Applied Logic Series – serie

The work provides analyses of the various fallacies arising from ambiguities themselves, and also by basing these analyses on a new pragmatic approach to the concept of ambiguity. It argues that ambiguity is itself ambiguous, and not easy to define clearly. However, it does advocate a new classification of types of ambiguity that is shown to be useful in helping to evaluate cases of fallacies arising from ambiguity.

Consisting of 15 research papers, this text deals with formal, mechanizable reasoning in modal logics. It brings together various directions in the development of generalized sequent-style proof systems. The first part contains papers which give a description of powerful proof-theoretic methods as applied to the normal modal logic S4. Part II is concerned with a number of generalizations of the standard proof-theoretic formats, while the third part presents new and important results on semantics-based proof systems for modal logic.

Modal Logic is a branch of logic with applications in many related disciplines such as computer science, philosophy, linguistics and artificial intelligence. Over the last twenty years, in all of these neighbouring fields, multi-dimensional modal systems have been developed. This book treats multi-dimensional modal logics in a uniform way, linking their mathematical theory to the research tradition in algebraic logic. It defines and discusses a number of systems in detail, focusing on such aspects as expressiveness, definability, axiomatics, decidability and interpolation.

This collection of papers offers a broad account of many topics in the study of logic, language and information. In particular, it addresses two important themes: how to handle quantification in natural language; and how to isolate genuine "logics of information". After the editor's introduction, which presents an overview of the interdisciplinary field, the collection begins with a group of fairly philosophical papers which address current issues in formal semantics from a logical perspective. It then moves on to papers which straddle the border between formal semantics and logic, and finishes with purely logical papers focusing on some non-classical logics.

Intensional logics have their origin and use in research areas ranging from linguistics, cognitive science and artificial intelligence, to philosophy and computer science. This volume presents an up-to-date account of current trends in intensional logic. Consisting of nine original research papers preceded by a survey of recent developments, the book highlights recent advances in a number of interdisciplinary areas, including traditional philosophical concerns about correct descriptions and abstract objects; the use of intensional languages as descriptive tools for finite graphs; proof-theoretical considerations; general strategies of 'modalizing' calculi usually perceived to be non-modal; and mathematical foundations of intensional logics. The book is aimed at graduate students and researchers in pure and applied logic.

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 co-operation and exchange of ideas led to considerable progress both in the theoretical foundations and in the application of deductive knowledge. This 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 automated deduction that can now be observed all over the world. Rather than restricting the interest to purely academic research, the focus now is on the investigation of problems derived from realistic applications. In fact industrial applications are already pursued on a trial basis.In consequence the emphasis of the volumes is not on the presentation of the theoretical foundations of logical deduction as such, as in a handbook; rather the books present the concepts and methods now available in automated deduction in a form which can be easily accessed by scientists working in applications outside of the field of deduction. This reflects the strong conviction that automated deduction is on the verge of being fully included in the evolution of technology. Volume I focuses on basic research in deduction and on the knowledge on which modern deductive systems are based. Volume II presents techniques of implementation and details about system building. Volume III deals with applications of deductive techniques mainly, but not exclusively, to mathematics and the verification of software. Each chapter was read by two referees, one an international expert from abroad and the other a knowledgeable participant in the national project. It has been accepted for inclusion on the basis of these review reports.The text should be of interest to researchers and developers in software engineering, formal methods, certification, verification, validation, specification of complex systems and software, expert systems and natural language processing.

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 co-operation and exchange of ideas led to considerable progress both in the theoretical foundations and in the application of deductive knowledge. This 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 automated deduction that can now be observed all over the world. Rather than restricting the interest to purely academic research, the focus now is on the investigation of problems derived from realistic applications. In fact industrial applications are already pursued on a trial basis.In consequence the emphasis of the volumes is not on the presentation of the theoretical foundations of logical deduction as such, as in a handbook; rather the books present the concepts and methods now available in automated deduction in a form which can be easily accessed by scientists working in applications outside of the field of deduction. This reflects the strong conviction that automated deduction is on the verge of being fully included in the evolution of technology. Volume I focuses on basic research in deduction and on the knowledge on which modern deductive systems are based. Volume II presents techniques of implementation and details about system building. Volume III deals with applications of deductive techniques mainly, but not exclusively, to mathematics and the verification of software. Each chapter was read by two referees, one an international expert from abroad and the other a knowledgeable participant in the national project. It has been accepted for inclusion on the basis of these review reports.The text should be of interest to researchers and developers in software engineering, formal methods, certification, verification, validation, specification of complex systems and software, expert systems and natural language processing.

