Vardanyan's Theorem states that the set of PA-valid principles of Quantified Modal Logic, QML, is complete 0 2. We generalize this result to a wide class of theories. The cru...
Ludics has been proposed by Girard as an abstract general approach to proof theory. We explain how its basic notions correspond to those of the "innocent strategy" apprao...
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing d...
Proofs of equalities may be built from assumptions using proof rules for reflexivity, symmetry, and transitivity. Reflexivity is an axiom proving x=x for any x; symmetry is a 1-p...
Completion procedures, originated from the seminal work of Knuth and Bendix, are wellknown as procedures for generating confluent rewrite systems, i.e. decision procedures for al ...