This paper gives an abstract description of decision procedures for Satisfiability Modulo Theory (SMT) as proof search procedures in a sequent calculus with polarities and focusing. In particular, we show how to simulate the execution of standard techniques based on the Davis-Putnam- Logemann-Loveland (DPLL) procedure modulo theory as the gradual construction of a proof tree in sequent calculus. The construction mimicking a run of DPLL-modulo-Theory can be obtained by a meta-logical control on the proof-search in sequent calculus. This control is provided by polarities and focusing features, which there- fore narrow the corresponding search space in a sense we discuss. This simulation can also account for backjumping and learning steps, which correspond to the use of general cuts in sequent calculus.
