(1) Department of Mathematics, Statistics and Computer Science, St. Francis Xavier University, P.O. Box 5000, Antigonish, N.S., B2G 2W5, Canada;(2) National Institute of Telecommunications, ul. Szachowa 1, 04-894 Warsaw, Poland
Abstract:
We present a general framework for proof systems for relational theories. We discuss principles of the construction of deduction rules and correspondences reflecting relationships between semantics of relational logics and the rules of the respective proof systems. We illustrate the methods developed in the paper with examples relevant for the Lambek calculus and some of its extensions.