Gentzen-type axiomatization for PAL

A Complete Gentzen-Style Axiomatization for Set Constraints

Set constraints are inclusion relations between expressions denoting sets of ground terms over a ranked alphabet They are the main ingredient in set based program analysis In this paper we pro vide a Gentzen style axiomatization for sequents where and are nite sets of set constraints based on the axioms of termset al gebra Sequents of the restricted form correspond to positive set constraints a...

Canonical Propositional Gentzen-Type Systems

Canoni al Propositional Gentzen-Type Systems

Gentzen-type Refutation Systems for Three-Valued Logics

While the purpose of a conventional proof calculus is to axiomatise the set of valid sentences of a given logic, a refutation system, or complementary calculus, is concerned with axiomatising the invalid sentences. Instead of exhaustively searching for counter models for some sentence, refutation systems establish invalidity by deduction and thus in a purely syntactic way. Such systems are rele...

Classical Gentzen-Type Methods in Propositional Many-Valued Logics

A classical Gentzen-type system is one which employs two-sided sequents, together with structural and logical rules of a certain characteristic form. A decent Gentzentype system should allow for direct proofs, which means that it should admit some useful forms of cut elimination and the subformula property. In this tutorial we explain the main difficulty in developing classical Gentzen-type sys...