Domain Theory Meets Default Logic
William C. Rounds, Guo‐Qiang Zhang · Journal of Logic and Computation · 1995
Abstract We present a development of the theory of default information structures, combining ideas from domain theory with ideas from non-monotonic logic. Conceptually, our treatment is distinguished from standard default logic in that we view default structures as generating models rather than theories. Reiter's default rules are viewed as non-deterministic algorithms for generating preferred partial models. Using domain-theoretical notions, we suggest a robust alternative to the standard definition of extensions in default logic, by introducing the notion of dilation. We prove the existence of such dilations for a new class of default information structures, called the class of rational structures, which properly includes the class of semi-normal structures.