Abstract
Quasi-metrics have been used in several places in the literature on domain theory and the formal semantics of programming languages. In this paper, we consider the role of quasi-metrics in the fixed point semantics of logic programs, examining in detail a quite general process by which fixed points of immediate consequence operators can be found. This work takes as its starting point: (i) Fitting's recent application of the Banach contraction mapping theorem in logic programming; (ii) a theorem of Rutten which generalizes both the contraction mapping theorem and the Knaster-Tarski theorem; (iii) Smyth's work on totally bounded spaces and compact ordered spaces as domains of computation. Our results therefore are theoretical and to be viewed as a contribution to the mathematical foundations of computer science.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.