This paper introduces a Hilbert system for lambda calculus called sequent combinators. Sequent combinators address many of the problems of Hilbert systems, which have led to the m...
Bi-intuitionistic logic is the union of intuitionistic and dual intuitionistic logic, and was introduced by Rauszer as a Hilbert calculus with algebraic and Kripke semantics. But ...
We see cut-free sequent systems for the basic normal modal logics formed by any combination the axioms d, t, b, 4, 5. These systems are modular in the sense that each axiom has a c...
This paper presents a step in the development of an operational approach to program extraction in type theory. In order to get a program from a lambda term, the logical parts need...
The family of normal propositional modal logic systems are given a highly systematic organisation by their model theory. This model theory is generally given using Kripkean frame s...