In this paper we investigate the propositional logic of standard algebras for Hájek’s Basic Fuzzy Logic BL in a language expanded with propositional constants for the idempotent elements delimiting the L-, G-, and Π-components of the algebra. We start from a fixed standard BL-algebra; introduce new propositional constants; present a suitable set of axioms; investigate completeness results; and ...

We present tableau systems and sequent calculi for the intuitionistic analogues and IS5 of the normal classical modal logics. We provide soundness and completeness theorems with respect to the models of intuitionistic logic enriched by a modal accessibility relation, as proposed by G. We also investigate the relationship of these logics with some other intuitionistic modal logics proposed in th...

In this paper, we introduce and study a new coloring problem of a graph called the dominated coloring. A dominated coloring of a graph G is a proper vertex coloring of G such that each color class is dominated by at least one vertex of G. The minimum number of colors among all dominated colorings is called the dominated chromatic number, denoted by χdom(G). In this paper, we establish the close...

We study hereditary completeness of systems exponentials on an interval such that the corresponding generating function G is small outside a lacunary sequence intervals Ik. show that, under some technical conditions, exponential system hereditarily complete if and only logarithmic length union these infinite, i.e., $$\sum\nolimits_k {\int_{{I_k}} {{{dx} \over {1 + \left| x \right|}} = \infty } ...