This book is a study of the logical and computational properties of
structure-preserving categorial grammars.
The first part of the book presents chart-parsers for non-associative
categorial grammars in the style of Ajdukiewicz and Bar-Hillel. These are
proposed in Chapter 3 as deductive parsers, that is as deductive systems
which take advantage of the linear order of the syntactic categories. In
Chapter 4 they are formulated as polynomial parsing algorithms. An
important aspect is the formulation of efficient methods for handling
product formulas in the parsing process.
The second part of the book deals with Lambek style categorial grammars. A
simple and elegant method for automatic recognition is formulated in
Chapter 5 and its syntactic and semantic properties are explored in the
subsequent chapters. A surprising result is the connection between the
number of semantic readings of a sequent and the binomial coefficient
discussed in Chapter 6. The results of polynomiality in Chapter 7 are
grounded on explicit algorithms which generalize and improve previous results.
The parsing techniques presented in this book are among the first complete
applications of chart-parsing methods to logical grammars and lay the
ground for a new approach to parsing with type-logical grammars.