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The Boolean Solution Problem from the Perspective of Predicate Logic [chapter]

Christoph Wernhard
2017 Lecture Notes in Computer Science  
Finding solution values for unknowns in Boolean equations was, along with second-order quantifier elimination, a principal reasoning mode in the Algebra of Logic of the 19th century.  ...  Schröder [19] investigated it as Auflösungsproblem (solution problem). It is closely related to the modern notion of Boolean unification.  ...  Finding solution values for unknowns in Boolean equations was, along with second-order quantifier elimination, a principal reasoning mode in the Algebra of Logic of the 19th century.  ... 
doi:10.1007/978-3-319-66167-4_19 fatcat:bpilus2ivrgwfeqswljpngbpum

Formalization of Human Categorization Process Using Interpolative Boolean Algebra

Vladimir Dobrić, Darko Kovačević, Bratislav Petrović, Dragan Radojević, Pavle Milošević
2015 Mathematical Problems in Engineering  
In this paper, the prototype theory is approached by using structure-functional fuzzy logic, the interpolative Boolean algebra. The proposed formalism is within the Boolean frame.  ...  The introduced formalism secures the principles of categorization showing that Boolean laws are fundamental in the categorization process.  ...  Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper.  ... 
doi:10.1155/2015/620797 fatcat:6m5b2rdvqzemnliwf43wm3hguy

The Vitali-Hahn-Saks theorem for Boolean algebras with the subsequential interpolation property

Francisco Jos{é Freniche
1984 Proceedings of the American Mathematical Society  
In [2, p. 36 ] the problem is raised of finding an algebraic characterization of those Boolean algebras for which the Vitali-Hahn-Saks theorem holds.  ...  Let A be a Boolean algebra with the Subsequential Interpolation Property, and let (pn)neu ue a sequence of complex-valued bounded variation finitely additive measures on A such that lim^^oo pn(a) = 0 for  ... 
doi:10.1090/s0002-9939-1984-0759653-1 fatcat:unjq5zpl7ndmhdgiwg47rzvkra

The Vitali-Hahn-Saks Theorem for Boolean Algebras with the Subsequential Interpolation Property

Francisco Jose Freniche
1984 Proceedings of the American Mathematical Society  
In [2, p. 36 ] the problem is raised of finding an algebraic characterization of those Boolean algebras for which the Vitali-Hahn-Saks theorem holds.  ...  Let A be a Boolean algebra with the Subsequential Interpolation Property, and let (pn)neu ue a sequence of complex-valued bounded variation finitely additive measures on A such that lim^^oo pn(a) = 0 for  ... 
doi:10.2307/2044835 fatcat:ebsux3txabbpth4jzlolzjwu44

Page 1666 of Mathematical Reviews Vol. , Issue 2000c [page]

2000 Mathematical Reviews  
In this direction we obtain an effective interpolation in the form of a protocol of small real communication complexity.  ...  Symbolic Logic 62 (1997), no. 2, 457-486; MR 98k:03116 (Definition 2.2)]) of small real communication complexity solving the monotone communi- cation complexity problem associated with the bipartite perfect  ... 

Supplier Selection Using Interpolative Boolean Algebra and Logic Aggregation [chapter]

Ksenija Mandic, Boris Delibasic
2014 Communications in Computer and Information Science  
Setting logical conditions between attributes was carried out by using the Boolean Interpolative Algebra.  ...  This process is essentially reducible to the problem of multi-attribute decision-making. Namely, the large number of quantitative and qualitative attributes is considered.  ...  The basis of this approach is interpolative realization of Boolean algebra that transforms logical conditions between attributes into a generalized Boolean polynomial, then the set logical conditions merge  ... 
doi:10.1007/978-3-319-08855-6_1 fatcat:q6qxvivr4jaetnxlxha6kp4mnq

A Consensus Model in Group Decision Making Based on Interpolative Boolean Algebra

Ana Poledica, Pavle Milosevic, Ivana Dragovic, Dragan Radojevic, Bratislav Petrovic
2013 Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology  
The aim of this paper is to propose a soft consensus model based on interpolative Boolean algebra for group decision making problems.  ...  In the illustrative example of sustainable development problem, we have shown that the proposed model is appropriate to determine the level of agreement among experts.  ...  Interpolative Realization of Boolean Algebra This section brings briefly overview of Interpolative Boolean Algebra, a consistent multi-valued ([0,1]valued) realization of finite (atomic) Boolean algebra  ... 
doi:10.2991/eusflat.2013.98 dblp:conf/eusflat/PoledicaMDRP13 fatcat:5xeowc5evbfavgo5ypktai4gfe

Page 1192 of Mathematical Reviews Vol. , Issue 90B [page]

1990 Mathematical Reviews  
More precisely, he introduces a lower bound on the Ostrowski complexity of division in finite extension fields and an optimal lower bound on the complexity of inversion in quadratic alternative algebras  ...  A general and interesting method for obtaining lower bounds on the contact circuit complexity of explicitly defined Boolean functions is presented.  ... 

