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

2017
*
Lecture Notes in Computer Science
*

Finding solution values for unknowns in

doi:10.1007/978-3-319-66167-4_19
fatcat:bpilus2ivrgwfeqswljpngbpum
*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. ...##
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Formalization of Human Categorization Process Using Interpolative Boolean Algebra

2015
*
Mathematical Problems in Engineering
*

In this paper, the prototype theory is approached by using structure-functional fuzzy logic, the

doi:10.1155/2015/620797
fatcat:6m5b2rdvqzemnliwf43wm3hguy
*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. ...##
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The Vitali-Hahn-Saks theorem for Boolean algebras with the subsequential interpolation property

1984
*
Proceedings of the American Mathematical Society
*

In [2, p. 36 ] the

doi:10.1090/s0002-9939-1984-0759653-1
fatcat:unjq5zpl7ndmhdgiwg47rzvkra
*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 ...##
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The Vitali-Hahn-Saks Theorem for Boolean Algebras with the Subsequential Interpolation Property

1984
*
Proceedings of the American Mathematical Society
*

In [2, p. 36 ] the

doi:10.2307/2044835
fatcat:ebsux3txabbpth4jzlolzjwu44
*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 ...##
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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]

2014
*
Communications in Computer and Information Science
*

Setting logical conditions between attributes was carried out by using the

doi:10.1007/978-3-319-08855-6_1
fatcat:q6qxvivr4jaetnxlxha6kp4mnq
*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 ...##
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A Consensus Model in Group Decision Making Based on Interpolative Boolean Algebra

2013
*
Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology
*

The aim

doi:10.2991/eusflat.2013.98
dblp:conf/eusflat/PoledicaMDRP13
fatcat:5xeowc5evbfavgo5ypktai4gfe
*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*...##
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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

1992
*
Papers from the international symposium on Symbolic and algebraic computation - ISSAC '92
*

Singer for the number

doi:10.1145/143242.143287
dblp:conf/issac/GrigorievKO92
fatcat:p4d43y452rf4nduinx7ranqlhe
*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~. ...##
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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

2008
*
Computer-Aided Design and Applications
*

On each triangle

doi:10.3722/cadaps.2008.730-742
pmid:21516262
pmcid:PMC3080140
fatcat:vcyz3b3xojdcvestphp4wrw6w4
*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 ...##
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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). ...##
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Algebras of bounded sequences

1965
*
Pacific Journal of Mathematics
*

Let ϊ°° be the

doi:10.2140/pjm.1965.15.1239
fatcat:bzmdzptk6nbd7ma3z2dkyyxwey
*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. ...##
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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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