Mathesis Universalis - No.6, Spring 1998
Wendy MacCaull
ABSTRACT
Relational tableaux for tree models,
language models and information networks
A proof calculus is given for formalisms for tree models and language models, which rests on an Orlowska-style relational semantics and a Rasiowa/Sikorski-style deduction method for the Lambek calculus. The extension of this method to Barwise's logics for information, which formalizes the flow of information through an information network, is outlined. The relationship of the Orlowska-stlye relational semantics to other relational semantics (such as the arrow logics of van Benthem/Venema and Vakarelov, and the gaggle theory of Dunn) is clarified. Some comparisons to Gabbay's labelled deduction method are made.
This paper is part of the general program to find effective, modular proof systems for nonclassical logics, based on relational semantics.