The categorial logic of vacuous components in natural language

Abstract

This paper develops LMP - a categorial type logic that is meant to formulate vacuous components in natural language. The vacuous components are those expressions which have no semantic referents, but syntactically function as grammatical links between expressions on its left and right hand side. In order to legitimatize the derivations of sentences containing these components in categorial type logic, the present paper proposes system LMP, which is based on a ternary composite category [A {B} C]. LMP's axiomatic presentation and Gentzen presentation are thereafter presented, and LMP's soundness, completeness and decidability are established. © 2011 Springer-Verlag.