A Sequent Calculus for Skeptical Reasoning in Predicate Default Logic (Extended Abstract)

A sound and complete sequent calculus for skeptical consequence in predicate default logic is presented. While skeptical consequence is decidable in the finite propositional case, the move to predicate or infinite theories increases the complexity of skeptical reasoning to being \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Pi^{\rm 1}_{\rm 1}$\end{document}-complete. This implies the need for sequent rules with countably many premises, and such rules are employed.