Minimal Proof Search for Modal Logic K Model Checking
Abstract
Most modal logics such as S5, LTL, or ATL are extensions of Modal Logic K. While the model checking problems for LTL and to a lesser extent ATL have been very active research areas for the past decades, the model checking problem for the more basic Multiagent Modal Logic K (MMLK) has important applications as a formal framework for perfect information multiplayer games on its own. We present Minimal Proof Search (MPS), an effort number based algorithm solving the model checking problem for MMLK. We prove two important properties for MPS beyond its correctness. The (dis)proof exhibited by MPS is of minimal cost for a general definition of cost, and MPS is an optimal algorithm for finding (dis)proofs of minimal cost. Optimality means that any comparable algorithm either needs to explore a bigger or equal state space than MPS, or is not guaranteed to find a (dis)proof of minimal cost on every input. As such, our work relates to A* and AO* in heuristic search, to Proof Number Search and DFPN+ in twoplayer games, and to counterexample minimization in software model checking.
 Publication:

arXiv eprints
 Pub Date:
 July 2012
 arXiv:
 arXiv:1207.1832
 Bibcode:
 2012arXiv1207.1832S
 Keywords:

 Computer Science  Artificial Intelligence;
 Computer Science  Logic in Computer Science
 EPrint:
 Extended version of the JELIA 2012 paper with the same title