  While model checking has often been considered as a practical alternative to
building formal proofs, we argue here that the theory of sequent calculus
proofs can be used to provide an appealing foundation for model checking. Since
the emphasis of model checking is on establishing the truth of a property in a
model, we rely on the proof theoretic notion of additive inference rules, since
such rules allow provability to directly describe truth conditions.
Unfortunately, the additive treatment of quantifiers requires inference rules
to have infinite sets of premises and the additive treatment of model
descriptions provides no natural notion of state exploration. By employing a
focused proof system, it is possible to construct large scale, synthetic rules
that also qualify as additive but contain elements of multiplicative inference.
These additive synthetic rules -- essentially rules built from the description
of a model -- allow a direct treatment of state exploration. This proof
theoretic framework provides a natural treatment of reachability and
non-reachability problems, as well as tabled deduction, bisimulation, and
winning strategies.