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 co-operation and exchange of ideas led to considerable progress both in the theoretical foundations and in the application of deductive knowledge. This 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 automated deduction that can now be observed all over the world. Rather than restricting the interest to purely academic research, the focus now is on the investigation of problems derived from realistic applications. In fact industrial applications are already pursued on a trial basis.In consequence the emphasis of the volumes is not on the presentation of the theoretical foundations of logical deduction as such, as in a handbook; rather the books present the concepts and methods now available in automated deduction in a form which can be easily accessed by scientists working in applications outside of the field of deduction. This reflects the strong conviction that automated deduction is on the verge of being fully included in the evolution of technology. Volume I focuses on basic research in deduction and on the knowledge on which modern deductive systems are based. Volume II presents techniques of implementation and details about system building. Volume III deals with applications of deductive techniques mainly, but not exclusively, to mathematics and the verification of software. Each chapter was read by two referees, one an international expert from abroad and the other a knowledgeable participant in the national project. It has been accepted for inclusion on the basis of these review reports.The text should be of interest to researchers and developers in software engineering, formal methods, certification, verification, validation, specification of complex systems and software, expert systems and natural language processing.

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 co-operation and exchange of ideas led to considerable progress both in the theoretical foundations and in the application of deductive knowledge. This three-volume set 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 automated deduction that can now be observed all over the world. Rather than restricting the interest to purely academic research, the focus now is on the investigation of problems derived from realistic applications. In fact industrial applications are already pursued on a trial basis.In consequence the emphasis of the volumes is not on the presentation of the theoretical foundations of logical deduction as such, as in a handbook; rather the books present the concepts and methods now available in automated deduction in a form which can be easily accessed by scientists working in applications outside of the field of deduction. This reflects the strong conviction that automated deduction is on the verge of being fully included in the evolution of technology. Volume I focuses on basic research in deduction and on the knowledge on which modern deductive systems are based. Volume II presents techniques of implementation and details about system building. Volume III deals with applications of deductive techniques mainly, but not exclusively, to mathematics and the verification of software. Each chapter was read by two referees, one an international expert from abroad and the other a knowledgeable participant in the national project. It has been accepted for inclusion on the basis of these review reports.The text should be of interest to researchers and developers in software engineering, formal methods, certification, verification, validation, specification of complex systems and software, expert systems and natural language processing.

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 sciences, and one that is expanding rapidly. A textbook covering this 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 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 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.

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 textbook 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 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.

Reasoning is an integral part of intelligent systems in fields like databases, logic programming, robotics, knowledge engineering, human/computer interfaces, and programming environments. 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. This text comprises several contributions to current ways of approaching this problem. On the one hand it surveys and synthesizes past research work, while on the other hand new research results are included. Among the topics treated are logics for reasoning about actions and planning, belief revision and the reconciliation of logically conflicting inputs, resolving of conflicts by merging of knowledge and issues in the evolution in object-oriented databases. The book is aimed at the researcher and advanced student active in this field.

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 a comprehensive account of this logical key concept. We have therefore asked leading scholars in various branches of logic to contribute to a volume on What is Negation? The result is the present neatly focused collection of research papers bringing together different approaches to a general characterization of kinds of negation and classifications thereof. Audience: Scholars and graduate students in the fields of philosophy, logic mathematics, computer science and linguistics.

