Automated deduction is a fundamental research area in the field of artificial intelligence. The aim of an automated deduction system is to find a formal proof for a given goal based on given axioms. Essentially automated deduction can be viewed as a search problem which spans huge search spaces. One main thrust of research in automated deduction is the development of techniques for achieving a reduction of the search space. A particularly promising approach for search space reduction relies on the integration of top-down and bottom-up reasoning. A possible approach employs bottom-up generated lemmas in top-down systems. Lemma use offers the possibility to shorten proofs and to overcome weaknesses of top-down systems like poor redundancy control. In spite of the possible advantages of lemma use, however, naive approaches for lemma integration even tend to slow down top-down systems. The main problem is the increased indeterminism in the search process. In this thesis important contributions for a successful application of lemmas in top-down deduction systems based on connection tableau calculi are made. New methods for lemma generation and for the estimation of the relevancy of lemmas are developed. As a practical contribution, the implementation of the new techniques leads to a powerful system for automated deduction which demonstrates the high potential of the new techniques.

Shared-workspace systems with structured graphical representations allow for the free user interaction and the joint construction of problem solutions for potentially open-ended tasks. However, group modelling in shared workspaces has to take on a process-orientated perspective due to the reduced system control in shared workspaces. This text is defined as the monitoring of user actions and the abstraction and interpretation of the raw data in the context of the group interaction and the problem representation. Formally based on plan recognition and the situation calculus, an approach has been developed that incorporates an operational hierarchy for generally modelling activities. The system performs an automatic inline analysis of group interactions and the results are visualized in different forms to give feedback and stimulating self-reflection.

This thesis presents an approach to learning good search guiding heuristics for the supposition-based theorom prover E in equational deductions. Search decisions from successful proof searches are represented as sets annotated clause patterns. Term Space Mapping, an alternative learning method for recursive structures is used to learn heuristic evaluation functions for the evaluation of potential new consequences. Experimental results with extended system E/TSM show the success of the approach. Additional contributions of the thesis are an extended superposition calculus and a description of both the proof procedure and the implementation of a state-of-the-art equational theorem prover.

Automated deduction is one of the fundamental disciplines in the field of artificial intelligence. The purpose of systems for automated deduction is to find formal proofs for given conjectures by drawing conclusions from formally specified knowledge. Their main strength is that they allow a purely declarative description of knowledge, i.e., procedural information on the drawing of conclusions need not be provided. In combination with the indeterminism in the drawing of possible conclusions, however, the ability to handle declarative specifications introduces the aspect of search into the deduction process. Usually, tremendous search spaces have to be explored in order to find a proof. Successful systems for automated deduction can be built, for example, on the basis of connection tableau calculi. In this thesis, an approach to a more intelligent search in connection tableau calculi is made. The approach is based on the compression of structurally similar formulas given to and derived by connection tableau calculi. Disjunctive constraints over first order terms are used to express the results of the compression. There are two main theoretical results of the thesis. Firstly, it introduces a new class of sound and complete connection tableau calculi, the so-called constrained-connection-tableau calculi, which are compatible with the most important search pruning techniques of conventional connection tableau calculi. Secondly, intelligent algorithms for solving disjunctive constraints over first order terms are developed. As a practical result, the implementation of the approach leads to a powerful system for automated deduction which demonstrates the high potential of the new developments.

This book constitutes the refereed proceedings of the 15th International Conference on Automated Deduction, CADE-15, held in Lindau, Germany, in July 1998. The volume presents three invited contributions together with 25 revised full papers and 10 revised system descriptions; these were selected from a total of 120 submissions. The papers address all current issues in automated deduction and theorem proving based on resolution, superposition, model generation and elimination, or connection tableau calculus, in first-order, higher-order, intuitionistic, or modal logics, and describe applications to geometry, computer algebra, or reactive systems.

This book constitutes the refereed proceedings of the 16th International Conference on Automated Deduction, CADE-16, held in Trento, Italy in July 1999 as part of FLoC'99. The 21 revised full papers presented were carefully reviewed and selected from a total of 83 submissions. Also included are 15 system descriptions and two invited full papers. The book addresses all current issues in automated deduction and theorem proving, ranging from logical foundations to deduction systems design and evaluation.

`Intellectics' seeks to understand the functions, structure and operation of the human intellect and to test artificial systems to see the extent to which they can substitute or complement such functions. The word itself was introduced in the early 1980s by Wolfgang Bibel to describe the united fields of artificial intelligence and cognitive science. The book collects papers by distinguished researchers, colleagues and former students of Bibel's, all of whom have worked together with him, and who present their work to him here to mark his 60th birthday. The papers discuss significant issues in intellectics and computational logic, ranging across automated deduction, logic programming, the logic-based approach to intellectics, cognitive robotics, knowledge representation and reasoning. Each paper contains new, previously unpublished, reviewed results. The collection is a state of the art account of the current capabilities and limitations of a computational-logic-based approach to intellectics. Readership: Researchers who are convinced that the intelligent behaviour of machines should be based on a rigid formal treatment of knowledge representation and reasoning.

Recent years have been blessed with an abundance of logical systems, arising from a multitude of applications. A logic can be characterised in many different ways. Traditionally, a logic is presented via the following three components: 1. an intuitive non-formal motivation, perhaps tie it in to some application area 2. a semantical interpretation 3. a proof theoretical formulation. There are several types of proof theoretical methodologies, Hilbert style, Gentzen style, goal directed style, labelled deductive system style, and so on. The tableau methodology, invented in the 1950s by Beth and Hintikka and later per fected by Smullyan and Fitting, is today one of the most popular, since it appears to bring together the proof-theoretical and the semantical approaches to the pre of a logical system and is also very intuitive. In many universities it is sentation the style first taught to students. Recently interest in tableaux has become more widespread and a community crystallised around the subject. An annual tableaux conference is being held and proceedings are published. The present volume is a Handbook a/Tableaux pre senting to the community a wide coverage of tableaux systems for a variety of logics. It is written by active members of the community and brings the reader up to frontline research. It will be of interest to any formal logician from any area.