A Logical Framework for Convergent Infinite Computations

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dc.creatorLi, Wei
dc.creatorMa, Shilong
dc.creatorSui, Yuefei
dc.creatorXu, Ke
dc.date2001-05-10
dc.date2002-02-07
dc.date.accessioned2026-07-07T03:17:08Z
dc.date.available2026-07-07T03:17:08Z
dc.descriptionClassical computations can not capture the essence of infinite computations very well. This paper will focus on a class of infinite computations called convergent infinite computations}. 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. A class of fixed points characterizing the logical properties of the limits can be represented by means of infinite-length terms defined by Cauchy sequences. We will show that the limit of sequence of first order theories can be defined in terms of distance, similar to the $ε-N$ style definition of limits in real analysis. On the basis of infinitary terms, a computation model for convergent infinite computations is proposed. Finally, the interpretations of logic programs are extended by introducing real Herbrand models of logic programs and a sufficient condition for computing a real Herbrand model of Horn logic programs using convergent infinite computation is given.
dc.description17 pages. Welcome any comments to kexu@nlsde.buaa.edu.cn
dc.identifierhttps://arxiv.org/abs/cs/0105020
dc.identifierhttp://arxiv.org/abs/cs/0105020
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/30612
dc.subjectLogic in Computer Science
dc.subjectProgramming Languages
dc.subjectF.4.1, D.1.6
dc.titleA Logical Framework for Convergent Infinite Computations
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