Existence of short proofs for nondivisibility of sparse polynomials under the extended Riemann hypothesis

Dima Yu. Grigoriev, Marek Karpinski, Andrew M. Odlyzko
1992 Papers from the international symposium on Symbolic and algebraic computation - ISSAC '92  
Singer for the number of interesting discussions. IEEE, 1990, pp. 840-846. [K 89] Karpinski, M., Boolean References  ...  The divisibility problem is closely related to the rational interpolation problem (whose complexity bounds were determined in [GKS 90 ] and [GK 91]) .  ...  We prove also that, surprisingly, the problem of deciding whether a rational function given by a black Then the multiplicity of this root in j equals mf and in g is at least rn~.  ... 
doi:10.1145/143242.143287 dblp:conf/issac/GrigorievKO92 fatcat:p4d43y452rf4nduinx7ranqlhe

Page 2 of Mathematical Reviews Vol. , Issue 89F [page]

1989 Mathematical Reviews  
V.] (6-ANDH) On some problems of BCK-algebras and Griss type algebras. Math. Japon. 33 (1988), no. 2, 301-302. The author solves Problems 4, 6 and 8 in a paper by K.  ...  complete Boolean algebras).  ... 

Page 718 of Mathematical Reviews Vol. , Issue 2001A [page]

2001 Mathematical Reviews  
In Chapters 8 and 9 the author turns to the Diffie- Hellman problem and investigates it from the viewpoint of the arithmetic complexity and the Boolean complexity, respectively.  ...  Analogous questions for the interpolation and approximation by real or complex polynomials are treated in Chapter 7.  ... 

Boolean Set Operations with Cubic Algebraic Patches

Chandrajit Bajaj, Alberto Paoluzzi, Simone Portuesi, Na Lei, Wenqi Zhao
2008 Computer-Aided Design and Applications  
On each triangle of a boundary representation of such linear approximation, a piecewise cubic algebraic interpolant is built, using a C 1 -continuous prism algebraic patch (prism A-patch) that interpolates  ...  In this paper we discuss a symbolic-numeric algorithm for Boolean operations, closed in the algebra of curved polyhedra whose boundary is triangulated with algebraic patches (A-patches).  ...  Acknowledgments This research was supported in part by NSF grant CNS-0540033, NIH contracts P20-RR020647, R01-EB00487, R01-GM074258, R01-GM07308, MIUR Finanziamento Dottorato SICS and NNSF of China 10601020  ... 
doi:10.3722/cadaps.2008.730-742 pmid:21516262 pmcid:PMC3080140 fatcat:vcyz3b3xojdcvestphp4wrw6w4

Page 4838 of Mathematical Reviews Vol. , Issue 81M [page]

1981 Mathematical Reviews  
(the Boolean algebra dual to) the base of the corresponding sheaf.  ...  Werner on representations of algebras as algebras © of sections of sheaves over Boolean spaces” (from the author’ ‘introduction).  ... 

Algebras of bounded sequences

Kenneth Hoffman, Arlan Ramsay
1965 Pacific Journal of Mathematics  
Let ϊ°° be the algebra of all bounded sequences of complex numbers.  ...  The primary purpose of this paper is to settle, by means of a counter-example, a conjecture about subalgebras of l°°: If A is a subalgebra of l°° which is closed under uniform convergence and separates  ...  Our interest in subalgebras of l°° stems from recent work on interpolation problems. In 1957, R. C.  ... 
doi:10.2140/pjm.1965.15.1239 fatcat:bzmdzptk6nbd7ma3z2dkyyxwey

Page 365 of Mathematics of Computation Vol. 2, Issue 20 [page]

1947 Mathematics of Computation  
This approach consists in the applica- tion of Boolean algebra to the design of relay circuits to possess given functional ability.  ...  The elements of this algebra are given and the conversion of the algebra into relay circuits is treated.  ... 
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