David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
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Journal of Logic, Language and Information 5 (3-4):387-422 (1996)
This paper gives a simple method for providing categorial brands of feature-based unification grammars with a model-theoretic semantics. The key idea is to apply the paradigm of fibred semantics (or layered logics, see Gabbay (1990)) in order to combine the two components of a feature-based grammar logic. We demonstrate the method for the augmentation of Lambek categorial grammar with Kasper/Rounds-style feature logic. These are combined by replacing (or annotating) atomic formulas of the first logic, i.e. the basic syntactic types, by formulas of the second. Modelling such a combined logic is less trivial than one might expect. The direct application of the fibred semantics method where a combined atomic formula like np (num: sg & pers: 3rd) denotes those strings which have the indicated property and the categorial operators denote the usual left- and right-residuals of these string sets, does not match the intuitive, unification-based proof theory. Unification implements a global bookkeeping with respect to a proof whereas the direct fibring method restricts its view to the atoms of the grammar logic. The solution is to interpret the (embedded) feature terms as global feature constraints while maintaining the same kind of fibred structures. For this adjusted semantics, the anticipated proof system is sound and complete.
|Keywords||categorial grammar feature logics combination of logics unification grammars|
|Categories||categorize this paper)|
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References found in this work BETA
Dag Prawitz (1965). Natural Deduction: A Proof-Theoretical Study. Dover Publications.
Michael R. Garey & David S. Johnson (1983). Computers and Intractability. A Guide to the Theory of NP-Completeness. Journal of Symbolic Logic 48 (2):498-500.
Joachim Lambek (1968). The Mathematics of Sentence Structure. Journal of Symbolic Logic 33 (4):627-628.
David N. Yetter (1990). Quantales and (Noncommutative) Linear Logic. Journal of Symbolic Logic 55 (1):41-64.
Citations of this work BETA
Raffaella Bernardi & Anna Szabolcsi (2008). Optionality, Scope, and Licensing: An Application of Partially Ordered Categories. Journal of Logic, Language and Information 17 (3):237-283.
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