Abstract. The concepts of P-compactness, countable P-compactness, the P-Lindelöf property are introduced in L-topological spaces by means of preopen L-sets and their inequalities when L is a complete DeMorgan algebra. These definitions do not rely on the structure of the basis lattice L

distributive DeMorgan lattice to standard, two-valued model check-ing. We then present a direct, automata-theoretic algorithm for multi-valued model checking with logics as expressive as the modal mu-calculus. As part of showing correctness of the algorithm, we present a new fun-damental result about extended

On a generalized deMorgan lattice (X, _<, V, A,') we introduce a family of join hyperoperations *p, parametrized by a parameter p X. As a result we obtain a family of join spaces (X, ,p). We show that: for every a, b X the family {a*p b}pex can be considered as the p-cuts of a L-fuzzy set

proper denotational universe for this lift, show that their symmetric versions are DeMorgan lattices, and classify both structures through (idempotent) order-isomorphisms on (self-dual) priority preorders in the finite case. In particular, this lift generalizes Fitting’s multiple-valued semantics

Abstract. A brief introduction to basic modifiers is given. Any modifier with its dual and the corresponding negation form a DeMorgan triple similar to that of t-norms, t-conorms, and negation. The lattice structure of the unit interval with the usual partial order is similar to that of the set