Filters








20,447 Hits in 5.8 sec

Set-theoretic mereology

Joel David Hamkins, Makoto Kikuchi
2016 Logic and Logical Philosophy  
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]

Joel David Hamkins, Makoto Kikuchi
2016 arXiv   pre-print
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

Douglas R. White
1996 Social Networks  
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

Guilin Qi, Weiru Liu
2005 Information Sciences  
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]

Ksenija Mandic, Boris Delibasic
2014 Communications in Computer and Information Science  
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]

Nicholas Meadows
2016 arXiv   pre-print
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]

S. S. Kutateladze
2009 arXiv   pre-print
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

Victor Lagerkvist, Magnus Wahlström
2016 Journal of Logic and Computation  
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  
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

Chrysafis Hartonas
1998 Theoretical Computer Science  
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]

A. Paoluzzi, V. Pascucci, G. Scorzelli
2004 Solid Modeling  
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

Brigitte E. Brecker, Christian Sacarea
2019 Studia Universitatis Babes-Bolyai Matematica  
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  
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]

Hannes Klarner, Frederike Heinitz, Sarah Nee, Heike Siebert
2018 arXiv   pre-print
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]

D. Balzani, J. Schröder, D. Brands
2010 IUTAM Bookseries  
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
« Previous Showing results 1 — 15 out of 20,447 results