We study the compatibility of a construction proposed by Aït-Kaci to extend a poset of sorts into a lattice with the specification on type constraints on the value of attributes, through Gloess assorted signatures. We first show that it is natural to extend the poset into a boolean algebra, when one wishes to obtain a complete and complementary lattice endowed with a smooth semantics. We then s...

It is well-known that the question of whether a given finite region can be tiled with a given set of tiles is NP-complete. We show that the same is true for the right tromino and square tetromino on the square lattice, or for the right tromino alone. In the process, we show that Monotone 1-in-3 Satisfiability is NP-complete for planar cubic graphs. In higher dimensions, we show NP-completeness ...

We define a regularity axiom for lattice-valued convergence spaces where the lattice is a complete Heyting algebra. To this end, we generalize the characterization of regularity by a ”dual form” of a diagonal condition. We show that our axiom ensures that a regular T1-space is separated and that regularity is preserved under initial constructions. Further we present an extension theorem for a c...