A survey of results is presented on relationships between the algebraic systems derived from the approximation spaces induced by information systems and various classes of algebras of relations. Rough relation algebras are presented and it is shown that they form a discriminator variety. A characterisation of the class of representable rough relation algebras is given. The family of closure ope...

In conventional computers, wiring between transistors is required to enable the execution of Boolean logic functions. This has resulted in processors in which billions of transistors are physically interconnected, which limits integration densities, gives rise to huge power consumption and restricts processing speeds. A method to eliminate wiring amongst transistors by condensing Boolean logic ...

We develop a computation model for solving Boolean networks that implements wires through quantum ground-state computation and implements gates through identities following from angular momentum algebra and statistics. The gates are static in the sense that they contribute Hamiltonian 0 and hold as constants of the motion; only the wires are dynamic. Just as a spin 1/2 makes an ideal 1-bit memo...

Recently we have proposed novel Boolean Single-Flux-Quantum (BSFQ) circuits, which just like CMOS circuits support Boolean primitives directly, and do not require local synchronization for each operation cell. However, previous BSFQ AND, OR, and XOR cells suffered from problems with narrow margin, where their critical margins hardly exceeded +lo% due to low flux gain. Furthermore, while being s...

Suppose that S ⊆ P (X) is a σ-field of subsets ofX and I ⊆ S is a σ-ideal. If I has the countable chain condition (ccc), i.e., every family of disjoint sets in S \ I is countable, then S/I is a complete boolean algebra. A boolean algebra is atomic iff there is an atom beneath every nonzero element. A function f : X → R is S-measurable iff f(U) ∈ S for every open set U . A sequence of S-measurab...

A Heyting algebra is supplemented if each element a has dual pseudo-complement $$a^+$$ , and centrally supplement it central. We show that extension in the same variety of algebras as original. use this tool to investigate new type completion arising context algebraic proof theory, so-called hyper-MacNeille completion. MacNeille its extension. This provides an description algebra, allows develo...

the aim of this paper is to extend results established by h. onoand t. kowalski regarding directly indecomposable commutative residuatedlattices to the non-commutative case. the main theorem states that a residuatedlattice a is directly indecomposable if and only if its boolean center b(a)is {0, 1}. we also prove that any linearly ordered residuated lattice and anylocal residuated lattice are d...

A regular language has the zero-one law if its asymptotic density converges to either zero or one. We prove that the class of all zero-one languages is closed under Boolean operations and quotients. Moreover, we prove that a regular language has the zero-one law if and only if its syntactic monoid has a zero element. Our proof gives both algebraic and automata characterisation of the zero-one l...

The study of perfect, local and bipartite IMTL-algebras presented in [29] is generalized in this paper to the general non-involutive case, i. e. to MTL-algebras. To this end we describe the radical of MTL-algebras and characterize perfect MTL-algebras as those for which the quotient by the radical is isomorphic to the two-element Boolean algebra, and a special class of bipartite MTL-algebras, B...