The notion of dependencies between ”attributes” arises in many areas such as relational databases, data analysis, data-mining, formal concept analysis, knowledge structures . . .. Formalization of dependencies leads to the notion of so-called full implicational systems (or full family of functional dependencies) which is in oneto-one correspondence with the other significant notions of closure ...

We investigate the complexity of the model checking problem for intuitionistic and modal propositional logics over transitive Kripke models. More specific, we consider intuitionistic logic IPC, basic propositional logic BPL, formal propositional logic FPL, and Jankov’s logic KC. We show that the model checking problem is P-complete for the implicational fragments of all these intuitionistic log...

We investigate cut-eliminability and decidability for implicational sequent calculi with prime contraction. The prime contraction is a restricted version of the contraction rule in LJ (the rule does not permit the contraction of implication formulas). Decision problems for the implicational sequent calculi LBB′IW (the system for the logic BB′IW) and FLc→ (the implicational fragment of the full ...

In Abstract Algebraic Logic, the general study of propositional non-classical logics has been traditionally based on the abstraction of the Lindenbaum-Tarski process. In this process one considers the Leibniz relation of indiscernible formulae. Such approach has resulted in a classification of logics partly based on generalizations of equivalence connectives: the Leibniz hierarchy. This paper p...

This paper presents a new abstract framework to deal in a uniform way with the increasing variety of fuzzy logics studied in the literature. By means of notions and techniques from Abstract Algebraic Logic, we perform a study of non-classical logics based on the kind of generalized implication connectives they possess. It yields the new hierarchy of implicational logics. In this framework the n...

In Abstract Algebraic Logic the general study of propositional non-classical logics has been traditionally based on the abstraction of the Lindenbaum-Tarski process. In this kind of process one considers the Leibniz relation of indiscernible, i.e. logically equivalent, formulae. Such approach has resulted in a classification of logics partly based on generalizations of equivalence connectives: ...

In this paper we consider k-meet-semidistributive lattices and we are interested in the computation of the set-colored poset associated to an implicational base. The parameter k is of interest since for any nite lattice L there exists an integer k for which L is k-meetsemidistributive. When k = 1 they are known as meet-semidistributive lattices. We rst give a polynomial time algorithm to comput...