Structural proof theory for first-order weak Kleene logics

Proof Theory for First Order Lukasiewicz Logic

An approximate Herbrand theorem is proved and used to establish Skolemization for first-order Łukasiewicz logic. Proof systems are then defined in the framework of hypersequents. In particular, extending a hypersequent calculus for propositional Łukasiewicz logic with usual Gentzen quantifier rules gives a calculus that is complete with respect to interpretations in safe MV-algebras, but lacks ...

Implementing Different Proof Calculi for First-order Modal Logics

Modal logics extend classical logic with the modalities ”it is necessarily true that” and ”it is possibly true that” represented by the unary operators 2 and 3, respectively. First-order modal logics (FMLs) extend propositional modal logics by domains specifying sets of objects that are associated with each world, and the standard universal and existential quantifiers [7]. FMLs have many applic...

First-Order Proof Theory of Arithmetic

Proof theory for hybrid(ised) logics

Article history: Received 24 April 2015 Received in revised form 3 March 2016 Accepted 3 March 2016 Available online 14 March 2016

First-order Gödel logics

First-order Gödel logics are a family of infinite-valued logics where the sets of truth values V are closed subsets of [0,1] containing both 0 and 1. Different such sets V in general determine different Gödel logics GV (sets of those formulas which evaluate to 1 in every interpretation into V ). It is shown that GV is axiomatizable iff V is finite, V is uncountable with 0 isolated in V , or eve...