The paper extends homogeneous functional calculus on vector lattices. It is shown that the function of elements of a relatively uniformly complete vector lattice can naturally be defined if the positively homogeneous function is defined on some conic set and is continuous on some closed convex subcone. An interplay between Minkowski duality and homogeneous functional calculus leads to the envel...

We discuss a class of constraint-based grammars, Lexicalized Well-Founded Grammars (LWFGs) and present the theoretical underpinnings for learning these grammars from a representative set of positive examples. Given several assumptions, we define the search space as a complete grammar lattice. In order to prove a learnability theorem, we give a general algorithm through which the top and bottom ...

Backelin proved that the multigraded Poincaré series for resolving a residue field over a polynomial ring modulo a monomial ideal is a rational function. The numerator is simple, but until the recent work of Berglund there was no combinatorial formula for the denominator. Berglund’s formula gives the denominator in terms of ranks of reduced homology groups of lower intervals in a certain lattic...

Let (G, τ ) be a commutative Hausdorff locally solid lattice group. In this paper we prove the following: (1) If (G, τ ) has the A(iii)-property, then its completion (Ĝ, τ̂ ) is an order-complete locally solid lattice group. (2) If G is order-complete and τ has the Fatou property, then the order intervals of G are τ -complete. (3) If (G, τ ) has the Fatou property, then G is order-dense in Ĝ and...

in this note by considering a complete lattice l, we define thenotion of an l-fuzzy hyperrelation on a given non-empty set x. then wedefine the concepts of (pom)l-fuzzy graph, hypergraph and subhypergroupand obtain some related results. in particular we construct the categories ofthe above mentioned notions, and give a (full and faithful) functor form thecategory of (pom)l-fuzzy subhypergroups ...

In this paper, we investigate the properties of join and meet preserving maps in complete residuated lattice using Zhang’s the fuzzy complete lattice which is defined by join and meet on fuzzy posets. We define L-upper (resp. L-lower) approximation operators as a generalization of fuzzy rough sets in complete residuated lattices. Moreover, we investigate the relations between L-upper (resp. L-l...

We deene the notion of meet-uniformity for closure operators on a complete lattice, which corresponds to co-additivity restricted to subsets mapped into the same element, and we study its properties. A class of closures given by principal lters and the downward closures are relevant examples of meet-uniform closures. Next, we introduce a lifting of a complete order by means of a meet-uniform cl...

Traditional automata accept or reject their input, and are therefore Boolean. Lattice automata generalize the traditional setting and map words to values taken from a lattice. In particular, in a fully-ordered lattice, the elements are 0, 1, . . . , n − 1, ordered by the standard ≤ order. Lattice automata, and in particular lattice automata defined with respect to fully-ordered lattices, have i...

We study the folding of the regular two-dimensional triangular lattice embedded in the regular three-dimensional Face-Centred Cubic lattice, a discrete model for the crumpling of membranes. Possible folds are complete planar folds, folds with the angle of a regular tetrahedron (71 •) or with that of a regular octahedron (109 •). We study this model in the presence of a negative bending rigidity...

We consider the problem of Data Flow Analysis over monotone data flow frameworks with a finite lattice. The problem of computing the Maximum Fixed Point (MFP) solution is shown to be P-complete even when the lattice has just four elements. This shows that the problem is unlikely to be efficiently parallelizable. It is also shown that the problem of computing the Meet Over all Paths (MOP) soluti...