We consider various classes of algebras obtained by expanding idempotent semirings with meet, residuals and Kleene-∗. An investigation of congruence properties (epermutability, e-regularity, congruence distributivity) is followed by a section on algebraic Gentzen systems for proving inequalities in idempotent semirings, in residuated lattices, and in (residuated) Kleene lattices (with cut). Fin...

The concepts of semicompactness, countable semicompactness, and the semi-Lindelöf property are introduced in L-topological spaces, where L is a complete de Morgan algebra. They are defined by means of semiopen L-sets and their inequalities. They do not rely on the structure of basis lattice L and no distributivity in L is required. They can also be characterized by semiclosed L-sets and their i...

Abstract This study examines a little-known case of grammaticalized distributivity in the Romance branch, as found tenth to fifteenth century texts produced Iberian Peninsula. Analysis newly compiled, hand-annotated corpus demonstrates that, Old Ibero-Romance, reduplication an adnominal cardinal numeral on internal argument verb mandates distributive reading at sentential level. The constructio...

Zimmermann (2002) identifies two kinds of distance-distributive items across languages. The first kind (e.g. each) is restricted to distribution over individuals; the second kind (e.g. German jeweils) can also be interpreted as distributing over salient occasions. I explain this behavior by formally relating this split to the two distributivity operators proposed in the work of Link (atomic ope...

We give in this paper an explicit formal account of plural semantics in the framework of continuation semantics introduced in [1] and extended in [4]. We deal with aspects of plural dynamic semantics such as plural quantification, plural anaphora, conjunction and disjunction, distributivity and maximality conditions. Those phenomena need no extra stipulations to be accounted for in this framewo...

In this paper, we shall introduce generalized fuzzy compactness in L-spaces where L is a complete de Morgan algebra. This definition does not rely on the structure of basis lattice L and no distributivity is required. The intersection of a generalized fuzzy compact L-set and a generalized closed Lset is a generalized fuzzy compact L-set. The generalized irresolute image of a generalized fuzzy c...

An algorithm to decide the emptiness of a regular type expression with set operators given a set of parameterised type definitions is presented. The algorithm can also be used to decide the equivalence of two regular type expressions and the inclusion of one regular type expression in another. The algorithm strictly generalises previous work in that tuple distributivity is not assumed and set o...

It is shown that operations of equivalence cannot serve for building algebras which would induce orthomodular lattices as the operations of implication can. Several properties of equivalence operations have been investigated. Distributivity of equivalence terms and several other 3 variable expressions involving equivalence terms have been proved to hold in any orthomodular lattice. Symmetric di...

In this paper we show that the so-called array Fréchet problem in Probability/Statistics is (max,+)-linear. The upper bound of Fréchet is obtained using simple arguments from residuation theory and lattice distributivity. The lower bound is obtained as a loop invariant of a greedy algorithm. The algorithm is based on the max-plus linearity of the Fréchet problem and the Monge property of bivari...

An algorithm to decide the emptiness of a regular type expression with set operators given a set of parameterised type deenitions is presented. The algorithm can also be used to decide the equivalence of two regular type expressions and the inclusion of one regular type expression in another. The algorithm strictly generalises previous work in that tuple distributivity is not assumed and set op...