The Potential of Interference-Based Proof Systems

We want to encourage researchers to investigate the potential of proof systems that modify a given set of formulas (e.g., a set of clauses in propositional logic) in a way that preserves satisfiability but not necessarily logical equivalence. We call such modifications interferences, because they can change the models of a given set of formulas. Interferences differ from classical inferences, which do not affect the models of a set of formulas, because they only allow the derivation of formulas (conclusions) that are implied by the original formulas (premises). Moreover, while inferences reason about the presence of formulas (the premises), interferences can be seen as reasoning about their absence. Most traditional proof systems such as Frege systems, sequent calculi, or resolution-based systems use conventional inference rules. Popular examples of these rules are the modus ponens (left) and the propositional resolution rule (right):