Automated Deduction A Basis For Applications Volume I Foundations Calculi And Methods Volume Ii Systems And Implementation Techniques Volume Iii Applications

We are invited to deal with mathematical activity in a sys tematic way [ ... ] one does expect and look for pleasant surprises in this requirement of a novel combination of psy chology, logic, mathematics and technology. Hao Wang, 1970, quoted from(Wang, 1970). The field of mathematics has been a key application area for automated theorem proving from the start, in fact the very first automatically found the orem was that the sum of two even numbers is even (Davis, 1983). The field of automated deduction has witnessed considerable progress and in the last decade, automated deduction methods have made their way into many areas of research and product development in computer science. For instance, deduction systems are increasingly used in software and hardware verification to ensure the correctness of computer hardware and computer programs with respect to a given specification. Logic programming, while still falling somewhat short of its expectations, is now widely used, deduc tive databases are well-developed and logic-based description and analysis of hard-and software is commonplace today.

On the history of the book: In the early 1990s several new methods and perspectives in au- mated deduction emerged. We just mention the superposition calculus, meta-term inference and schematization, deductive decision procedures, and automated model building. It was this last ?eld which brought the authors of this book together. In 1994 they met at the Conference on Automated Deduction (CADE-12) in Nancy and agreed upon the general point of view, that semantics and, in particular, construction of models should play a central role in the ?eld of automated deduction. In the following years the deduction groups of the laboratory LEIBNIZ at IMAG Grenoble and the University of Technology in Vienna organized several bilateral projects promoting this topic. This book emerged as a main result of this cooperation. The authors are aware of the fact, that the book does not cover all relevant methods of automated model building (also called model construction or model generation); instead the book focuses on deduction-based symbolic methods for the construction of Herbrand models developed in the last 12 years. Other methods of automated model building, in particular also ?nite model building, are mainly treated in the ?nal chapter; this chapter is less formal and detailed but gives a broader view on the topic and a comparison of di?erent approaches. Howtoreadthisbook: In the introduction we give an overview of automated deduction in a historical context, taking into account its relationship with the human views on formal and informal proofs.

Labelled deduction is an approach to providing frameworks for presenting and using different logics in a uniform and natural way by enriching the language of a logic with additional information of a semantic proof-theoretical nature. Labelled deduction systems often possess attractive properties, such as modularity in the way that families of related logics are presented, parameterised proofs of metatheoretic properties, and ease of mechanisability. It is thus not surprising that labelled deduction has been applied to problems in computer science, AI, mathematical logic, cognitive science, philosophy and computational linguistics - for example, formalizing and reasoning about dynamic `state oriented' properties such as knowledge, belief, time, space, and resources.

From the very beginning of their investigation of human reasoning, philosophers have identified two other forms of reasoning, besides deduction, which we now call abduction and induction. Deduction is now fairly well understood, but abduction and induction have eluded a similar level of understanding. The papers collected here address the relationship between abduction and induction and their possible integration. The approach is sometimes philosophical, sometimes that of pure logic, and some papers adopt the more task-oriented approach of AI. The book will command the attention of philosophers, logicians, AI researchers and computer scientists in general.

`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.

This book provides an overview of type theory. The first part of the book is historical, yet at the same time, places historical systems in the modern setting. The second part deals with modern type theory as it developed since the 1940s, and with the role of propositions as types (or proofs as terms. The third part proposes new systems that bring more advantages together.

Fuzzy Sets, Logics and Reasoning about Knowledge reports recent results concerning the genuinely logical aspects of fuzzy sets in relation to algebraic considerations, knowledge representation and commonsense reasoning. It takes a state-of-the-art look at multiple-valued and fuzzy set-based logics, in an artificial intelligence perspective. The papers, all of which are written by leading contributors in their respective fields, are grouped into four sections. The first section presents a panorama of many-valued logics in connection with fuzzy sets. The second explores algebraic foundations, with an emphasis on MV algebras. The third is devoted to approximate reasoning methods and similarity-based reasoning. The fourth explores connections between fuzzy knowledge representation, especially possibilistic logic and prioritized knowledge bases. Readership: Scholars and graduate students in logic, algebra, knowledge representation, and formal aspects of artificial intelligence.