Journal of Automated Reasoning 15: 95-165, 1995. @ 1995 Kluwer Academic Publishers. Printed in the Netherlands. 95 A New Methodology for Query Answering in Default Logics via Structure-Oriented Theorem Proving T. SCHAUB IRISA, Campus de Beaulieu, F-35042 Rennes Cedex, France e-mail: torsten@ irisa.fr (Received: 30 March 1994; in final form: 1 September 1994) Abstract. We present a new approach to query answering in default logics. The basic idea is to treat default rules as classical implications along with some qualifying conditions restricting the use of such rules while query answering. We accomplish this by taking advantage of the conception of structure-oriented theorem proving provided by Bibel's connection method. We show that the structure-sensitive nature of the connection method allows for an elegant characterization of proofs in default logic. After introducing our basic method for query answering in default logics, we present a corresponding algorithm and describe its implementation. Both the algorithm and its implementation are obtained by slightly modifying an existing algorithm and an existing implementation of the standard connection method. In turn, we give a couple of refinements of the basic method that lead to conceptually different algorithms. The approach turns out to be extraordinarily qualified for implementations by means of existing automated theorem proving techniques. We substantiate this claim by presenting implementations of the various algorithms along with some experimental analysis. Even though our method has a general nature, we introduce it in the first part of this paper with the example of constrained default logic. This default logic is tantamount to a variant due to Brewka, and it coincides with Reiter's default logic and a variant due to Lukaszewicz on a large fragment of default logic. Accordingly, our exposition applies to these instances of default logic without any modifications. Key words: default logics, query answering, credulous reasoning, theorem proving, connection method. AMS Subject Classification: 68T15, 68T27 1. Introduction Reasoning in the absence of complete information constitutes one of the most important facets of commonsense reasoning. This form of reasoning is frequently accomplished by making default assumptions or simply by default reasoning. A versatile approach to this is Reiter's default logic [30]. Since its introduction, it has proven to be extremely valuable for formalizing default reasoning in various domains. Among others, it has been applied to diagnosis [31], natural language [23], inheritance networks [16], terminological logics [1], and databases [8]. In particular, it provides semantics for truth maintenance systems [6] and diverse