. Database and Artificial Intelligence applications are briefly discussed and it is argued that they need deduction methods that are not only refutation complete but also complete for finite satisfiability. A novel deduction method is introduced for such applications. Instead of relying on Skolemization, as most refutation methods do, the proposed method processes existential quantifiers in a special manner which makes it complete not only for refutation, but also for finite satisfiability. A main contribution of this paper is the proof of these results. Keywords: Artificial Intelligence, Expert Systems, Databases, Automated Reasoning, Finite Satisfiability. 1 Introduction For many applications of automated reasoning, the tableaux methods [32, 16, 34, 18] have the following advantages: They not only detect unsatisfiability but also generate models; they are close to common sense reasoning, hence easy to enhance with an explanation tool; and they are quite easy to adapt to the special...

In this paper, we argue that the resolution of anaphoric expressions in an utterance is essentially an abductive task following [HSAM93] who use a weighted abduction scheme on horn clauses to deal with reference. We give a semantic representation for utterances containing anaphora that enables us to compute possible antecedents by abductive inference. We extend the disjunctive model construction procedure of hyper tableaux [BFN96, Kuh97] with a clause transformation turning the abductive task into a model generation problem and show the completeness of this transformation with respect to the computation of abuctive explanations. This abductive inference is applied to the resolution of anaphoric expressions in our general model constructing framework for incremental discourse representation [Kuh99] which we argue to be useful for computing information updates from natural language utterances [Vel96].

We present a novel reasoning calculus for the description logic SHOIQ + —a knowledge representation formalism with applications in areas such as the Semantic Web. Unnecessary nondeterminism and the construction of large models are two primary sources of inefficiency in the tableau-based reasoning calculi used in state-of-the-art reasoners. In order to reduce nondeterminism, we base our calculus on hypertableau and hyperresolution calculi, which we extend with a blocking condition to ensure termination. In order to reduce the size of the constructed models, we introduce anywhere pairwise blocking. We also present an improved nominal introduction rule that ensures termination in the presence of nominals, inverse roles, and number restrictions—a combination of DL constructs that has proven notoriously difficult to handle. Our implementation shows significant performance improvements over state-of-the-art reasoners on several well-known ontologies.

Abstract. This paper investigates the use of hyperresolution as a decision procedure and model builder for guarded formulae. In general hyperresolution is not a decision procedure for the entire guarded fragment. However we show that there are natural fragments which can be decided by hyperresolution. In particular, we prove decidability of hyperresolution with or without splitting for the fragment GF1 − and point out several ways of extending this fragment without loosing decidability. As hyperresolution is closely related to various tableaux methods the present work is also relevant for tableaux methods. We compare our approach to hypertableaux, and mention the relationship to other clausal classes which are decidable by hyperresolution. 1

We present a collection of simple but powerful techniques for enhancing the efficiency of tableau-based model generators such as Satchmo. The central ideas are to compile a clausal first order theory into a procedural Prolog program and to avoid redundant work of a naive implementation. We have compared various combinations of our techniques among each other and with theorem provers based on various calculi, using the TPTP Problem Library as a benchmark. Our implementation has turned out to be the most efficient for range-restricted problems and for a class of problems we call "non-nesting".

Abstract. During the past few years mobile phones have become an ubiquitous companion. In parallel the semantic web provides enabling technologies to annotate and match information with a user’s interests. In this paper the necessary definitions and optimizations of annotations and profiles are given to make the mobile phone a first class participant of a semantic environment rather than a mere displaying client of services running elsewhere. The implementation of the system – including a first order model generating theorem prover and a description logic interface – renders the idea viable in the real world and even enables explanations within the matchmaking process. The profile does not have to leave the personal device and ensures privacy by doing so. 1

We demonstrate that theorem provers using model elimination (ME) can be used as answer-complete interpreters for disjunctive logic programming. More specifically, we introduce a mechanism for computing answers into the restart variant of ME. Building on this we develop a new calculus called ancestry restart ME. This variant admits a more restrictive regularity restriction than restart ME, and, as a side effect, it is in particular attractive for computing definite answers. The presented calculi can also be used successfully in the context of automated theorem proving. We demonstrate experimentally that it is more difficult to compute (non-trivial) answers to goals, instead of only proving the existence of answers. Keywords. Automated reasoning; theorem proving; model elimination; logic programming; computing answers. In first order automatic theorem proving one is interested in the question whether a given formula follows logically from a set of axioms. This is a rather artificial t...

. We combine techniques originally developed for refutational first-order theorem proving within the clause tree framework with techniques for minimal model computation developed within the hyper tableau framework. This combination generalizes well-known tableaux techniques like complement splitting and folding-up/down. We argue that this combination allows for efficiency improvements over previous, related methods. It is motivated by application to diagnosis tasks; in particular the problem of avoiding redundancies in the diagnoses of electrical circuits with reconvergent fanouts is addressed by the new technique. In the paper we develop as our main contribution in a more general way a sound and complete calculus for propositional circumscriptive reasoning in the presence of minimized and varying predicates. 1 Introduction Recently clause trees [6], a data structure and calculus for automated theorem proving, introduced a general method to close branches based on so-calle...

. In [NF96] a very efficient system for solving diagnosis tasks has been described, which is based on belief revision procedures and uses first order logic system descriptions. In this paper we demonstrate how such a system can be rigorously formalized from the viewpoint of deduction by using the calculus of hyper tableaux [BFN96]. The benefits of this approach are twofold: first, it gives us a clear logical description of the diagnosis task to be solved; second, as our experiments show, the approach is feasible in practice and thus serves as an example of a successful application of deduction techniques to real-world applications. 1 Introduction In this paper we will demonstrate that model generation theorem proving is very well suited for solving consistency-based diagnosis tasks. According to Reiter ([Rei87]) a simulation model of the technical device under consideration is constructed and is used to predict its normal behavior. By comparing this prediction with the actual behavior ...

. In recent years, much work was devoted to the study of theoretical foundations of Disjunctive Logic Programs and Disjunctive Deductive Databases. While the semantics of non-disjunctive programs is fairly well understood the declarative and computational foundations of disjunctive programming proved to be much more elusive and difficult. Quite recently, two new and very promising semantics have been proposed for the class of disjunctive logic programs. Both of them extend the well-founded semantics of normal programs. The first one is the static semantics proposed by Przymusinski and the other is the D-WFS semantics proposed by Brass and Dix. Although the two semantics are based on very different ideas, we show in this paper that they turn out to be very closely related. In fact, we show that it is possible to restrict the underlying language of STATIC to get D-WFS. We also show how to use this characterization for an efficient implementation based on a prover for computing minimal ...