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A formal proof system for infinitary rational expressions
[chapter]

1985
*
Lecture Notes in Computer Science
*

HAL Id: inria-00076340 https://hal.inria.fr/inria-00076340
Submitted on 24 May 2006 HAL is

doi:10.1007/3-540-15641-0_24
fatcat:soubz2rnpjfxnohy2vhb56ebpi
*a*multi-disciplinary open access archive*for*the deposit and dissemination of scientific research documents, ...##
###
Page 4272 of Mathematical Reviews Vol. , Issue 86i
[page]

1986
*
Mathematical Reviews
*

Kott, “

*A**formal**proof**system**for**infinitary**rational*languages” , INRIA Rep. ... {*For*the entire collection see MR 85m:68002. } 861:68086 Darondeau, Ph. (F-RENN-B); Kott, L. (F-RENN-B) Towards*a**formal**proof**system**for*w-*rational**expressions*. Inform. Process. ...##
###
On the adequacy of graph rewriting for simulating term rewriting

1994
*
ACM Transactions on Programming Languages and Systems
*

*Infinitary*graph rewriting may be

*formalized*by analogy with

*infinitary*term rewriting. ...

*For*the

*formalization*of

*infinitary*rewriting, we will require certain mathematical concepts: metric spaces, continuity, and ordinal numbers. ... Adequacy can therefore be expected to hold only

*for*orthogonal

*systems*of rewrite rules which are Church-l? osser

*for*transfinite term reduction, that is, the almost noncollapsing

*systems*. ...

##
###
Page 440 of Mathematical Reviews Vol. , Issue 92a
[page]

1992
*
Mathematical Reviews
*

It is noted that in the case of

*infinitary*codes, freeability alone is not enough*for**a*submonoid of*A*® to have*a*code as base.” 92a:68076 68Q45 20M35 Pin, Jean Enric [Pin, Jean-Eric] (F-PARIS6-C)*Rational*... Using this result, the author proves that*for*any*rational*number x € [0,1],*A*(x)° is also*a*context-free language. ...##
###
"Mathematics is the Logic of the Infinite": Zermelo's Project of Infinitary Logic

2021
*
Studies in Logic, Grammar and Rhetoric
*

In this paper I discuss Ernst Zermelo's ideas concerning the possibility of developing

doi:10.2478/slgr-2021-0042
fatcat:nnowhogl3bhklm234xa7dion7u
*a**system*of*infinitary*logic that, in his opinion, should be suitable*for*mathematical inferences. ... The presentation of Zermelo's ideas is accompanied with some remarks concerning the development of*infinitary*logic. ... Mathematical*proof*is*for*him*a*well-founded*system*of propositions. ...##
###
Some problems in automata theory which depend on the models of set theory

2011
*
RAIRO - Theoretical Informatics and Applications
*

We prove

doi:10.1051/ita/2011113
fatcat:dv7hrrq5w5forkchqzlcrh3kx4
*a*very similar result*for*the complement of an*infinitary**rational*relation accepted by*a*2-tape Büchi automaton B. ... As*a*corollary, this proves that the Continuum Hypothesis may be not satisfied*for*complements of 1-counter omega-languages and*for*complements of*infinitary**rational*relations accepted by 2-tape Büchi ... and*for**infinitary**rational*relations. ...##
###
Continuous lattices in formal topology
[chapter]

1998
*
Lecture Notes in Computer Science
*

As an application,

doi:10.1007/bfb0097800
fatcat:kjpcicvqtzgs3cpdqst5jtbaji
*a*representation theorem*for*locally compact spaces is obtained. ...*A*representation of continuous and prime-continuous lattices via*formal*topology is found. ...*systems*and generators*for*cover relations. ...##
###
A Logical Framework for Convergent Infinite Computations
[article]

2002
*
arXiv
*
pre-print

On the basis of

arXiv:cs/0105020v3
fatcat:rfe3p54xtnblvb2t44b7g6td4m
*infinitary*terms,*a*computation model*for*convergent infinite computations is proposed. ...*A*logic*for*convergent infinite computations is proposed by extending first order theories using Cauchy sequences, which has stronger*expressive*power than the first order logic. ... We give*a**formal*computation model on the*infinitary*terms in section 5. ...##
###
Page 1063 of Mathematical Reviews Vol. , Issue 88b
[page]

1988
*
Mathematical Reviews
*

(F-RENN-B)

*A**formal**proof**system**for**infinitary**rational**expressions*. Automata on infinite words (Le Mont-Dore, 1984), 68-80, Lecture Notes in Comput. Sci., 194, Springer, Berlin-New York, 1985. ... The aim of this paper is to design*a**formal**system**for*proving the equality (actually the inclusion) and emptiness of intersection*for*@-*rational**expressions*(w-regular*expressions*). ...##
###
Page 3763 of Mathematical Reviews Vol. , Issue 86h
[page]

1986
*
Mathematical Reviews
*

This

*proof**system*uses one*infinitary*inference rule, the ‘lub rule’.*A*‘Birkhoff variety theorem’ is also 68Q Theory of computing 86h:68110 proved*for*semivarieties. ...*A*deductive*system**for*proving inequalities in which*a**proof*is represented as*a*well-founded tree is shown to be sound and complete. ...##
###
Page 1493 of Mathematical Reviews Vol. , Issue 87c
[page]

1987
*
Mathematical Reviews
*

The case of bounded parallelism is analyzed: there,

*infinitary**rational**expressions*may be used to specify the observationally meaningful properties of programs, and no induction is needed to prove those ...*Systems*Scz., 14, Springer, Berlin-New York, 1985. Summary: “*A*structured presentation of*a**proof**system**for*CSP programs is given. The presentation is based on the approach of the author, N. ...##
###
Highly Undecidable Problems For Infinite Computations

2009
*
RAIRO - Theoretical Informatics and Applications
*

context-free ω-languages or

doi:10.1051/ita/2009001
fatcat:m4l7v7vugncgdb2be4wy6ys53a
*for**infinitary**rational*relations. ... Topological and arithmetical properties of 1-counter ω-languages, context free ω-languages, or*infinitary**rational*relations, are also highly undecidable. ...*infinitary**rational*relation. ...##
###
On evaluations of propositional formulas in countable structures

2016
*
Filomat
*

The purpose of such

doi:10.2298/fil1601001p
fatcat:7ynmsazn7rdebpsljku5667gh4
*a**formalism*is to provide*a*general propositional framework*for*reasoning about F-valued evaluations of propositional formulas, where F is*a*C-valued L-structure. ... We provide*a*complete*infinitary*propositional logic (formulas remain finite sequences of symbols, but we use inference rules with countably many premises)*for*description of C-valued L-structures, where ... The central technical result is the*proof*of the strong completeness theorem (every consistent set of formulas is satisfiable)*for*the introduced*system*. ...##
###
Page 6243 of Mathematical Reviews Vol. , Issue 96j
[page]

1996
*
Mathematical Reviews
*

Bowen,

*expressing*the zeta function of*a*sofic*system*as*a**rational*function. ... The advantages of this notion are*proof*-theoretic: the*proof**system**for*observational first-order formulae needs just one additional (*infinitary*)*proof*schema, the so-called context-induction. ...##
###
Page 3007 of Mathematical Reviews Vol. , Issue 2002E
[page]

2002
*
Mathematical Reviews
*

The purpose is to ascertain how far the former can be said to embody

*a*coherentist account of*rationality*, and how far the latter can be rendered more precise by the*formal*work of the logic of belief ... The important result of the paper is*a**proof*of the cor- ...
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