General default logic

Abstract

In this paper, we propose a new nonmonotonic logic called general default logic. On the one hand, it generalizes Reiter's default logic by adding to it rulelike operators used in logic programming. On the other hand, it extends logic programming by allowing arbitrary propositional formulas. We show that with this new logic, one can formalize naturally rule constraints, generalized closed world assumptions, and conditional defaults. We show that under a notion of strong equivalence, sentences of this new logic can be converted to a normal form. We also investigate the computational complexity of various reasoning tasks in the logic, and relate it to some other nonmonotonic formalisms such as Lin and Shoham's logic of GK and Moore's autoepistemic logic. This paper is an extended version of the authors' LPNMR'07 [43] and NMR'08 [44] papers.

Sequent-Type Calculi for Three-Valued and Disjunctive Default Logic

“…Both versions have been introduced to address certain representational shortcomings of standard default logic. Other variants of default logic include, e.g., justified default logic [12], constrained default logic [13,14], rational default logic [15], general default logic [16], and four-valued default logic [17] (an overview about different versions of default logic is given by Antoniou and Wang [18]).…”