Section: New Results

Proof theory for model checking

Participant : Dale Miller.

While model checking has often been considered as a practical alternative to building formal proofs, we have argued that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking [7]. Given that the emphasis of model checking is on establishing the truth of a property in a model, our framework concentrates on additive inference rules since these provide a natural description of truth values via inference rules. Unfortunately, using these rules alone can force the use of inference rules with an infinite number of premises. In order to accommodate more expressive and finitary inference rules, multiplicative rules must be used, but limited to the construction of additive synthetic inference rules: such synthetic rules are described using the proof-theoretic notions of polarization and focused proof systems. This framework provides a natural, proof-theoretic treatment of reachability and non-reachability problems, as well as tabled deduction, bisimulation, and winning strategies. (Q. Heath collaborated on several parts of this research effort.)