2 research outputs found
Formula size games for modal logic and -calculus
We propose a new version of formula size game for modal logic. The game
characterizes the equivalence of pointed Kripke-models up to formulas of given
numbers of modal operators and binary connectives. Our game is similar to the
well-known Adler-Immerman game. However, due to a crucial difference in the
definition of positions of the game, its winning condition is simpler, and the
second player does not have a trivial optimal strategy. Thus, unlike the
Adler-Immerman game, our game is a genuine two-person game. We illustrate the
use of the game by proving a non-elementary succinctness gap between
bisimulation invariant first-order logic and (basic) modal logic
. We also present a version of the game for the modal
-calculus and show that is also
non-elementarily more succinct than .Comment: This is a preprint of an article published in Journal of Logic and
Computation Published by Oxford University Press. arXiv admin note:
substantial text overlap with arXiv:1604.0722