Bisimulation Safe Fixed Point Logic

Faried Abu Zaid, Erich Grädel, Stephan Jaax
2014 Advances in Modal Logic  
We define and investigate a new modal fixed-point logic, called bisimulation safe fixed-point logic BSFP, which is a calculus of binary relations that extends both PDL and the modal µ-calculus. The logic is motivated by concepts and results due to van Benthem and Hollenberg on bisimulation safety which plays a similar role for binary relations as the more familiar notion of bisimulation invariance plays for monadic ones. We prove that BSFP is indeed bisimulation invariant for state formulae and
more » ... bisimulation safe for action formulae. We investigate the expressive power of BSFP and show that it is not limited to monadic second-order definability. Further, we reveal a close relationship of BSFP with context-free languages. We identify a fragment of BSFP that is equivalent to the extension of PDL by context-free grammars. Although BSFP is far more expressive than the modal µ-calculus, its model-checking problem has the same complexity. On the other side, the satisfiability problem for BSFP is highly undecidable.
dblp:conf/aiml/ZaidGJ14 fatcat:mlgku77fbzbe5edqe53ggbyvfq