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A Logical Framework for Convergent Infinite Computations

Wei Li·Shilong Ma·Yuefei Sui·Ke Xu
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Abstract

Classical 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.

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Wei Li, Shilong Ma, Yuefei Sui, Ke Xu. 2002-02-07. A Logical Framework for Convergent Infinite Computations. https://arxiv.org/abs/cs/0105020

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