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Set-theoretic mereology
2016
Logic and Logical Philosophy
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We consider a set-theoretic version of mereology based on the inclusion relation ⊆ and analyze how well it might serve as a foundation of mathematics. ...
After establishing the non-definability of ∈ from ⊆, we identify the natural axioms for ⊆-based mereology, which constitute a finitely axiomatizable, complete, decidable theory. ...
The structure of hereditarily finite sets HF under inclusion is an elementary substructure of the entire set-theoretic universe V under inclusion: HF, ⊆ ≺ V, ⊆ . Proof. ...
doi:10.12775/llp.2016.007
fatcat:xrj2bzsp7nf2ho33fwyi2thbx4
Set-theoretic mereology
[article]
2016
arXiv
pre-print
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We consider a set-theoretic version of mereology based on the inclusion relation ⊆ and analyze how well it might serve as a foundation of mathematics. ...
After establishing the non-definability of ∈ from ⊆, we identify the natural axioms for ⊆-based mereology, which constitute a finitely axiomatizable, complete, decidable theory. ...
The structure of hereditarily finite sets HF under inclusion is an elementary substructure of the entire set-theoretic universe V under inclusion. HF, ⊆ ≺ V, ⊆ Proof. ...
arXiv:1601.06593v2
fatcat:z7twbd7w6fhunk7z77xzdqxpfu
Statistical entailments and the Galois lattice
1996
Social Networks
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of null hypotheses of statistical independence as a potential source of binary data structure, and second at constructing a discrete structure (Boolean) model of those statistical interactions that remain ...
on Boolean patterns that occur in the data) that can be used to simplify (by approximation) the lattice of empirical patterns. ...
Cutoffs based on the level of exceptions which maximizes the Pearson Product-moment correlation based on four cells (a, b, c, d) for strong inclusions, as in Table 1 , are repeated for weak inclusion, ...
doi:10.1016/0378-8733(95)00273-1
fatcat:cq4waqdahngz3b2cku2gqubf3a
Rough operations on Boolean algebras
2005
Information Sciences
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The inclusion relation in the Boolean algebra χ 0 is that of χ, restricted to χ 0 . ...
In this paper, we introduce two pairs of rough operations on Boolean algebras. First we define a pair of rough approximations based on a partition of the unity of a Boolean algebra. ...
In Section 4, we first define a pair of rough approximations based on a partition of the unity of a Boolean algebra, then propose a pair of generalized rough approximations after defining a basic assignment ...
doi:10.1016/j.ins.2004.06.006
fatcat:mwnoxkzsu5fqjhry3xeswaymaa
Supplier Selection Using Interpolative Boolean Algebra and Logic Aggregation
[chapter]
2014
Communications in Computer and Information Science
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The interest of the decision makers in the selection process of suppliers is constantly growing as a reliable supplier reduces costs and improves the quality of products/services. ...
Setting logical conditions between attributes was carried out by using the Boolean Interpolative Algebra. ...
The principle of structural functionality indicates that the structure of any element of IBA may be directly calculated based on the structure of its components. ...
doi:10.1007/978-3-319-08855-6_1
fatcat:q6qxvivr4jaetnxlxha6kp4mnq
The Local Joyal Model Structure
[article]
2016
arXiv
pre-print
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It is shown that the Joyal quasi-category model structure for simplicial sets extends to a model structure on simplicial presheaves, for which the weak equivalences are local (or stalkwise) Joyal equivalences ...
The article [2] of Jardine gives a proof of the existence of the Jardine model structure based on the technique of Boolean localization. ...
Introduction The purpose of this paper is develop an analog of the Jardine model structure on simplicial presheaves in which, rather than having the weak equivalences be 'local Kan equivalences', the weak ...
arXiv:1507.08723v2
fatcat:d5koc75mdjfuniqtojfwnglmcy
Boolean Models and Simultaneous Inequalities
[article]
2009
arXiv
pre-print
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Boolean models are applied to deriving operator versions of the classical Farkas Lemma in the theory of simultaneous linear inequalities. ...
That is what we have learned from the Boolean models elaborated in the 1960s by Scott, Solovay, and Vopěnka. ...
