A constructive investigation of satisfiability

We present a constructive analysis of the logical notions of satisfiability and consistency for first-order intuitionistic formulae. In particular, we use formal topology theory to provide a positive semantics for satisfiability. Then we propose a “co-inductive” logical calculus, which captures the positive content of consistency.

► We study satisfiability of a first-order intuitionistic formula.
► We give a constructive algebraic semantics for satisfiability.
► We extend usual sequent calculus by introducing a primitive for satisfiability.
► We prove a soundness and completeness result for our calculus.