Boolean semantics is a version of formal semantics in which models are supposed to have algebraic, preferably Boolean, structure (Keenan and Faltz 1985). Thus for any category C there is a corresponding denotational Boolean algebra DC of possible denotations of expressions of category C. Furthermore, given that most categories are functionally related (in principle all ”major” categories are Bo...

Boolean algebras have an exceptionally rich and smooth structure theory, of which Stone’s representation theorem is a prominent example. What is so special about Boolean algebras that is responsible for this nice behaviour? Given a similarity type ν, can we always find a class of algebras of type ν that displays Boolean-like features? And what does it mean, for an algebra of a given type ν that...

By a strong conceptual completeness (XC) statement for a logical doctrine we mean an assertion that says that any theory of the doctrine can be recovered from an appropriate structure formed by the models of the theory. The expression ‘logical doctrine’ is used here as in [9] to mean a specific selection of logical operations giving rise to a notion of theory, in the form of a structured catego...

One can prove the following propositions: (1) For every set D and for every finite sequence p and for every natural number n such that p ∈ D holds p↾ Segn ∈ D. (2) For every binary tree T holds every element of T is a finite sequence of elements of Boolean. Let T be a binary tree. We see that the element of T is a finite sequence of elements of Boolean. Next we state several propositions: (3) F...

this paper is the first of a two part series. in this paper, we first prove that the variety of dually quasi-de morgan stone semi-heyting algebras of level 1 satisfies the strongly blended $lor$-de morgan law introduced in cite{sa12}. then, using this result and the results of cite{sa12}, we prove our main result which gives an explicit description of simple algebras(=subdirectly irreducibles) ...

‎The notion of (Boolean) uni-soft filters‎ ‎in MTL-algebras is introduced‎, ‎and several properties of them are‎ ‎investigated‎. ‎Characterizations of (Boolean) uni-soft filters are discussed‎, ‎and some (necessary and sufficient) conditions‎ ‎for a uni-soft filter to be Boolean are provided‎. ‎The condensational property for a Boolean uni-soft filter is established.

This paper suggests a new approach for modeling of Boolean neural networks on fieldprogrammable gate arrays (FPGAs) using UML. The presented Boolean neural networks (BNN) allow a decreasing of the required number of configurable logic blocks (CLB) for the realizing of Boolean neuron. The element of BNN, called Boolean neuron, may be mapped directly to lookup table (LUT) and configurable logic b...

in this paper the concept of an $omega$- almost boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $omega$- almost boolean ring over a locally boolean space.

Let A =< A,≤A> and B =< B,≤B> be lattices such that A ∩ B is a filter in A and an ideal in B, and the orderings ≤A and ≤B coincide on A ∩ B. Then ≤A ∪ ≤B ∪ (≤A ◦ ≤B), is a lattice ordering on A ∪ B and the resulting lattice, called a sum of A and B, is denoted by A ⊕ B. The sum operation was introduced by Wroński [5], and its special case with A∩B = {1A} = {0B} by Troelstra [4]. In particular, ...