Affiliations: Logic and Computation Group, College of Engineering and
Computer Science, The Australian National University, Canberra, ACT, 0200,
Australia. Rajeev.Gore@anu.edu.au | Institute of Informatics, University of Warsaw, Banacha
2, 02-097 Warsaw, Poland. nguyen@mimuw.edu.pl
Note: [] Address for correspondence: Institute of Informatics, University
of Warsaw, Banacha 2, 02-097 Warsaw, Poland
Abstract: We develop clausal tableau calculi for six multimodal logics
variously designed for reasoning about multi-degree belief, reasoning about
distributed systems of belief and for reasoning about epistemic states of
agents in multi-agent systems. Our tableau calculi are sound, complete,
cut-free and have the analytic superformula property, thereby giving decision
procedures for all of these logics. We also use our calculi to obtain
complexity results for five of these logics. The complexity of the remaining
logic was known.
Keywords: modal logics for agent-based systems, theorem proving for modal logics, complexity and decidability of modal logics
