Abstract
We present and discuss a novel language restriction for modal logics for multiagent systems, called modal context restriction, that reduces the complexity of the satisfiability problem from EXPTIME complete to NPTIME complete. We focus on BDI multimodal logics that contain fix-point modalities like common beliefs and mutual intentions together with realism and introspection axioms. We show how this combination of modalities and axioms affects complexity of the satisfiability problem and how it can be reduced by restricting the modal context of formulas.
Highlights
Checking the satisfiability of formulas (Garey and Johnson 1990), along with checking whether formulas are satisfied in a given model, is an important computational task associated with formalisms used for specifying software systems (Huth and Ryan 2004)
We show that the basic modal context restriction, R1, leads to PSPACE completeness of the satisfiability problem
In this paper we study two modal context restrictions for the language of TeamLog that lead to PSPACE completeness of the satisfiability problem
Summary
1980), is an important computational task associated with formalisms used for specifying software systems (Huth and Ryan 2004). 2009; Shoham and Leyton-Brown 2008), the satisfiability problem underlies the following two tasks, appearing during system development. Checking whether there exists a system that satisfies the given specification is essentially the satisfiability problem. The second task is related to implementation of individual agents (Shoham 1993). Often such implementations are based on logical formalisms and execution of programs of agents involves reasoning tasks related to that formalism. These tasks are based on checking the satisfiability of formulas
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