Abstract We study (strictly) join irreducible varieties in the lattice of subvarieties residuated lattices. explore connections with well-connected algebras and suitable generalizations, focusing particular on representable varieties. Moreover, we find weakened notions Halldén completeness that characterize irreducibility. strictly basic hoops use generalized rotation construction to $\mathsf{M...

The in-plane mechanics of two-dimensional heterogeneous hexagonal lattices are investigated. heterogeneity originates from two physically realistic considerations: different constituent materials and wall thicknesses. Through the combination multi-material multi-thickness elements, most general form 2D is proposed in this paper. By exploiting a unit cell with characteristics, exact closed-form ...

The paper is devoted to complete proofs of theorems on consistency on cubic lattices for 3 × 3 determinants. The discrete nonlinear equations on Z defined by the condition that the determinants of all 3×3 matrices of values of the scalar field at the points of the lattice Z that form elementary 3 × 3 squares vanish are considered; some explicit concrete conditions of general position on initial...

We give the simple general principle of studying the relations among fuzzy t-filters on residuated lattices. Using the general principle, we can easily determine the relations among fuzzy t-filters on different logical algebras.

Noticing certain limitations of concept lattices in the fuzzy context, especially view their practical applications, this paper, we propose a more general approach based on what call graded preconcept lattices. We believe that is adequate for dealing with information then one consider two possible gradation methods lattice—an inner one, called D-gradation and an outer M-gradation, study propert...

We give a new existence proof for the rank 2d even lattices usually called the Barnes-Wall lattices, and establish new results on uniqueness, structure and transitivity of the automorphism group on certain kinds of sublattices. Our proofs are relatively free of calculations, matrix work and counting, due to the uniqueness viewpoint. We deduce the labeling of coordinates on which earlier constru...

We prove that the f -vector of members in a certain class of meet semi-lattices satisfies Macaulay inequalities 0 ≤ ∂k(fk) ≤ fk−1 for all k ≥ 0. We construct a large family of meet semi-lattices belonging to this class, which includes all posets of multicomplexes, as well as meet semi-lattices with the ”diamond property”, discussed by Wegner [11], as special cases. Specializing the proof to the...

Approximation and Refinement Techniques for Hard Model-Checking Problems Mihaela Bobaru (née Gheorghiu) Doctor of Philosophy Graduate Department of Computer Science University of Toronto 2009 Formal verification by model checking verifies whether a system satisfies some given correctness properties, and is intractable in general. We focus on several problems originating from the usage of model ...

Recent work has shown that translating segmentation lattices (lattices that encode alternative ways of breaking the input to an MT system into words), rather than text in any particular segmentation, improves translation quality of languages whose orthography does not mark morpheme boundaries. However, much of this work has relied on multiple segmenters that perform differently on the same inpu...