A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Overlap Algebras: a Constructive Look at Complete Boolean Algebras
[article]

2020
*
arXiv
*
pre-print

The notion of

arXiv:1904.13320v3
fatcat:sd5z454gqbbyrpm3bxu27xk5pi
*a**complete**Boolean**algebra*, although*completely*legitimate in*constructive*mathematics, fails to capture some natural structures such as the lattice of subsets of*a*given set. ... Sambin's notion of an*overlap**algebra*, although classically equivalent to that of*a**complete**Boolean**algebra*, has powersets and other natural structures as instances. ... The latter fails*constructively*;*a**constructive*version can be obtained by replacing*complete**Boolean**algebras*by Sambin's*overlap**algebras*, as we now see. Definition 2.1. ...##
###
Overlap Algebras: a Constructive Look at Complete Boolean Algebras

2019
*
Logical Methods in Computer Science
*

The notion of

doi:10.23638/lmcs-16(1:13)2020
fatcat:lr2val2apfgjvcmell2eoyljq4
*a**complete**Boolean**algebra*, although*completely*legitimate in*constructive*mathematics, fails to capture some natural structures such as the lattice of subsets of*a*given set. ... Sambin's notion of an*overlap**algebra*, although classically equivalent to that of*a**complete**Boolean**algebra*, has powersets and other natural structures as instances. ... The latter fails*constructively*;*a**constructive*version can be obtained by replacing*complete**Boolean**algebras*by Sambin's*overlap**algebras*, as we now see. Definition 2.1. ...##
###
Overlap Algebras as Almost Discrete Locales
[article]

2021
*
arXiv
*
pre-print

Our claim is that Sambin's

arXiv:1601.04830v2
fatcat:5adeucvv6rgiho6vwt47ijrfeq
*Overlap**Algebras*have good enough features to deserve to be called that. ...*Boolean*locales are "almost discrete", in the sense that*a*spatial*Boolean*locale is the same thing as the frame of open subsets of*a*discrete space, that is, the powerset of*a*set. ... Introduction If the open sets of*a*topological space form*a**complete**Boolean**algebra*, instead of*a*mere*complete*Heyting*algebra*, then the space is "almost discrete": every Kolmogorov almost discrete space ...##
###
The overlap algebra of regular opens

2010
*
Journal of Pure and Applied Algebra
*

Since they are

doi:10.1016/j.jpaa.2010.02.002
fatcat:lurhv2gx5re5han2n3mnzfqbqm
*a**constructive*counterpart to*complete**Boolean**algebras*and,*at*the same time, they have*a*more powerful axiomatization than Heyting*algebras*,*overlap**algebras*are expected to turn out useful ...*Overlap**algebras*can be seen as particular open (or overt) locales and, from*a*classical point of view, they essentially coincide with*complete**Boolean**algebras*. ... In particular, it was he who first noticed the connection with open locales and with*complete**Boolean**algebras*. ...##
###
Formalising Overlap Algebras in Matita

2011
*
Mathematical Structures in Computer Science
*

*Overlap*

*Algebras*are new

*algebraic*structures designed to ease reasoning about subsets in an

*algebraic*way within intuitionistic logic. ... We describe some formal topological results, formalized in Matita 1/2, presented in predicative intuitionistic logic and in terms of

*Overlap*

*Algebras*. ...

*Overlap*

*Algebras*are to intuitionistic subset theory what

*Boolean*

*algebras*are to classical subset theory. ...

##
###
Intuitionistic overlap structures

2013
*
Logic and Logical Philosophy
*

The main thesis of this paper is that the

doi:10.12775/llp.2013.011
fatcat:hhir5heupvc2xhcf4tzthkqaxu
*overlap*relation in the latter sense is*a*necessary tool for*a**constructive*and intuitionistic development of point-free geometry. ... We study some connections between two kinds of*overlap*relations: that of point-free geometries in the sense of Grzegorczyk, Whitehead and Clarke, and that recently introduced by Sambin within his*constructive*... It is*a*fact of life that Pow(S) is no longer*a**Boolean**algebra*as long as you*look**at*it from an intuitionistic point of view. ...##
###
Regular opens in constructive topology and a representation theorem for overlap algebras

2013
*
Annals of Pure and Applied Logic
*

Giovanni Sambin has recently introduced the notion of an

doi:10.1016/j.apal.2012.10.006
fatcat:gmp4gog6ivci3f3kyhmcxjjkf4
*overlap**algebra*in order to give*a**constructive*counterpart to*a**complete**Boolean**algebra*. ... In particular we show that there exists*a*duality between the category of set-based*overlap**algebras*and*a*particular category of topologies in which all open subsets are regular. ... With classical logic,*overlap**algebras*are precisely*complete**Boolean**algebras*and hence the notion of an*overlap**algebra*is strictly stronger than that of*a**complete*Heyting*algebra*. ...##
###
Small overlap monoids II: Automatic structures and normal forms

