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Page 7142 of Mathematical Reviews Vol. , Issue 95m
[page]

1995
*
Mathematical Reviews
*

Kosta Dosen (F-TOUL3-IR; Toulouse)
95m:03015 03B20 03B15 Polacik, Tomasz (PL-SILS-IM; Katowice)

*Operators**defined**by**propositional**quantification**and**their**interpretation**over**Cantor**space*. ... These systems have modal*operators*0, indexed*by*individual variables x,*and**their*characteristic axiom schemata, originating from G. ...##
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Semi-decidability of May, Must and Probabilistic Testing in a Higher-type Setting

2009
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Electronical Notes in Theoretical Computer Science
*

Choices can only be performed at powertypes,

doi:10.1016/j.entcs.2009.07.092
fatcat:3wzlzrjh6zawhj5cijidfmuiaq
*and*the different powertypes have different*operational**interpretations*of choice. ... The types are closed under finite products*and*function*spaces*,*and*certain powertype constructors,*interpreted*as powerdomain monads, which capture various kinds of non-determinism. ...*Quantification**and*integration*over*the*Cantor**space*. For the*operational*semantics*defined*in Section 5 below, we need*quantification**and*integration*over*the*Cantor*type*Cantor*= (Nat → Bool). ...##
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Synthetic Topology

2004
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Electronical Notes in Theoretical Computer Science
*

We are aware of other applications of synthetic topology, e.g. to locales, convergence

doi:10.1016/j.entcs.2004.09.017
fatcat:qb7ckcpuvzgbrmkq2fdsom7vae
*spaces*, sequential*spaces*, equilogical*spaces*,*and*some sheaf*and*realizability toposes, but this will be reported ... In fact, we start*by*developing synthetic topology of programming-language data types in Part I, without assuming any background in classical topology*and*without introducing any. ... The functional program for universal*quantification**over*the*Cantor**space*provided here is due to the author but it is related to a program formerly discovered*by*Berger [13] , which we present in Chapter ...##
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Synthetic Topologyof Data Types and Classical Spaces

2004
*
Electronical Notes in Theoretical Computer Science
*

We are aware of other applications of synthetic topology, e.g. to locales, convergence

doi:10.1016/s1571-0661(04)05135-7
fatcat:2z7ew7j3erarxioan4uqjnjssy
*spaces*, sequential*spaces*, equilogical*spaces*,*and*some sheaf*and*realizability toposes, but this will be reported ... In fact, we start*by*developing synthetic topology of programming-language data types in Part I, without assuming any background in classical topology*and*without introducing any. ... The functional program for universal*quantification**over*the*Cantor**space*provided here is due to the author but it is related to a program formerly discovered*by*Berger [13] , which we present in Chapter ...##
###
Why topology in the minimalist foundation must be pointfree

2013
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Logic and Logical Philosophy
*

We heartily thank Francesco Ciraulo, Per Martin-Löf

doi:10.12775/llp.2013.010
fatcat:djpf6wtw4fd2lc3wpobxmbmsue
*and*Claudio Sacerdoti Coen for fruitful discussions on the topics of this paper. ... the set of positive natural numbers {x ∈ N | x ≥ 1},*and*to*define**operations*on such sets, we need to think of*propositions*as types of*their*proofs: small*propositions*are seen as sets of*their*proofs ... ,*Cantor**space*, . . . ) do not give rise to a point-wise topology since*their*points do not form a set. ...##
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Measure theory and higher order arithmetic
[article]

2015
*
arXiv
*
pre-print

We investigate the statement that the Lebesgue measure

arXiv:1312.1531v2
fatcat:tctxumkoyvb6rapk3hdhc7553e
*defined*on all subsets of the*Cantor**space*exists. As base system we take ACA_0^ω + (μ). ... The system ACA_0^ω is the higher order extension of Friedman's system ACA_0,*and*(μ) denotes Feferman's μ, that is a uniform functional for arithmetical comprehension*defined**by*f(μ(f))=0 if ∃ n f(n)=0 ... We will denote*by*(λ) the statement the Lebesgue measure*defined*on all subsets of the*Cantor*-*space*exists. ...##
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Infinite sets that admit fast exhaustive search

2007
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22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)
*

How fast can exhaustive search

doi:10.1109/lics.2007.25
dblp:conf/lics/Escardo07
fatcat:ntbideqoyzhlzge62whz7y32xa
*over*infinite sets be performed? ... consult his paper [18] for a more accurate*and*detailed account. ... I also thank Dag Normann for having answered questions regarding the history*and*technical ramifications of the subject,*and*for sending me a copy of Tait's unpublished manuscript -but the reader should ...##
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Quantum set algebra for quantum set theory
[article]

