David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Linguistics and Philosophy 18 (2):175 - 219 (1995)
Discontinuity refers to the character of many natural language constructions wherein signs differ markedly in their prosodic and semantic forms. As such it presents interesting demands on monostratal computational formalisms which aspire to descriptive adequacy. Pied piping, in particular, is argued by Pollard (1988) to motivate phrase structure-style feature percolation. In the context of categorial grammar, Bach (1981, 1984), Moortgat (1988, 1990, 1991) and others have sought to provide categorial operators suited to discontinuity. These attempts encounter certain difficulties with respect to model theory and/or proof theory, difficulties which the current proposals are intended to resolve.Lambek calculus is complete for interpretation byresiduation with respect to the adjunction operation of groupoid algebras (Buszkowski 1986). In Moortgat and Morrill (1991) it is shown how to give calculi for families of categorial operators, each defined by residuation with respect to an operation of prosodic adjunction (associative, non-associative, or with interactive axioms). The present paper treats discontinuity in this way, by residuation with respect to three adjunctions: + (associative), (.,.) (split-point marking), andW (wrapping) related by the equations 1+s 2+s 3=(s 1,s 3)Ws 2. We show how the resulting methods apply to discontinuous functors, quantifier scope and quantifier scope ambiguity, pied piping, and subject and object antecedent reflexivisation.
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References found in this work BETA
Dag Prawitz (1965/2006). Natural Deduction: A Proof-Theoretical Study. Dover Publications.
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Citations of this work BETA
Glyn Morrill, Oriol Valentín & Mario Fadda (2011). The Displacement Calculus. Journal of Logic, Language and Information 20 (1):1-48.
Graeme Forbes (2010). Intensional Verbs in Event Semantics. Synthese 176 (2):227 - 242.
Glyn Morrill (1996). Grammar and Logic. Theoria 62 (3):260-293.
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