Each Boolean algebra is isomorphic to an algebra of sets. This fact was already mentioned in the preceding chapters. Below, we give an exact formulation and a complete proof of the celebrated Stone Theorem and discuss the problems that arise in connection with this theorem....
摘要: Boolean contact algebras are the abstract counterpart of region–based theories of space, which date back to the early 1920s. In this paper, we survey the development of these algebras and relevant construction and representation theorems....
This paper proposes a mathematical model based on a Boolean algebra involving a 44 social capital matrix [Shah (2008)], that emerges through interaction within and across individuals, communities, institutions and state. The framework provides a coding system for the existence or otherwise of various...
Nechaev, Ideal representation of Reed-Solomon and Reed-Muller codes, Algebra and Logic, vol.51, no.3 (2012).E. Couselo, S. Gonzalez, VT. Markov,... E Couselo,S Gonz - 《Algebra & Logic》 被引量: 4发表: 2012年 Reed–Solomon and Simplex Codes for Peak-to-Average Power Ratio Reduc...
Effect algebraMV-algebraAn {\\em MV-pair} is a pair $(B,G)$ where $B$ is a Boolean algebra and $G$ is a subgroup of the automorphism group of $B$ satisfying certain conditions. Let $\\sim_G$ be the equivalence relation on $B$ naturally associated with $G$. We prove that for...
We sketch the proof. Let D be an atomic co-diagonalizable algebra. At(D) denotes the set of all atoms in D. The mapping h : D →P(At(D)) defined by: h(a) = {x ∈ At(D) : x ≤ a} is a Boolean monomorphism of the Boolean algebra (D, ∪, ∩, −, 0, 1) into...
All image processing algorithms can be expressed compactly and often transparently in the language of image algebra. Convolutional operations and mathematical morphological transforms can be represented particularly easily. The representation of median and the many related filters is less obvious, however. ...
Logic of Rough Sets The collection of all subsets of a set forms a Boolean algebra under the usual set theoretic operations, while the collection of rough sets of an approxima... M Banerjee,MK Chakraborty - Springer-Verlag 被引量: 46发表: 1993年 Spectra of Maximal 1-Sided Ideals and Prim...
MV-algebrastateintegral representationpartition of unity03B5228E9903E72MV-algebras stand for the many-valued ukasiewicz logic the same as Boolean algebras for the classical logic. States on MV-algebras were first mentioned [20] in probability theory and later also introduced in effort to capture a...
Starting with the digital pattern data representations; the binary arithmetic operations of addition, 2’s complement subtraction, multiplication and division together with Boolean algebra and logic gates are developed with sufficient rigor to support the material presented in following chapters. ...