A Logical Framework for Convergent Infinite Computations [article]

Wei Li, Shilong Ma, Yuefei Sui, Ke Xu
2002 arXiv   pre-print
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
more » ... d 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.
arXiv:cs/0105020v3 fatcat:rfe3p54xtnblvb2t44b7g6td4m