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A formal proof system for infinitary rational expressions [chapter]

Ph. Darondeau, L. Kott
1985 Lecture Notes in Computer Science  
HAL Id: inria-00076340 Submitted on 24 May 2006 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents,  ... 
doi:10.1007/3-540-15641-0_24 fatcat:soubz2rnpjfxnohy2vhb56ebpi

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

J. R. Kennaway, J. W. Klop, M. R. Sleep, F. J. de Vries
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.  ... 
doi:10.1145/177492.177577 fatcat:7eyaob6drfh3tkukuinorwzauy

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

Jerzy Pogonowski
2021 Studies in Logic, Grammar and Rhetoric  
In this paper I discuss Ernst Zermelo's ideas concerning the possibility of developing 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.  ... 
doi:10.2478/slgr-2021-0042 fatcat:nnowhogl3bhklm234xa7dion7u

Some problems in automata theory which depend on the models of set theory

Olivier Finkel
2011 RAIRO - Theoretical Informatics and Applications  
We prove 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.  ... 
doi:10.1051/ita/2011113 fatcat:dv7hrrq5w5forkchqzlcrh3kx4

Continuous lattices in formal topology [chapter]

Sara Negri
1998 Lecture Notes in Computer Science  
As an application, 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.  ... 
doi:10.1007/bfb0097800 fatcat:kjpcicvqtzgs3cpdqst5jtbaji

A Logical Framework for Convergent Infinite Computations [article]

Wei Li, Shilong Ma, Yuefei Sui, Ke Xu
2002 arXiv   pre-print
On the basis of 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.  ... 
arXiv:cs/0105020v3 fatcat:rfe3p54xtnblvb2t44b7g6td4m

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

Olivier Finkel
2009 RAIRO - Theoretical Informatics and Applications  
context-free ω-languages or 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.  ... 
doi:10.1051/ita/2009001 fatcat:m4l7v7vugncgdb2be4wy6ys53a

On evaluations of propositional formulas in countable structures

Aleksandar Perovic, Dragan Doder, Zoran Ognjanovic, Miodrag Raskovic
2016 Filomat  
The purpose of such 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.  ... 
doi:10.2298/fil1601001p fatcat:7ynmsazn7rdebpsljku5667gh4

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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