2009
*
Journal of Algebra
*

We show that any finite monoid or semigroup presentation satisfying the small

doi:10.1016/j.jalgebra.2008.12.028
fatcat:u7pqoqnjgvgd7atr4h62v2qj3m
*overlap*condition C (4) has word problem which is*a*deterministic rational relation. ... It follows that the set of lexicographically minimal words forms*a*regular language of normal forms, and that these normal forms can be computed in linear time. ... Remeslennikov for*a*number of helpful conversations. ...##
###
A Cube Algebra with Comparative Operations: Containment, Overlap, Distance and Usability
[article]

2022
*
arXiv
*
pre-print

new cube from

arXiv:2203.09390v1
fatcat:qvqjwxc7sjfcve4d32nkd432ty
*a*previous one, defined*at**a*different level of abstraction. ... In this paper, we provide*a*comprehensive rigorous modeling for multidimensional spaces with hierarchically structured dimensions in several layers of abstractions and data cubes that live in such spaces ... We thus need*a*mechanism to detect inclusion,*overlap*and non-*overlap*of queries*at*the detailed level,*at*least as*a*pre-requisite to facilitate the assessment of novelty. ...##
###
Partiality II: Constructed relation algebras

2012
*
The Journal of Logic and Algebraic Programming
*

It will be shown how these can be fruitfully applied concerning

doi:10.1016/j.jlap.2012.05.005
fatcat:kxx3hpgzwjekpe2bvifvxk4bxq
*constructions*with temporarily non-connected relation*algebras*. ... Matrices of partialities will considerably improve the possibility to study non-strictness, streams, partial evaluation, and net properties in*a*compact relation-*algebraic*form. ... First, we take*a**look**at**a*very primitive*construction*. Proposition. ...##
###
Axioms, Algebras and Topology
[chapter]

2007
*
Handbook of Spatial Logics
*

Another way of

doi:10.1007/978-1-4020-5587-4_3
fatcat:ano2fojxs5c3lo2sbdrkqxwsg4
*looking**at*these*algebras*is via*a*certain class of lattices: An*algebra**A*, +, ·, ⇒, 0, 1 of type 2, 2, 2, 0, 0 is called*a*Heyting*algebra*(or pseudo-*Boolean**algebra*[89] ) if*A*, +, · ... We have*looked**at*the relationships between*algebraic*models, point-set topology and axiomatic theories of spatial regions. ...##
###
Strongly representable algebras
[article]

2013
*
arXiv
*
pre-print

We give

arXiv:1305.4532v1
fatcat:7oac6zr3wjbtvihfyaocqurxr4
*a*simpler proof of*a*result of Hodkinson in the context of*a*blow and blur up*construction*argueing that the idea*at*heart is similar to that adopted by Andréka et all sayed. ... This*construction*, which works for both relation and cylindric*algebras*, further shows that the class of strongly representable atom structures is not elementary. ... As before, for each u ∈*At*, choose any countable*Boolean*elementary*complete*subalgebra of*A*u , B u say. Le u i : i < m be elements in*At*, and let v = τ (u 1 , . . . u m ). ...##
###
Orthomodular algebraic lattices related to combinatorial posets

2014
*
Italian Conference on Theoretical Computer Science
*

An orthomodular lattice is always regular ( [7] ) and hence can be seen as

dblp:conf/ictcs/BernardinelloPR14
fatcat:3wuka6uf55fctpfdj6p2v2os54
*a*family of partially*overlapping**Boolean**algebras*. ... Orthomodular lattices are families of partially*overlapping**Boolean**algebras*and have been studied as the*algebraic*model of quantum logic [7] . ... Hence, if*A*⊂ B then B contains*at*least an element x concurrent with*A*. The orthomodular law is weaker than the distributive law. Orthocomplemented distributive lattices are called*Boolean**algebras*. ...##
###
Algebraic Neighbourhood Logic

2008
*
The Journal of Logic and Algebraic Programming
*

*A*further simplification is achieved, since the semiring methods used are easy and fairly standard. ... We present an

*algebraic*embedding of Neighbourhood Logic (NL) into the framework of semirings which yields various simplifications. ... More precisely we have

*a*

*look*

*at*the chop operator and

*at*Allen's 13 relations between intervals. ...

##
###
Chain homogeneous Souslin algebras
[article]

2010
*
arXiv
*
pre-print

Assuming Jensen's principle diamond-plus we

arXiv:1005.4948v1
fatcat:24cbla4pt5bwbj2lcjjdybntdi
*construct*Souslin*algebras*all of whose maximal chains are pairwise isomorphic as total orders, thereby answering questions of Koppelberg and Todorcevic ... Thanks are due to Sabine Koppelberg for asking the initial question, to Stevo Todorçević for asking*a*question which led to*a*significant improvement of my results and to Peter Krautzberger and Stefan ... The main reference for*looking*up undefined notions is the first volume of the Handbook of*Boolean**Algebras*, [Kop89] . Let B be*a**Boolean**algebra*. ...
« Previous

*Showing results 1 — 15 out of 7,610 results*