Bøger i Applied Logic Series serien

This monograph provides a new account of justified inference as a cognitive process. In contrast to the prevailing tradition in epistemology, the focus is on low-level inferences, i.e., those inferences that we are usually not consciously aware of and that we share with the cat nearby which infers that the bird which she sees picking grains from the dirt, is able to fly. Presumably, such inferences are not generated by explicit logical reasoning, but logical methods can be used to describe and analyze such inferences. Part 1 gives a purely system-theoretic explication of belief and inference. Part 2 adds a reliabilist theory of justification for inference, with a qualitative notion of reliability being employed. Part 3 recalls and extends various systems of deductive and nonmonotonic logic and thereby explains the semantics of absolute and high reliability. In Part 4 it is proven that qualitative neural networks are able to draw justified deductive and nonmonotonic inferences on the basis of distributed representations. This is derived from a soundness/completeness theorem with regard to cognitive semantics of nonmonotonic reasoning. The appendix extends the theory both logically and ontologically, and relates it to A. Goldman's reliability account of justified belief. This text will be of interest to epistemologists and logicians, to all computer scientists who work on nonmonotonic reasoning and neural networks, and to cognitive scientists.

Time is a fascinating subject and has long since captured mankind's imagination, from the ancients to modern man, both adult and child alike. It has been studied across a wide range of disciplines, from the natural sciences to philosophy and logic. Today, thirty plus years since Prior's work in laying out foundations for temporal logic, and two decades on from Pnueli's seminal work applying of temporal logic in specification and verification of computer programs, temporal logic has a strong and thriving international research community within the broad disciplines of computer science and artificial intelligence. Areas of activity include, but are certainly not restricted to: Pure Temporal Logic, e. g. temporal systems, proof theory, model theory, expressiveness and complexity issues, algebraic properties, application of game theory; Specification and Verification, e. g. of reactive systems, ofreal-time components, of user interaction, of hardware systems, techniques and tools for verification, execution and prototyping methods; Temporal Databases, e. g. temporal representation, temporal query- ing, granularity of time, update mechanisms, active temporal data- bases, hypothetical reasoning; Temporal Aspects in AI, e. g. modelling temporal phenomena, in- terval temporal calculi, temporal nonmonotonicity, interaction of temporal reasoning with action/knowledge/belief logics, temporal planning; Tense and Aspect in Natural Language, e. g. models, ontologies, temporal quantifiers, connectives, prepositions, processing tempo- ral statements; Temporal Theorem Proving, e. g. translation methods, clausal and non-clausal resolution, tableaux, automata-theoretic approaches, tools and practical systems.

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 failed proof attempts and subsequent error corrections. Different interactive theorem provers may actually look quite different: They may support different logics (first-or higher-order, logics of programs, type theory etc.), may be generic or special-purpose tools, or may be tar- geted to different applications. Nevertheless, they share common concepts and paradigms (e.g. architectural design, tactics, tactical reasoning etc.). The aim of this chapter is to describe the common concepts, design principles, and basic requirements of interactive theorem provers, and to explore the band- width of variations. Having a 'person in the loop', strongly influences the design of the proof tool: proofs must remain comprehensible, - proof rules must be high-level and human-oriented, - persistent proof presentation and visualization becomes very important.

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 years ago, I myself coined the phrase "e;direct deductive reasoning in application areas"e;, advocating the methodology of model-based reasoning in the strongest possible terms. Certainly my discipline of Labelled Deductive Systems allows to bring "e;pieces"e; of the application areas as "e;labels"e; into the logic. I therefore heartily welcome this important book to Volume 25 of the Applied Logic Series and see it as an important contribution in our overall coverage of applied logic.

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 are presented. Using different selections from the formal sections, according to the author's detailed advice, allows the book to be used at all levels of university education. A supplementary volume contains solutions to the 210 exercises. The volume's unique, comprehensive coverage means that it can also be used by specialists in the field of belief dynamics and related areas, such as non-monotonic reasoning and knowledge representation.

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.

First International Workshop, Munich, March 1996

The present work is a fair record of work I've done on the fallacies and related matters in the fifteen years since 1986. If I had to characterize the difference that has manifested itself in our later work, I would venture that Walton has strayed more, and I less, from what has come to be called the Woods-Walton Approach to the study of fallacies.

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);

THIRTY FIVE YEARS OF AUTOMATING MATHEMATICS: DEDICATED TO 35 YEARS OF DE BRUIJN'S AUTOMATH N. De Bruijn's contributions to mathematics also included his work on generalized function theory, analytic number theory, optimal control, quasicrystals, the mathematical analysis of games and much more.

This is an authoritative collection of papers addressing the key challenges that face the Bayesian interpretation of probability today. The volume includes important criticisms of Bayesian reasoning and gives an insight into some of the points of disagreement amongst advocates of the Bayesian approach.

Free logic - i.e., logic free of existential presuppositions in general and with respect to singular terms in particular- began to come into its own as a field of research in the 1950s. In an introductory essay we give a survey of the present status of and new directions in free logic.

Frontiers in Belief Revision is a unique collection of leading edge research in Belief Revision.

Goal Directed Proof Theory presents a uniform and coherent methodology for automated deduction in non-classical logics, the relevance of which to computer science is now widely acknowledged.

We welcome Volume 20, Formal Aspects of Context.

`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.

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.

The editors of the Applied Logic Series are happy to present to the reader the fifth volume in the series, a collection of papers on Logic, Language and Computation.

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.

This volume represents an advanced, comprehensive state-of-the-art survey of the field of rational agency as it stands today. It covers the philosophical foundations of rational agency, logical and decision-theoretic approaches to rational agency, multi-agent aspects of rational agency and a number of approaches to programming rational agents.

Michael Dunn in Chapter 2 (A Comparative Study of Various Model-theoretic Treatments of Negation: A History of Formal Negation) surveys a detailed correspondence-theoretic classifcation of various notions of negation in terms of properties of a binary relation interpreted as incompatibility.