First we show that the cosets of a fuzzy ideal μ in a BCK-algebraX form another BCK-algebra  X/μ (called the fuzzy quotient BCK-algebra of X by μ). Also we show thatX/μ is a fuzzy partition of X and we prove several some isomorphism theorems. Moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition P of a commutative BCK-algebra iscompatible, then P is a fuzzy quo...

In this note first we define a BCK‐algebra on the states of a deterministic finite automaton. Then we show that it is a BCK‐algebra with condition (S) and also it is a positive implicative BCK‐algebra. Then we find some quotient BCK‐algebras of it. After that we introduce a hyper BCK‐algebra on the set of all equivalence classes of an equivalence relation on the states of a deterministic finite...

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Sometimes it is needed in approximate reasoning to deal simultaneously with both fuzziness of propositions and modalities, for instance one may try to assign a degree of truth to propositions like “John is possibly tall”or “John is necessarily tall”, where “John is tall”is presented as a fuzzy proposition. Fuzzy logic should be a suitable tool to model not only vagueness but also other kinds of...

In a paper of 1933 Godel proved that every satisfiable first-order V2?3* sentence has a finite model. Actually he constructed a finite model in an ingenious and sophisticated way. In this paper we use a simple and straightforward probabilistic argument to establish existence of a finite model of an arbitrary satisfiable V123* sentence. ?0. Introduction. We consider the usual first-order logic o...

. 1 Preliminaries Consider the variety Eω generated by the algebra ω := (N, ·), where i · j := max (i, j) for i 6= j, and i · j := 1 for i = j, i, j ∈ N1. These variety is a subvariety of the variety of equivalential algebras E . By an equivalential algebra we mean a grupoid A = (A,↔) that is a subreduct of a Brouwerian semilattice (or, equivalently, a Heyting algebra) with the operation ↔ give...

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1079–1082, 2008 21. Hartleben B, Godel M, Meyer-Schwesinger C, Liu S, Ulrich T, Kobler S, Wiech T, Grahammer F, Arnold SJ, Lindenmeyer MT, Cohen CD, Pavenstadt H, Kerjaschki D, Mizushima N, Shaw AS, Walz G, Huber TB: Autophagy influences glomerular disease susceptibility and maintains podocyte homeostasis in aging mice. J Clin Invest 120: 1084–1096, 2010 22. Samanovic M, Molina-Portela MP, Ches...

Correspondence and offprint requests to: Michael S. Goligorsky; E-mail: [email protected] Comment on Hartleben B, Godel M, Meyer-Schwesinger C et al. Autophagy influences glomerular disease susceptibility and maintains podocyte homeostasis in aging mice. J Clin Invest 2010; 120: 1084–1096. Kume S, Uzu T, Horiike K et al. Calorie restriction enhances cell adaptation to hypoxia through ...