We show that it is possible to base fuzzy control on fuzzy logic programming. Indeed, we observe that the class of fuzzy Herbrand interpretations gives a semantics for fuzzy programs and we show that the fuzzy function associated with a fuzzy system of IF-THEN rules is the fuzzy Herbrand interpretation associated with a suitable fuzzy program.
B. L. Clarke, following a proposal of A. N. Whitehead, presents an axiomatized calculus of individuals based on a primitive predicate "x is connected with y". In this article we show that a proper subset of Clarke's system of axioms characterizes the complete orthocomplemented lattices, while the whole of Clarke's system characterizes the complete atomless Boolean algebras.
Connection structuresLet R be a nonempty set and C a binary relation on R, set C(x) = [y G R/xCy] and suppose the following axioms are true of every x 9 y E R:We call regions the elements of R and, if x,y G R and xCy, we say that x is connected with y. If X is a nonempty subset of R, we say that x is the fusion of X just in case for every y ELR, xCy iff for some zGX, zCy; in other words, x is the fusion of x provided that (1) C{x)=U[C{z)/zeX).
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