Generation as Deduction on Labelled Proof Nets

In the framework of labelled proof nets the task of parsing in categorial grammar can be reduced to the problem of first-order matching under theory. Here we shall show how to use the same method of labelled proof nets to reduce the task of generating to the problem of higher-order matching.

[1]  Gilles Dowek.  Third order matching is decidable , 1992, [1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science.

[2]  Gérard Huet,et al.  Constrained resolution: a complete method for higher-order logic. , 1972 .

[3]  Glyn Morrill,et al.  Clausal Proofs and Discontinuity , 1995, Log. J. IGPL.

[4]  Glyn Morrill,et al.  Higher-order Linear Logic Programming of Categorial Deduction , 1995, EACL.

[5]  Vincent Danos,et al.  The structure of multiplicatives , 1989, Arch. Math. Log..

[6]  Wayne Snyder,et al.  Designing Unification Procedures Using Transformations: A Survey , 1992 .

[7]  Gérard P. Huet,et al.  A Unification Algorithm for Typed lambda-Calculus , 1975, Theor. Comput. Sci..

[8]  David H. D. Warren,et al.  Parsing as Deduction , 1983, ACL.

[9]  Jordi Levy.  Linear Second-Order Unification , 1996, RTA.

[10]  G. Morrill.  Memoisation of categorial proof nets: parallelism in categorial processing , 1996 .

[11]  Wayne Snyder,et al.  Higher-Order Unification Revisited: Complete Sets of Transformations , 1989, J. Symb. Comput..

[12]  Glyn Morrill,et al.  Difference lists and difference bags for logic programming of categorial deduction , 1995 .

[13]  Patrick Lincoln,et al.  Linear logic , 1992, SIGA.

[14]  M. Nivat.  Fiftieth volume of theoretical computer science , 1988 .

[15]  Warren D. Goldfarb,et al.  The Undecidability of the Second-Order Unification Problem , 1981, Theor. Comput. Sci..

[16]  Dirk Roorda,et al.  Resource Logics : Proof-Theoretical Investigations , 1991 .

[17]  J. Lambek.  The Mathematics of Sentence Structure , 1958 .

[18]  Glyn Morrill,et al.  Type Logical Grammar: Categorial Logic of Signs , 1994 .