A Fibred Tableau Calculus for Modal Logics of Agents

Abstract

In [15,19] we showed how to combine propositional multimodal logics using Gabbay's fibring methodology. In this paper we extend the above mentioned works by providing a tableau-based proof technique for the combined/fibred logics. To achieve this end we first make a comparison between two types of tableau proof systems, (graph & path), with the help of a scenario (The Friend's Puzzle). Having done that we show how to uniformly construct a tableau calculus for the combined logic using Governatori's labelled tableau system KEM. We conclude with a discussion on KEM's features. This work was supported by the Australian Research Council under Discovery Project DP0558854 on "A Formal Approach to Resource Allocation in Service Oriented Marketplaces". 1 General modal systems with an arbitrary set of normal modal operators all characterised by the axiom K: 2(ϕ → ψ) → (2ϕ → 2ψ) and the necessitation rule. i.e., ϕ/ 2ϕ.