## 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.)