Current theories of grammar handle both extraction and anaphorization by introducing variables into syntactic representations. Combinatory categorial grammar eliminates variables corresponding to gaps. Using the combinator W, the paper extends this approach to anaphors, which appear to act as overt bound variables. [Slightly extended version in Bartsch et al 1989.].

[1]. Recently renewed interest in non transformational approaches to syntax [2] suggests that it might be well to take another look at categorial grammars, since they seem to have been neglected largely because they had been shown to be equivalent to context free phrase structure grammars in weak generative capacity and it was believed that such grammars were incapable of describing natural languages in a natural way. It is my purpose here to sketch a theory of grammar which represents a (...) generalization of categorial grammars of the sort invented by Ajdukiewicz (1935) and further elaborated especially by Bar Hillel (1953) and Lambek (1961). (shrink)

This volume examines the notion of an analytic proof as a natural deduction, suggesting that the proof's value may be understood as its normal form--a concept with significant implications to proof-theoretic semantics.

This important book provides a new unifying methodology for logic. It replaces the traditional view of logic as manipulating sets of formulas with the notion of structured families of labelled formulas with algebraic structures. This approach has far reaching consequences for the methodology of logics and their semantics, and the book studies the main features of such systems along with their applications. It will interest logicians, computer scientists, philosophers and linguists.

Combinatory logic and lambda-conversion were originally devised in the 1920s for investigating the foundations of mathematics using the basic concept of 'operation' instead of 'set'. They have now developed into linguistic tools, useful in several branches of logic and computer science, especially in the study of programming languages. These notes form a simple introduction to the two topics, suitable for a reader who has no previous knowledge of combinatory logic, but has taken an undergraduate course in predicate calculus and recursive (...) functions. The key ideas and basic results are presented, as well as a number of more specialised topics, and man), exercises are included to provide manipulative practice. (shrink)

This paper studies the relation between some extensions of the non-associative Lambek Calculus NL and their interpretation in tree models (free groupoids). We give various examples of sequents that are valid in tree models, but not derivable in NL. We argue why tree models may not be axiomatizable if we add finitely many derivation rules to NL, and proceed to consider labeled calculi instead.We define two labeled categorial calculi, and prove soundness and completeness for interpretations that are almost the intended (...) one, namely for tree models where some branches of some trees may be resp. all branches of all trees must be infinitely extending. Extrapolating from the experiences in our quite simple systems, we briefly discuss some problems involved with the introduction of labels in categorial grammar, and argue that many of the basic questions are not yet understood. (shrink)