A new hierarchy of “exact” unification types is introduced, motivated by the study of admissible rules for equational classes and non-classical logics. In this setting, unifiers of identities in an equational class are preordered, not by instantiation, but rather by inclusion over the corresponding sets of unified identities. Minimal complete sets of unifiers under this new preordering always h...

This paper extends the l-complete approximation method developed for time invariant systems to a larger system class, ensuring that the resulting approximation can be realized by a finite state machine. To derive the new abstraction method, called asynchronous l-complete approximation, an asynchronous version of the well-known concepts of state property, memory span and l-completeness is introd...

The Grätzer-Schmidt theorem of lattice theory states that each algebraic lattice is isomorphic to the congruence lattice of an algebra. A lattice is algebraic if it is complete and generated by its compact elements. We show that the set of indices of computable lattices that are complete is Π 1 -complete; the set of indices of computable lattices that are algebraic is Π 1 -complete; and that th...

We prove that (1) for any complete lattice $L$, the set $\mathcal {D}(L)$ of all non-empty saturated compact subsets Scott space $L$ is a Heyting algebra (with reverse inclusion order); and (2) if latti

Given two complete atomistic lattices L 1 and L 2 , we define a set S = S(L 1 , L 2) of complete atomistic lattices by means of four axioms (natural regarding the logic of compound quantum systems), or in terms of a universal property with respect to a given class of bimorphisms (Th. 3.3). S is a complete lattice (Th. 0.10). The bottom element L 1 ∧ L 2 is the separated product of Aerts [1]. Fo...

We study the monoid generalizationMk,1 of the Thompson-Higman groups, and we characterize the Rand the L-preorder ofMk,1. Although Mk,1 has only one non-zero J -class and k−1 non-zero D-classes, the Rand the L-preorder are complicated; in particular, <R is dense (even within an L-class), and <L is dense (even within an R-class). We study the computational complexity of the Rand the L-preorder. ...

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...