Technical Report TR-ARP-5-95

Automated Reasoning Project

Research School of Information Sciences and Engineering

and Centre for Information Science Research

Australian National University

January, 1, 1995

Combining Possibilities and Negations

Greg Restall

Abstract Combining non-classical (or `sub-classical') logics is not

easy, but it is very interesting. In this paper, we combine

nonclassical logics of negation and possibility (in the presence of

conjunction and disjunction), and then we combine the resulting

systems with intuitionistic logic. We will find that Kracht's results

on the undecidability of classical modal logics generalise to a

non-classical setting. We will also see conditions under which

intuitionistic logic can be combined with a non-intuitionistic

negation without corrupting the intuitionistic fragment of the logic.