We present a simple logic that combines, in a conservative way, the implicative fragments of both classical and intuitionistic logics, thus settling a problem posed by Dov Gabbay in [5]. We also show that the logic can be given a nice complete axiomatization by adding four simple mixed axioms to the usual axiomatizations of classical and intuitionistic implications.

The study seeks to analyses ethnocentric factors impact on the freedom of competition and business activity. Xenophobia, morality and rationality patriotism and nationalism, economic and war animosity influence one way or another, Greek students’ opinions towards freedom of competition in the era of a vast fiscal crisis in Greece. Key-Words: Implicative statistical analysis, freedom of competit...

In this note first we define the notion of dual positive implicative hyper Kideal of type 4, where for simplicity is written by DPIHKI − T4. Then we give some related results. Finally we determine all of hyper K-algebras of order 3, which have D1 = {1}, D2 = {1, 2} or D3 = {0, 1} as a DPIHKI − T4.

The notion of a fantastic filter in a lattice implication algebra is introduced, and the relations among filter, positive implicative filter, and fantastic filter are given. We investigate an equivalent condition for a filter to be fantastic, and state an extension property for fantastic filter.

We introduce a special set in an implicative semigroup. Using it, an equivalent condition of an ordered filter is stated. We prove that an ordered filter can be represented by the union of such sets. 2000 Mathematics Subject Classification. 20M12, 06F05, 06A06, 06A12.

In this brief note, which has simply the role of an epistemological survey paper, some of the main basic elements of Implicative Statistical Analysis (ISA) pattern are put into a possible critical comparison with some of the main aspects of Probability Theory, Inductive Inference Theory, Nonparametric and Multivariate Statistics, Optimization Theory and Dynamical System Theory which point out t...

Filters of a lattice, maximal filters (ultrafilters), operation to create a filter generating by an element or by a non-empty subset of the lattice are discussed. Besides, there are introduced implicative lattices such that for every two elements there is an element being pseudo-complement of them. Some facts concerning these concepts are presented too, i.e. for any proper filter there exists a...

In this article, it is proposed to consider classification reasoning based on inducing and using implicative dependencies as a model of commonsense reasoning. The main concept of this reasoning is a good classification test considered as a formal concept of the FCA. The Galois lattice is used for constructing good classification tests. Special rules are determined for constructing Galois lattic...