Finitely generated free Heyting algebras via Birkhoff duality and coalgebra

Algebras axiomatized entirely by rank 1 axioms are algebras for a functor and thus the free algebras can be obtained by a direct limit process. Dually, the final coalgebras can be obtained by an inverse limit process. In order to explore the limits of this method we look at Heyting algebras which have mixed rank 0-1 axiomatizations. We will see that Heyting algebras are special in that they are almost rank 1 axiomatized and can be handled by a slight variant of the rank 1 coalgebraic methods

Admissible Bases Via Stable Canonical Rules

We establish the dichotomy property for stable canonical multi-conclusion rules for IPC, K4, and S4. This yields an alternative proof of existence of explicit bases of admissible rules for these logics

Admissible Bases Via Stable Canonical Rules

We establish the dichotomy property for stable canonical multi-conclusionrules for IPC, K4, and S4. This yields an alternative proof of existence of explicit bases of admissible rules for these logics

Decidability of admissibility:On a problem by friedman and its solution by rybakov

Rybakov (1984) proved that the admissible rules of IPC are decidable. We give a proof of the same theorem, using the same core idea, but couched in the many notions that have been developed in the mean time. In particular, we illustrate how the argument can be interpreted as using refinements of the notions of exactness and extendibility

Inference Rules in Nelson’s Logics, Admissibility and Weak Admissibility

© 2015, Springer Basel. Our paper aims to investigate inference rules for Nelson’s logics and to discuss possible ways to determine admissibility of inference rules in such logics. We will use the technique offered originally for intuitionistic logic and paraconsistent minimal Johannson’s logic. However, the adaptation is not an easy and evident task since Nelson’s logics do not enjoy replacement of equivalences rule. Therefore we consider and compare standard admissibility and weak admissibility. Our paper founds algorithms for recognizing weak admissibility and admissibility itself – for restricted cases, to show the problems arising in the course of study

Using Tree Automata to Investigate Intuitionistic Propositional Logic

Intuitionistic logic is an important variant of classical logic, but it is not as well-understood, even in the propositional case. In this thesis, we describe a faithful representation of intuitionistic propositional formulas as tree automata. This representation permits a number of consequences, including a characterization theorem for free Heyting algebras, which are the intutionistic analogue of free Boolean algebras, and a new algorithm for solving equations over intuitionistic propositional logic