The chase of truth not only leads us close to the truth we pursue but also enables us to nearly catch up with many other instances of truth which we were not aware nor even foresaw at the start of the ...
arXiv:0907.0060v4
fatcat:qv4xp446pbdj5b4zbv3fpxjheu
The power of primitive positive definitions with polynomially many variables
2016
Journal of Logic and Computation
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The latter do however have limited expressivity, and the corresponding lattice of strong partial clones is of uncountably innite cardinality even for the Boolean domain. ...
Sets of relations closed under p.p. denitions are known as co-clones and sets of relations closed under q.f.p.p. denitions as weak partial co-clones. ...
Acknowledgements The authors are grateful toward Peter Jonsson, Karsten Schölzel and Bruno Zanuttini, for helpful comments and suggestions. ...
doi:10.1093/logcom/exw005
fatcat:vdf5onpuz5a2jplxgi7zaq6say
Page 5309 of Mathematical Reviews Vol. , Issue 93j
[page]
1993
Mathematical Reviews
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The author demonstrates that the set of equivalence classes (rough sets) of such a relation is par- tially ordered with respect to the relation of rough (approximate) inclusion. ...
Then they study the structure of prime filters of a P-algebra and give a canonical form of any P-algebra homomorphism. ...
Duality for modal μ-logics
1998
Theoretical Computer Science
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The special case of completeness for the Boolean p-calculus is an improvement over that presented in [3] but weaker than the theorem of [35] . ...
the Boolean modal p-logics. ...
Acknowledgements I wish to thank Robert Goldblatt for spoting an inaccuracy in the way my completeness theorem was phrased in an earlier version. ...
doi:10.1016/s0304-3975(97)00233-8
fatcat:bkuwgqcg2fg6lmhw55wds2a5vm
Progressive Dimension-Independent Boolean Operations
[article]
2004
Solid Modeling
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Boolean set operations are computed progressively by reading in input a stream of incremental refinements of the operands. ...
Each refinement of the input is mapped immediately to a refinement of the output so that the result is also represented as a stream of progressive refinements. ...
generated BSP tree and on a lattice-based Split data structure of the cell decomposition. ...
doi:10.2312/sm.20041391
fatcat:gmldqku35vdclpdkufbzxwperu
A topological representation of double Boolean lattices
2019
Studia Universitatis Babes-Bolyai Matematica
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In this paper, we provide a topological representation for double Boolean algebras based on the so-called DB-topological contexts. ...
A double Boolean algebra is then represented as the algebra of clopen protoconcepts of some DB-topological context. Mathematics Subject Classification (2010): 18B35, 54B30, 68T30. ...
Each filter of the Boolean algebra D ⊓ is a base of some filter of D; in particular, F ∩ D ⊓ is a base of F . ...
doi:10.24193/subbmath.2019.1.02
fatcat:obbh5yufova53bcpsa3hmipgmm
Page 1688 of Mathematical Reviews Vol. 55, Issue 6
[page]
1978
Mathematical Reviews
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The proof of the last result is based on the author’s theorem [ibid. 94 (1977), no. 2, 121-128; MR 55 #10269] of the finite axiomatizability of any nuclear X,-categorical structure. ...
The proof uses the fact that the weak second order theory of linear order is decidable and also the fact that any countable Boolean algebra is isomorphic to a Boolean algebra generated by all left closed ...
Basins of Attraction, Commitment Sets and Phenotypes of Boolean Networks
[article]
2018
arXiv
pre-print
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The attractors of Boolean networks and their basins have been shown to be highly relevant for model validation and predictive modelling, e.g., in systems biology. ...
In the realm of asynchronous, non-deterministic modeling not only is the repertoire of software even more limited, but also the formal notions for basins of attraction are often lacking. ...
The work was partially funded by the German Federal Ministry of Education and Research (BMBF), grant no. 0316195. ...
arXiv:1807.10103v1
fatcat:aws7v5enczeprcrsy7szv6z5xy
FE2-Simulation of Microheterogeneous Steels Based on Statistically Similar RVEs
[chapter]
2010
IUTAM Bookseries
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We focus on random microstructures consisting of a continuous matrix phase with a high number of embedded inclusions. ...
The basic idea of the underlying procedure is to find a simplified SSRVE, whose selected statistical measures under consideration are as close as possible to the ones of the original microstructure. ...
Acknowledgement The financial support of the "Deutsche Forschungsgemeinschaft" (DFG), project no. SCHR 570-8/1, is gratefully acknowledged. ...
doi:10.1007/978-90-481-9195-6_2
fatcat:selnjyi6sjh3fodzpfw42kvo5q
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