Defects in the gene encoding Bruton's tyrosine kinase (Btk) result in a disease called X-linked agammaglobulinemia, in which there is a profound decrease of mature B cells due to a block in B cell development. Recent studies have shown that Btk is tyrosine phosphorylated and activated upon B cell antigen receptor (BCR) stimulation. To elucidate the functions of this kinase, we examined BCR sign...

Evidence is given that implication (and its special case, negation) carry the logical strength of a system of formal logic. This is done by proving normalization and cut elimination for a system based on combinatory logic or λ-calculus with logical constants for and, or, all, and exists, but with none for either implication or negation. The proof is strictly finitary, showing that this system i...

We study hyper pseudo BCC-algebras which are a common generalization of and BCK-algebras. In particular, we introduce different notion describe the relationship among them. Then, by choosing one these definitions, investigate for its related properties.

In this paper we define cut-free hypersequent calculi for some intermediate logics semantically characterized by bounded Kripke models. In particular we consider the logics characterized by Kripke models of bounded width Bwk, by Kripke models of bounded cardinality Bck and by linearly ordered Kripke models of bounded cardinality Gk. The latter family of logics coincides with finite-valued Gödel...

The polyadic algebras that arise from the algebraization of the first-order extensions of a SIC are characterized and a representation theorem is proved. Standard implicational calculi (SIC)’s were considered by H. Rasiowa [19] and include classical and intuitionistic logic and their various weakenings and fragments, the many-valued logics of Post and Lukasiewicz, modal logics that admit the ru...

In this paper, we apply the concept of linear Diophantine fuzzy sets in BCK/BCI-algebras. respect, notions subalgebras and (commutative) ideals are introduced some vital properties discussed. Additionally, characterizations considered. Moreover, associated results for subalgebras, commutative obtained.