Over the past decade, rational agency has come to be recognized as a central theme in artificial intelligence. Drawing upon research on rational action and agency in philosophy, logic, game theory, decision theory, and the philosophy of language, 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 (including speech acts, joint plans, and co-operation protocols), and, finally, describes a number of approaches to programming rational agents. Although written from the standpoint of artificial intelligence, this interdisciplinary text should be of interest to researchers in logic, mainstream computer science, the philosophy of rational action and agency, and economics.

These papers are reports on end-of-millennium results concerning the genuinely logical aspects of fuzzy sets in relation to algebraic considerations, knowledge representation and commonsense reasoning. They 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.

Time is a fascinating subject that has captured mankind's imagination from ancient times to the present. It has been, and continues to be studied across a wide range of disciplines, from the natural sciences to philosophy and logic. More than two decades before 1999, Pnueli showed the value of temporal logic in the specification and verification of computer programs. Today, a strong, vibrant international research community exists in the broad community of computer science and AI. This volume presents a number of articles from leading researchers containing results in such areas as pure temporal/modal logic, specification and verification, temporal databases, temporal aspects in AI, tense and aspect in natural language, and temporal theorem proving. Earlier versions of some of the articles were given at an International Conference on Temporal Logic, at the University of Manchester, UK.

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, parameterized proofs of metatheoretic properties, and ease of mechanizability. 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 should be of interest to 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 previously unpublished, reviewed results. The collection is an account of the current capabilities and limitations of a computational-logic-based approach to intellectics in the year 2000.

The First International and Interdisciplinary Conference on Modelling and Using Context, held in Rio de Janeiro, in January 1997, gave rise to the present book, which contains a selection of the papers presented there, thoroughly refereed and revised. The treatment of contexts as bona fide objects of logical formalization has gained wide acceptance, following the seminal impetus given by McCarthy in his Turing Award address. The field of natural language offers a particularly rich variety of examples and challenges to researchers concerned with the formal modelling of context, and several chapters in the volume deal with contextualization in the setting of natural language. Others adopt a purely formal-logical viewpoint, seeking to develop general models of even wider applicability. The 12 chapters are organized in three groups: formalization of contextual information in natural language understanding and generation; the application of context in mechanized reasoning domains; and novel non-classical logics for contextual application.

This guide presents a uniform and coherent methodology for automated deduction in non-classical logics, the relevance of which to computer science is widely acknowledged. The methodology is based on goal-directed provability. It is a generalization of the logic programming style of deduction, favourable for proof search. The methodology is applied in a uniform way to a wide range of non-classical systems, covering intuitionistic, intermediate, modal and substructural logics. The book can also be used as an introduction to these logical systems from a procedural perspective. The text should be useful to computer scientists, mathematicians and philosophers, and anyone interested in the automation of reasoning based on non-classical logics. It is also suitable for self study, its only prerequisite being some elementary knowledge of logic and proof theory.

"Frontiers in Belief Revision" is a collection of leading edge research in Belief Revision. It contains the innovative ideas of respected and pioneering experts in the area, including Isaac Levi, Krister Segerberg, Sven Ove Hansson, Didier Dubois, and Henri Prade. The book addresses foundational issues of inductive reasoning and minimal change, generalizations of the standard belief revision theories, strategies for iterated revisions, probabilistic beliefs, multiagent environments and a variety of data structures and mechanisms for implementations. This book is suitable for students and researchers interested in knowledge representation and in the state of the art of the theory and practice of belief revision.

This volume contains a collection of contemporary papers on free logic which cover a wide range of topics. These topics show that free logic is applied not only in traditional philosophical areas, but also in various contexts of modern formal logic as well as in the discussion of theoretical aspects of programming. Part I of the book covers theories of names and definite descriptions. Part II contains papers on various topics in the logic of modalities. Part III is devoted to semantics and programming. In part IV free logic is used to analyze and discuss topics from the history of philosophy. In addition, one of the founders of free logic, Karel Lambert, not only contributes an article to this volume, but he also comments the papers of all the other authors. As a result, this book should be of interest not only to philosophers and logicians, but also to computer scientists and researchers interested in foundational aspects of computer programming.

