We generalize the double negation construction of Boolean algebras in Heyting algebras, to a double negation construction of the same in Visser algebras (also known as basic algebras). This result allows us to generalize Glivenko’s Theorem from intuitionistic propositional logic and Heyting algebras to Visser’s basic propositional logic and Visser algebras. Mathematics Subject Classification: P...

Sugeno integral is one of the basic aggregation operations on a qualitative scale where only minimum and maximum, as well as order-reversing maps are allowed. Recently some variants of this aggregation operation, named soft and drastic integrals, have been introduced in a previous work by three of the authors. In these operations, importance weights play the role of tolerance thresholds enablin...

Abstract We build a topological model, based on intuitionistic logic, for multi-agent biological systems (such as Physarum polycephalum , bacterial colonies or any other swarm), reacting to external nourishment stimuli. Our construction follows the description of brain activity, where particles (neurons) are activated by an environment, represented space X with open cover $$\{U_i:i\in I\}$$ <mm...

In this paper, we solve an open problem in an special case. The problem is to give a characterization for Heyting algebras by means of fractions. Here, we give a representation for a class of Heyting algebras by means of fractions. Fractions on a bounded distributive lattice is a new algebraic structure, which was recently studied by the authors. Mathematics Subject Classification: 06Axx, 06Dxx

In the paper we introduce the notion of →-irreducibility and we show that the set of all →-irreducible elements of a finite Heyting lattice L forms the skeleton of L. We also discuss a parallel concept of ↔-irreducibility and give a similar characterization. Finally, we present generalizations of these results for some class of infinite Heyting lattices.

Part One of this paper is a case against classical mereology and for Heyting mereology. This case proceeds by first undermining the appeal of classical mereology and then showing how it fails to cohere with our intuitions about a measure of quantity. Part Two shows how Heyting mereology provides an account of sets and classes without resort to any nonmereological primitive.

If the influence of visual-motor integration (copying forms) on the quality of handwriting has been widely investigated, the influence of eye-hand coordination (tracing item) has been less well analyzed. The Concise Assessment Scale for Children’s Handwriting (BHK), the Developmental Test of Visual Perception (DTVP-2), and the section “Manual Dexterity” of the Movement Assessment Battery for Ch...