Abstract This paper provides a systematic matrix description for finite Boolean- type algebras (BTAs). A BTA is decomposed into Boolean-type lattice (BTL) and complementation algebra (CA). When the object set finite, expressions of BTL CA (and then BTA) are presented. Via their expression, construction certain properties BTAs investigated, including homomorphism isomorphism, as well decompositi...

We investigate the duality between algebraic and coalgebraic recognition of languages to derive a generalization of the local version of Eilenberg’s theorem. This theorem states that the lattice of all boolean algebras of regular languages over an alphabetΣ closed under derivatives is isomorphic to the lattice of all pseudovarieties ofΣ-generated monoids. By applying our method to different cat...

We present a refinement of Ramsey numbers by considering graphs with a partial ordering on their vertices. This is a natural extension of the ordered Ramsey numbers. We formalize situations in which we can use arbitrary families of partially-ordered sets to form host graphs for Ramsey problems. We explore connections to well studied Turán-type problems in partially-ordered sets, particularly th...

If L is a lattice, the automorphism group of L is denoted Aut(L). It is known that given a finite abstract group H, there exists a finite distributive lattice D such that Aut(D) £= H. It is also known that one cannot expect to find a finite orthocomplemented distributive (Boolean) lattice B such that Aut(B) s= H. In this paper it is shown that there does exist a finite orthomodular lattice L su...

The category D of finite directed graphs is cartesian closed, hence it has a product and exponential objects. For a fixed K, let K be the class of all directed graphs of the formK, preordered by the existence of homomorphisms, and quotiented by homomorphic equivalence. It has loong been known that K, is always boolean lattice. In this paper we prove that for any complete graph Kn with n ≥ 3, K ...

Contrasting to Description Logics (DLs), there are some inherent shortcomings in classical fuzzy Description Logics (FDLs). For example, they no longer satisfy the complementary laws. In this paper, to analyze these shortcomings derived from Zadeh semantics, an improved fuzzy set definition using Boolean lattices is approached, whereas, the analogous definition of Zadeh Fuzzy Set can only use a...

Canfield and Mason have conjectured that for all subgroups G of the automorphism group of the Boolean lattice Bn (which can be regarded as the symmetric group Sn) the quotient order Bn/G is a symmetric chain order. We provide a straightforward proof of a generalization of a result of K. K. Jordan: namely, Bn/G is an SCO whenever G is generated by powers of disjoint cycles. In addition, the Bool...

2014 The two-dimensional random Boolean networks suggested by Kauffman have a transition to chaos. We find by Monte Carlo simulation the periods of the limit cycles, both for each site as well as for the lattice as a whole, at the transition point and away from it, for the square lattice. The triangular lattice seems to have the same fractal dimensions as the square lattice. J. Physique 48 (198...

An orthogonality space is a set equipped with symmetric, irreflexive relation called orthogonality. Every has an associated complete ortholattice, the logic of space. To every poset, we associate consisting proper quotients (that means, nonsingleton closed intervals), certain relation. We prove that finite bounded poset lattice if and only its orthomodular lattice. chain Boolean algebra.

A computably enumerable Boolean algebra B is effectively dense if for each x ∈ B we can effectively determine an F (x) ≤ x such that x 6= 0 implies 0 < F (x) < x. We give an interpretation of true arithmetic in the theory of the lattice of computably enumerable ideals of such a Boolean algebra. As an application, we also obtain an interpretation of true arithmetic in all theories of intervals o...