Unsound Theorem Proving

Automated theorem proving is the task of trying to prove a conjecture true or
show it is false.  There are two important properties for automated theorem
proving systems: soundness and completeness.  If a system is sound, then all
proofs are correct.  If a system is complete, then all true conjectures will
eventually be proved.

Applications of theorem proving in program verification often require determining
the satisfiability of first-order formulae with respect to some background
theories. If we guarantee completeness and soundness, the search space can
become large, possibly infinite.

During development, conjectures are usually false.  Therefore, it is desirable
to have a theorem prover that terminates on true conjectures.  In other words,
completeness is more important than soundness in this case. Hence, unsound but
complete theorem proving is a natural method to increase the efficiency and
reduce the search space during the inference procedure. In this talk, we are
going to give a calculus of unsound theorem proving based on DPLL(\Gamma + T)
which integrates an SMT solver with an inference system. At last, we apply it to
finite theories and make it a decision procedure.

This talk is based on the paper On Deciding Satisfiability by DPLL(\Gamma+\cal T)
and Unsound Theorem Proving, by Maria Paola Bonacina, Christopher Lynch and
Leonardo de Moura.