A minimal formula of a given logic L is a formula which is provable in L and is not a non-trivial substitution instance of other provable formulas in L. In [5], Y. Komori asked whether normal proofs of minimal formulas are unique in the implicational fragments of natural deduction systems for the intuitionistic logic and the logic BCK. It was already shown that the answer is positive for BCK, w...

Pseudo equality algebras were initially introduced by Jenei and Kóródi as a possible algebraic semantic for fuzzy type theory, and they have been revised by Dvurečenskij and Zahiri under the name of JK-algebras. The aim of this paper is to investigate the internal states and the state-morphisms on pseudo equality algebras. We define and study new classes of pseudo equality algebras, such as com...

Equilibrium moisture contents (EMCs) and diffusion coefficients of a high pressure laminate (HPL) overlay, a wood particleboard (PB) substrate, and an HPL backer (BCK) were measured at different levels of relative humidity (RH). The EMCs as a function of RH were fitted to the Nelson's sorption isotherm. It was found that Nelson's model reproduced accurately the experimental data of these differ...

We introduce the notion of hypergroupoids HBinX, , and show that HBinX, is a super-semigroup of the semigroup BinX, via the identification x ↔ {x}. We prove that HBin * X, , ∅ is a BCK-algebra, and obtain several properties of HBin * X, .

An ideal tentacle manipulator is a non-conventional robotic arm with an infinite mobility. It has the capability of taking sophisticated shapes and of achieving any position and orientation in a 3D space. A tentacle manipulator is a hyper redundant or hyper degree of freedom manipulator. Hyper redundant robots produce changes of configuration using a continuous backbone made of sections which b...

There were two kinds of methods in information retrieval, based on content and based on hyper-link. The quantity of computation in systems based on content was very large and the precision in systems based on hyper-link only was not ideal. It was necessary to develop a technique combining the advantages of two systems. In this paper, we drew up a framework by using the two methods. We set up th...

A unifying semantic framework for different reasoning approaches provides an ideal tool to compare these competing alternatives. A historic example is Kripke’s possible world semantics that provided a unifying framework for different systems of modal logic. More recently, Shoham’s work on preferential semantics similarly provided a much needed framework to uniformly represent and compare a vari...

Using the notion of anti fuzzy points and its besideness to and non-quasi-coincidence with a fuzzy set, new concepts of an anti fuzzy subalgebras in BCK/BCI-algebras are introduced and their inter-relations and related properties are investigated in [3]. The notion of the new fuzzy subalgebra with thresholds are introduced and relationship between this notion and the new fuzzy subalgebra of a B...

Based on fuzzy set theory, extensions, translations and multiplications of ideals in BCK/BCI-algebras are discussed. Relations among fuzzy translations, fuzzy extensions and fuzzy multiplications of fuzzy ideals are investigated.