Combinators and Grammars

The attraction of Categorial Grammar (CG) as a notation for natural language grammar has always been the direct relation that it embodies between the syntax of a language and an applicative semantics. Common sense suggests that just such a relation should hold for natural languages, just as it does in the systems of logic which gave rise to CG in the first place. However, the existence of discontinuous constituents, extractions, and all the other phenomena whose importance was first and most clearly exposed by Chomsky (1957) makes it clear that something more is required than the basic ingredients of function and argument categories, plus functional application, prescribed by Ajdukiewicz (1935). Those who have attempted to cope with these phenomena within CG have proposed to ‘generalise’ (Bach, 1983) or ‘extend’ (Levin, 1982) the basic context-free apparatus by the addition of various operations on the functions and arguments, over and above simple functional application. These additions have included functional composition and type raising (Lambek, 1958, 1961; Geach, 1972), ‘wrapping’ (Bach, 1979, 1980), and some others.

[1]  Rasmus Lerdorf,et al.  Introduction to combinatory logic , 1972 .

[2]  Edward L. Keenan,et al.  Logical Types for Natural Language , 1978 .

[3]  D. A. Turner,et al.  A new implementation technique for applicative languages , 1979, Softw. Pract. Exp..

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

[5]  Eric Bach,et al.  Generalized Categorial Grammars and the English Auxiliary , 1983 .

[6]  R. J. M. Hughes,et al.  Super-combinators a new implementation method for applicative languages , 1982, LFP '82.

[7]  Emmon Bach,et al.  In defense of passive , 1980 .

[8]  D. A. Turner.  Another Algorithm for Bracket Abstraction , 1979, J. Symb. Log..

[9]  Peter Buneman,et al.  An implementation technique for database query languages , 1982, TODS.

[10]  Emmon W. Bach,et al.  Control in Montague Grammar , 1979 .

[11]  Mark Steedman,et al.  Dependency and Coordination in the Grammar of Dutch and English , 1985 .

[12]  Mark Steedman,et al.  On the order of words , 1982 .

[13]  Harold T. Hodes,et al.  The | lambda-Calculus. , 1988 .

[14]  David Kaplan,et al.  How to Russell a Frege-Church , 1975 .

[15]  Gerald Gazdar,et al.  Unbounded Dependencies and Coordinate Structure , 1981 .

[16]  William H. Burge,et al.  Recursive Programming Techniques , 1975 .

[17]  A. C. Norman,et al.  Some practical methods for rapid combinator reduction , 1984, LFP '84.

[18]  Sören Stenlund.  Combinators, λ-Terms and Proof Theory , 2011 .

[19]  M. Baltin,et al.  The Mental representation of grammatical relations , 1985 .

[20]  Sebastian Shaumyan.  Applicational Grammar As a Semantic Theory of Natural Language , 1977 .

[21]  Mark Steedman,et al.  Combinatory grammars and parasitic gaps , 1987 .

[22]  Y. Bar-Hillel.  A Quasi-Arithmetical Notation for Syntactic Description , 1953 .

[23]  Frederic B. Fitch,et al.  Dictionary of Symbols of Mathematical Logic , 1969 .

[24]  M. Schönfinkel.  Über die Bausteine der mathematischen Logik , 1924 .