A collection of papers addressing the key challenges that face the Bayesian interpretation of probability today. Some of these papers seek to clarify the relationships between Bayesian, causal and logical reasoning. Others consider the application of Bayesianism to artificial intelligence, decision theory, statistics and the philosophy of science and mathematics. The volume includes important criticisms of Bayesian reasoning and also gives an insight into some of the points of disagreement amongst advocates of the Bayesian approach. The upshot is a plethora of new problems and directions for Bayesians to pursue. The book should be of interest to graduate students or researchers who wish to learn more about Bayesianism than can be provided by introductory textbooks to the subject. Those involved with the applications of Bayesian reasoning will find useful discussion on the validity of Bayesianism and its limits, while philosophers and others interested in pure reasoning should find ideas on normativity and the logic of belief.

A new attitude to applied logic has evolved, where researchers tailor a logic for their own use in the same way they define a computer language, and where auto­ mated deduction for the logic and its fragments is as important as the logic itself.

The study of diagnostic, visual, spatial, analogical, and temporal reasoning has demonstrated that there are many ways of performing intelligent and creative reasoning that cannot be described with the help only of traditional notions of reasoning such as classical logic. Understanding the contribution of modeling practices to discovery and conceptual change in science requires expanding scientific reasoning to include complex forms of creative reasoning that are not always successful and can lead to incorrect solutions. The study of these heuristic ways of reasoning is situated at the crossroads of philosophy, artificial intelligence, cognitive psychology, and logic; that is, at the heart of cognitive science. There are several key ingredients common to the various forms of model-based reasoning. The term "model" comprises both internal and external representations. The models are intended as interpretations of target physical systems, processes, phenomena, or situations. The models are retrieved or constructed on the basis of potentially satisfying salient constraints of the target domain. Moreover, in the modeling process, various forms of abstraction are used.Evaluation and adaptation take place in light of structural, causal, and/or functional constraints. Model simulation can be used to produce new states and enable evaluation of behaviors and other factors. The various contributions of the book are written by interdisciplinary researchers who are active in the area of creative reasoning in science and technology, and are logically and computationally oriented: the most recent results and achievements about the topics above are illustrated in detail in this book.

This monograph provides a thorough account of the model theory, proof theory and computational interpretations of BI, the logic of bunched implications, which freely combines intuitionistic logic and multiplicative intuitionistic linear logic. Starting, on the one hand, from elementary observations about modelling resources and, on the other, from a desire to develop a system of logic within which additive (or extensional) and multiplicative (or intentional) implications co-exist with equal logical status, the book gives natural deduction, l-calculi, sequent calculus, categorical semantics, Kripke models, topological models, logical relations and computational interpretations for both propositional and predicate BI, within which both additive and multiplicative quantifiers also co-exist.

This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs.A computer program called ETPS which is available from the web facilitates doing and checking such exercises.

The study of diagnostic, visual, spatial, analogical, and temporal reasoning has demonstrated that there are many ways of performing intelligent and creative reasoning that cannot be described with the help only of traditional notions of reasoning such as classical logic. Understanding the contribution of modeling practices to discovery and conceptual change in science requires expanding scientific reasoning to include complex forms of creative reasoning that are not always successful and can lead to incorrect solutions. The study of these heuristic ways of reasoning is situated at the crossroads of philosophy, artificial intelligence, cognitive psychology, and logic; that is, at the heart of cognitive science. There are several key ingredients common to the various forms of model-based reasoning. The term "model" comprises both internal and external representations. The models are intended as interpretations of target physical systems, processes, phenomena, or situations. The models are retrieved or constructed on the basis of potentially satisfying salient constraints of the target domain. Moreover, in the modeling process, various forms of abstraction are used.Evaluation and adaptation take place in light of structural, causal, and/or functional constraints. Model simulation can be used to produce new states and enable evaluation of behaviors and other factors. The various contributions of the book are written by interdisciplinary researchers who are active in the area of creative reasoning in science and technology, and are logically and computationally oriented: the most recent results and achievements about the topics above are illustrated in detail in this book.