Information technology has been, in recent years, under increasing commercial pressure to provide devices and systems which help/ replace the human in his daily activity. This pressure requires the use of logic as the underlying foundational workhorse of the area. New logics were developed as the need arose and new foci and balance has evolved within logic itself. One aspect of these new trends in logic is the rising impor- tance of model based reasoning. Logics have become more and more tailored to applications and their reasoning has become more and more application dependent. In fact, some...

"Hybrid Logic and its Proof-Theory" demonstrates that hybrid-logical proof-theory remedies the lack of uniformity in ordinary modal-logical proof systems. Various versions and proof systems for hybrid logic are considered, providing a detailed overview of the topic.

We are happy to present to the reader the first book of our Applied Logic Series. Walton's book on the fallacies of ambiguity is firmly at the heart of practical reasoning, an important part of applied logic. There is an increasing interest in artifIcial intelligence, philosophy, psychol- ogy, software engineering and linguistics, in the analysis and possible mechanisation of human practical reasoning. Continuing the ancient quest that began with Aristotle, computer scientists, logicians, philosophers and linguists are vigorously seeking to deepen our understanding of human reasoning and...

Proof Theory of Modal Logic is devoted to a thorough study of proof systems for modal logics, that is, logics of necessity, possibility, knowledge, belief, time, computations etc. It contains many new technical results and presentations of novel proof procedures. The volume is of immense importance for the interdisciplinary fields of logic, knowledge representation, and automated deduction.

The nationwide research project Deduktion', funded by the Deutsche Forschungsgemeinschaft (DFG)' for a period of six years, brought together almost all research groups within Germany engaged in the field of automated reasoning. Intensive cooperation and exchange of ideas led to considerable progress both in the theoretical foundations and in the application of deductive knowledge. This three-volume book covers these original contributions moulded into the state of the art of automated deduction.
The three volumes are intended to document and advance a development in the field of...

1. BASIC CONCEPTS OF INTERACTIVE THEOREM PROVING Interactive Theorem Proving ultimately aims at the construction of powerful reasoning tools that let us (computer scientists) prove things we cannot prove without the tools, and the tools cannot prove without us. Interaction typi- cally is needed, for example, to direct and control the reasoning, to speculate or generalize strategic lemmas, and sometimes simply because the conjec- ture to be proved does not hold. In software verification, for example, correct versions of specifications and programs typically are obtained only after a number of...

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...

The mid-1980s saw the discovery of logical tools that make it possible to model changes in belief and knowledge in entirely new ways. These logical tools turned out to be applicable to both human beliefs and to the contents of databases. Philosophers, logicians, and computer scientists have contributed to making this interdisciplinary field one of the most exciting in the cognitive scientists - and one that is expanding rapidly.
This, the first textbook in the new area, contains both discursive chapters with a minimum of formalism and formal chapters in which proofs and proof methods...

Reasoning is an integral part of intelligent systems in fields like databases, logic programming, robotics, knowledge engineering, human/computer interfaces, programming environments, etc. In reality any such system has to cope with a changing world and its dynamics. Hence it is of great importance that reasoning must account for coping with change in order to be truly useful in practice.
The book comprises several contributions to current ways of approaching this problem. On the one hand it surveys and synthesizes recent research work, while on the other hand new research results are...

The notion of negation is one of the central logical notions. It has been studied since antiquity and has been subjected to thorough investigations in the development of philosophical logic, linguistics, artificial intelligence and logic programming. The properties of negation-in combination with those of other logical operations and structural features of the deducibility relation-serve as gateways among logical systems. Therefore negation plays an important role in selecting logical systems for particular applications. At the moment negation is a 'hot topic', and there is an urgent need for...