In this paper we investigate the following two questions: Q1: Do there exist optimal proof systems for a given language L? Q2: Do there exist complete problems for a given promise ...
G¨odel’s completeness theorem is concerned with provability, while Girard’s theorem in ludics (as well as full completeness theorems in game semantics) are concerned with proo...
Equality logic with or without uninterpreted functions is used for proving the equivalence or refinement between systems (hardware verification, compiler’s translation, etc). C...
Propositional type theory, first studied by Henkin, is the restriction of simple type theory to a single base type that is interpreted as the set of the two truth values. We show ...
Sound and complete modal propositional logic C is presented, in which 2P has the interpretation “ P is true in all states”. The interpretation is already known as the Carnapia...