2014
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arXiv
*
pre-print

Quantum field theory can be physically regularized

arXiv:1403.3725v1
fatcat:3etni7bgxncntioclxx3mix34i
*by*modularizing it on several levels of aggregation. ... Since computation is already thoroughly modularized, physical experiments are treated here as quantum relativistic cellular computations with spins for cells, address, memory,*and*control registers. ... I*define*the quantum binary field with domain port*space*X*and*binary range 2 to have the port*space*2 X , the Grassmann algebra*over*X . ...##
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Exhaustible sets in higher-type computation

2008
*
Logical Methods in Computer Science
*

The

doi:10.2168/lmcs-4(3:3)2008
fatcat:ptu4qbbbgjaeboe3rtxros5uoq
*Cantor**space*of infinite sequences of binary digits is known to be searchable. ... We also show that, in the non-empty case, they are precisely the computable images of the*Cantor**space*. ...*and*closed sets*by**their*characteristic functions),*and*compact sets (using the function*space*S S X*and*representing compact sets*by**their*universal*quantification*functionals). ...##
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Measure theory and higher order arithmetic

2015
*
Proceedings of the American Mathematical Society
*

We investigate the statement that the Lebesgue measure

doi:10.1090/proc/12671
fatcat:ff3tab76nnffzmmfrqsxedjv7u
*defined*on all subsets of the*Cantor*-*space*exists. As a base system we take ACA ω 0 +(μ). ... The system ACA ω 0 is the higher order extension of Friedman's system ACA 0 ,*and*(μ) denotes Feferman's μ, that is, a uniform functional for arithmetical comprehension*defined**by*f (μ(f )) = 0 if ∃n f ... measure*defined*on all subsets of the*Cantor*-*space*exists. ...##
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Girard's !() as a reversible fixed-point operator
[article]

2013
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arXiv
*
pre-print

We demonstrate that it may be thought of as a fixed-point

arXiv:1309.0361v1
fatcat:lll6fjokojdsvfled6qzhcnucu
*operation*for reversible logic & computation. ... () exponential in the Geometry of Interaction system, with particular emphasis on the fact that the GoI*interpretation*'forgets types'. ... Although the system described was logically degenerate (i.e. conjunction*and*disjunction were identified, as were universal*and*existential*quantification*,*and**propositions**and**their*negations), the computational ...##
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Applications of type theory
[chapter]

1993
*
Lecture Notes in Computer Science
*

-calculus which truly solve the equation of reflexive domains,

doi:10.1007/3-540-56610-4_75
fatcat:atgs6zm335d3xmwn5md3ty7o2u
*and*e T-logic, a first-order theory of*propositions*with selfreference*and*impredicative*quantification*allowing for intcnsional models of ... Proofs*and*derivations are conventionally*defined**and*give rise to tile notion of consequence R 1> J where R is a set of rules*and*J is a judgement that can be derivc~l using tile rules of R. ...*quantification**over**propositions*. ...##
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What sequential games, the tychonoff theorem and the double-negation shift have in common

2010
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Proceedings of the third ACM SIGPLAN workshop on Mathematically structured functional programming - MSFP '10
*

The functional makes sense for finite

doi:10.1145/1863597.1863605
dblp:conf/icfp/EscardoO10
fatcat:y4rnbuktjzds3avoyxawcvd5s4
*and*infinite (lazy) lists,*and*in the binary case it amounts to an*operation*that is available in any (strong) monad. ...*operation*. ... When we run this, using the*interpreter*this time, we get: A non-trivial application of*quantification**over*the*Cantor**space*is given in [16] . ...##
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Natural Density and The Quantifier 'Most'
[article]

2019
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arXiv
*
pre-print

We consider sentences of the form "Most A are B", where A

arXiv:1901.10394v2
fatcat:dnsqipunpzcmja7xrfzgka5tme
*and*B are plural nouns*and*the*interpretations*of A*and*B are infinite subsets of N . ... This paper proposes a formalization of the class of sentences quantified*by*most, which is also*interpreted*as proportion of or majority of depending on the domain of discourse. ... Moss, John Corcoran*and*Georges Grekos for many useful discussions*and*patiently answering our questions. ...##
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The Limits of Computation

2021
*
Axiomathes
*

Moreover, it is claimed that typed systems of the lambda calculus give rise naturally to a functional

doi:10.1007/s10516-021-09561-8
fatcat:w6nlldlpxvblpjgxp37u6jejke
*interpretation*of rich systems of types*and*to a hierarchy of ordinal recursive functionals of arbitrary ... type that can be reduced*by*substitution to natural number functions. ...*over*types (written ), 8 which corresponds to "second-order"*propositional*logic with*quantification**over**propositions*. ...
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