LFP: a logic for linguistic descriptions and an analysis of its complexity

Abstract

We investigate the weak expressive power of a notation using first-order logic, augmented with a facility for recursion, to give linguistic descriptions. The notation is precise and easy to read, using ordinary conventions of logic. Two versions of the notation are presented. One, called CLFP, speaks about strings and concatenation, and generates the class EXPTIME of languages accepted by Turing machines in time 2cn for some c > 0. The other, called ILFP, speaks about integer positions in strings, and generates the class PTIME of languages recognizable in polynomial time. An application is given, showing how to code Head Grammars in ILFP, showing why these grammars generate only polynomial time languages.