TAILIEUCHUNG - Báo cáo khoa học: "Parsing with polymorphism"

Certain phenomena resist coverage within the Lambek Calculus, such as scopeambiguity and non-peripheral extraction. I have argued in previous work that an extension called Polymorphic Lambek Calculus (PLC), which adds variables and their universal quantification, covers these phenomena. However, a major problem is the absence of a known decision procedure for PLC grammars. This paper proposes a decision procedure which covers a subset of all the possible PLC grammars, a subset which, however, includes the PLC grammars with wide coverage. . | Parsing with polymorphism Martin Emms The CIS Leopoldstr 139 8000 Munchen 40 Germany Abstract Certain phenomena resist coverage within the Lambek Calculus such as scopeambiguity and non-peripheral extraction. I have argued in previous work that an extension called Polymorphic Lambek Calculus PLC which adds variables and their universal quantification covers these phenomena. However a major problem is the absence of a known decision procedure for PLC grammars. This paper proposes a decision procedure which covers a subset of all the possible PLC grammars a subset which however includes the PLC grammars with wide coverage. The decision procedure is shown to be terminating and correct and a Prolog implementation of it is described. 1 The Lambek Calculus To begin I give a brief description of Lambek categorial grammar Lambek 1958 . The categories are built up from basic categories using the binary categorial connectives 7 and 1 Then a set of categorial rules involving these categories is defined of the form Xi . .xn y n 1 Xi and y being categories. A distinctive feature is that the set of rules is defined inductively. Using a term adopted from This work was done whilst the author was in receipt of a six month scholarship from the German Academic Exchange Service whose support is gratefully acknowledged 1Lambek also considered a third connective the product . I in common with several authors use the name Lambek calculus to refer to what is really the product-free calculus logic sequent in place of categorial rule Lambek presented this inductive definition as a close variant of Gentzen s sequent calculus for propositional logic. Lambek s calculus is given below Ax X X L u y V w T X u y x T v w L L T X u y v w U T y x V w L R T x y p R T y x T y R T y x Here u T V are sequences of categories U v possibly empty w x y are categories. In the two premise rules the T X premise is called the minor premise. The fact that derives r I will notate as r. With regard to the names of

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