The theory of quasivarieties constitutes an independent direction in algebra and
mathematical logic and specializes in a fragment of first-order logic-the so-called universal …

We find an explicit basis for all admissible rules of the modal logic S4. Our basis consists of
an infinite sequence of rules which have compact and simple, readable form and depend on …

Questions connected with the admissibility of rules of inference and the solvability of the
substitution problem for modal and intuitionistic logic are considered in an algebraic …

We axiomatize the provability logic of HA and show that it is decidable. Moreover we
axiomatize the preservativity and relative admissibility for several modal logics extending …

We study the problem of finding a basis for all rules admissible in the intuitionistic
propositional logic IPC. The main result is Theorem 3.1 which gives a basis consisting of all …

What is an inference rule? This question does not have a unique answer. One usually finds
two distinct standard answers in the literature; validity inference (σ⊦ vφ for every substitution …

This paper concerns modal logics of provability—Gödel-Löb system GL and Solovay logic S—
the smallest and the greatest representation of arithmetical theories in propositional logic …

The main result of this paper is the following theorem: each modal logic extending K 4
having the branching property below m and the effective m-drop point property is decidable …

This paper studies relative unification and admissibility in the intuitionistic logic. We
generalize results of [Ghilardi, 1999; Iemhoff, 2001a] and prove them relative in NNIL (par) …

Intensional logic has emerged, since the 1960's, as a powerful theoretical and practical tool
in such diverse disciplines as computer science, artificial intelligence, linguistics, philosophy …