. Such architectural decisions about a field form a pervasive implicit definition which determines professional practice  through the structure of textbooks, as well as the research agenda that determines ' ..."
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Cited by 5 (1 self)
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Modern logic is often defined in terms of specific formal languages, rules, and calculi. Such architectural decisions about a field form a pervasive implicit definition which determines professional practice  through the structure of textbooks, as well as the research agenda that determines 'interest', and hence acceptance and academic status. Such a practice may come to contain a lot of historical accident, or force of habit. Therefore, it seems worth thinking about the defining agenda of a field once in a while. In this brief essay, we explore alternative views of logic, locating the nature of the field in more abstract themes, concerns and attitudes. The new definition does not remove the need for the old agenda, but we advocate a shift in emphasis, toward greater generality and range of application. The outcome is a conception of logic as a broad methodological stance, looking for invariants in (information) structures and processes. to appear in A. Varzi, ed. "The European Revie...
The Categorial FineStructure of Natural Language
, 2003
"... Categorial grammar analyzes linguistic syntax and semantics in terms of type theory and lambda calculus. A major attraction of this approach is its unifying power, as its basic function/argument structures occur across the foundations of mathematics, language and computation. This paper considers, i ..."
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Cited by 3 (1 self)
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Categorial grammar analyzes linguistic syntax and semantics in terms of type theory and lambda calculus. A major attraction of this approach is its unifying power, as its basic function/argument structures occur across the foundations of mathematics, language and computation. This paper considers, in a light examplebased manner, where this elegant logical paradigm stands when confronted with the wear and tear of reality. Starting from a brief history of the Lambek tradition since the 1980s, we discuss three main issues: (a) the fit of the lambda calculus engine to characteristic semantic structures in natural language, (b) the coexistence of the original typetheoretic and more recent modal interpretations of categorial logics, and (c) the place of categorial grammars in the complex total architecture of natural language, which involves  amongst others  mixtures of interpretation and inference.
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"... Abstract Categorial grammar analyzes linguistic syntax and semantics in terms of type theory and lambda calculus. A major attraction of this approach is its unifying power, as its basic function/argument structures occur across the foundations of mathematics, language and computation. This paper con ..."
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Abstract Categorial grammar analyzes linguistic syntax and semantics in terms of type theory and lambda calculus. A major attraction of this approach is its unifying power, as its basic function/argument structures occur across the foundations of mathematics, language and computation. This paper considers, in a light examplebased manner, where this elegant logical paradigm stands when confronted with the wear and tear of reality. Starting from a brief history of the Lambek tradition since the 1980s, we discuss three main issues: (a) the fit of the lambda calculus engine to characteristic semantic structures in natural language, (b) the coexistence of the original typetheoretic and more recent modal interpretations of categorial logics, and (c) the place of categorial grammars in the complex total architecture of natural language, which involves amongst others mixtures of interpretation and inference. 1 From Montague Grammar to Categorial Grammar Logic and linguistics have had lively connections from Antiquity right until today (GAMUT 1991). A recurrent theme in this history is the categorial structure of language and ontology, from Aristotle's grammatical categories to Russell's theory of types in the foundations of mathematics. Further bridges were thrown as logic and