Electronic Notes in Theoretical Computer Science

Abstract

Abstract Dynamic Epistemic Logic (DEL) deals with the representation of situations in a multi-agent and dynamic setting. It can express in a uniform way statements about: (i) what is true about an initial situation (ii) what is true about an event occurring in this situation (iii) what is true about the resulting situation after the event has occurred. After proving that what we can infer about (ii) given (i) and (iii) and what we can infer about (i) given (ii) and (iii) are both reducible to what we can infer about (iii) given (i) and (ii), we provide a tableau method deciding whether such an inference is valid. We implement it in LOTRECscheme and show that this decision problem is NEXPTIME-complete. This contributes to the proof theory and the study of the computational complexity of DEL which have rather been neglected so far. Keywords: Dynamic epistemic logic, tableau method, computational complexity 1 This paper corrects the paper published under the same name and the same authors in the proceedings of M4M 2011. The rule ⊥ of the tableau method was missing. 2 We thank Sophie Pinchinat for helpful discussions and three reviewers for comments.