Algebraic properties of pre-logics
Autonomous posets and quantales
Corcoran's Aristotelian syllogistic as a subsystem of first-order logic.
Definitions: the primitive concept of logics or The Leśniewski-Tarski legacy [Book]
Ein Henkin-Vollständigkeitsbeweis für die intuitionistische Prädikatelogik bezüglich der Kripke-Semantik.
Information frames, implication systems and modalities.
We investigate the logical systems which result from introducing the modalities L and M into the family of substructural implication logics (including relevant, linear and intuitionistic implication). Our results lead to the formulation of a uniform labelled refutation system for these logics.
Kripke-Semantik der derivativen Prädikatelogik.
O intuicionismu
On a fragment of intuitionistic logic which is complete with respect to the Kripke frames with finite domains.
On independent recursive axiomatisation in intuitionistic logic
On sequent calculi for intuitionistic propositional logic
The well-known Dyckoff's 1992 calculus/procedure for intuitionistic propositional logic is considered and analyzed. It is shown that the calculus is Kripke complete and the procedure in fact works in polynomial space. Then a multi-conclusion intuitionistic calculus is introduced, obtained by adding one new rule to known calculi. A simple proof of Kripke completeness and polynomial-space decidability of this calculus is given. An upper bound on the depth of a Kripke counter-model is obtained.
Polyadic algebras over nonclassical logics
The polyadic algebras that arise from the algebraization of the first-order extensions of a SIC are characterized and a representation theorem is proved. Standard implicational calculi (SIC)'s were considered by H. Rasiowa [19] and include classical and intuitionistic logic and their various weakenings and fragments, the many-valued logics of Post and Łukasiewicz, modal logics that admit the rule of necessitation, BCK logic, etc.
Presentation of Natural Deduction
Remark on intuitionistic fuzzy logic and intuitionistic logic.
It is shown that the axioms of the intuitionistic logic can be proved as theorems in the frames of the intuitionistic fuzzy logic.
The Neg.-propositional Calculus
Theorem Provers for Substructural Logics
Базисы допустимых правил модальной системы Grz и интуиционистской логики
Гливенковские классы секвенций
Дизъюнктивная интерпретация исчисления LJ
Допустимые и производные правила