Michael A. Arbib – författare

Computing the Brain provides readers with an integrated view of current informatics research related to the field of neuroscience. This book clearly defines the new work being done in neuroinformatics and offers information on resources available on the Web to researchers using this new technology. It contains chapters that should appeal to a multidisciplinary audience with introductory chapters for the nonexpert reader. Neuroscientists will find this book an excellent introduction to informatics technologies and the use of these technologies in their research. Computer scientists will be interested in exploring how these technologies might benefit the neuroscience community.- An integrated view of neuroinformatics for a multidisciplinary audience- Explores and explains new work being done in neuroinformatics- Cross-disciplinary with chapters for computer scientists and neuroscientists- An excellent tool for graduate students coming to neuroinformatics research from diverse disciplines and for neuroscientists seeking a comprehensive introduction to the subject- Discusses, in-depth, the structuring of masses of data by a variety of computational models- Clearly defines computational neuroscience - the use of computational techniques and metaphors to investigate relations between neural structure and function- Offers a guide to resources and algorithms that can be found on the Web- Written by internationally renowned experts in the field

After decades of research on minds and brains and a decade of conversations with architects, Michael Arbib presents When Brains Meet Buildings as an invitation to the science behind architecture, richly illustrated with buildings both famous and domestic. As he converses with the reader, he presents action-oriented perception, memory, and imagination as well as atmosphere, aesthetics, and emotion as keys to analyzing the experience and design of architecture. He also explores what it might mean for buildings to have "brains" and illuminates all this with an appreciation of the biological and cultural evolution that supports the diverse modes of human living that we know today. These conversations will not only raise the level of interaction between architecture and neuroscience but, by explaining the world of each group to the other, will also engage all readers who share a fascination with both the brains within them and the buildings around them. Michael Arbib is a pioneer in the interdisciplinary study of computers and brains and has long studied brain mechanisms underlying the visual control of action. His expertise makes him a unique authority on the intersection of architecture and neuroscience.

After decades of research on minds and brains and a decade of conversations with architects, Michael Arbib presents When Brains Meet Buildings as an invitation to the science behind architecture, richly illustrated with buildings both famous and domestic. As he converses with the reader, he presents action-oriented perception, memory, and imagination as well as atmosphere, aesthetics, and emotion as keys to analyzing the experience and design of architecture. He also explores what it might mean for buildings to have "brains" and illuminates all this with an appreciation of the biological and cultural evolution that supports the diverse modes of human living that we know today.These conversations will not only raise the level of interaction between architecture and neuroscience but, by explaining the world of each group to the other, will also engage all readers who share a fascination with both the brains within them and the buildings around them.Michael Arbib is a pioneer in the interdisciplinary study of computers and brains and has long studied brain mechanisms underlying the visual control of action. His expertise makes him a unique authority on the intersection of architecture and neuroscience.

After decades of research on minds and brains and a decade of conversations with architects, Michael Arbib presents When Brains Meet Buildings as an invitation to the science behind architecture, richly illustrated with buildings both famous and domestic. As he converses with the reader, he presents action-oriented perception, memory, and imagination as well as atmosphere, aesthetics, and emotion as keys to analyzing the experience and design of architecture. He also explores what it might mean for buildings to have "brains" and illuminates all this with an appreciation of the biological and cultural evolution that supports the diverse modes of human living that we know today.These conversations will not only raise the level of interaction between architecture and neuroscience but, by explaining the world of each group to the other, will also engage all readers who share a fascination with both the brains within them and the buildings around them.Michael Arbib is a pioneer in the interdisciplinary study of computers and brains and has long studied brain mechanisms underlying the visual control of action. His expertise makes him a unique authority on the intersection of architecture and neuroscience.

The idea that some day robots may have emotions has captured the imagination of many and has been dramatized by robots and androids in such famous movies as 2001 Space Odyssey''s HAL or Star Trek''s Data. By contrast, the editors of this book have assembled a panel of experts in neuroscience and artificial intelligence who have dared to tackle the issue of whether robots can have emotions from a purely scientific point of view. The study of the brain now usefully informs study of the social, communicative, adaptive, regulatory, and experimental aspects of emotion and offers support for the idea that we exploit our own psychological responses in order to feel others'' emotions. The contributors show the many ways in which the brain can be analyzed to shed light on emotions. Fear, reward, and punishment provide structuring concepts for a number of investigations. Neurochemistry reveals the ways in which different "neuromodulators" such as serotonin, dopamine, and opioids can affect the emotional valence of the brain. And studies of different regions such as the amygdala and orbitofrontal cortex provide a view of the brain as a network of interacting subsystems. Related studies in artificial intelligence and robotics are discussed and new multi-level architectures are proposed that make it possible for emotions to be implemented. It is now an accepted task in robotics to build robots that perceive human expressions of emotion and can "express" simulated emotions to ease interactions with humans. Looking towards future innovations, some scientists posit roles for emotion with our fellow humans. All of these issues are covered in this timely and stimulating book which is written for researchers and graduated students in neuroscience, cognitive science, psychology, robotics, and artificial intelligence.

The idea that some day robots may have emotions has captured the imagination of many and has been dramatized by robots and androids in such famous movies as 2001: A Space Odyssey's HAL or Star Trek's Lt. Commander Data. By contrast, the editors of this book have assembled a panel of experts in neuroscience and artificial intelligence who have dared to tackle the issue of whether robots can have emotions from a purely scientific point of view. The study of the brain now usefully informs study of the social, communicative, adaptive, regulatory, and experiential aspects of emotion and offers support for the idea that we exploit our own psychological responses in order to feel others' emotions. The contributors show the many ways in which the brain can be analyzed to shed light on emotions. Fear, reward, and punishment provide structuring concepts for a number of investigations. Neurochemistry reveals the ways in which different "neuromodulators" such as serotonin, dopamine and opioids can affect the emotional balance of the brain. And studies of different regions such as the amygdala and orbitofrontal cortex provide a view of the brain as a network of interacting subsystems. Related studies in artificial intelligence and robotics are discussed and new multi-level architectures are proposed that make it possible for emotions to be implanted. It is now an accepted task in robotics to build robots that perceived human expressions of emotion and can "express" simulated emotions to ease interactions with humans. Looking towards future innovations, some scientists posit roles for emotion as a powerful self-motivational tool as well as a way to work effectively in a group. But daunting questions remain as we ask what may be the nature of emotions in future generations of robots that share neither our biological heritage nor our need to share emotions with our fellow humans. All of these issues are covered in this timely and stimulating book which is written for researchers and graduate students in neuroscience, cognitive science, psychology, robotics and artificial intelligence.

The idea that some day robots may have emotions has captured the imagination of many and has been dramatized by robots and androids in such famous movies as 2001 Space Odyssey''s HAL or Star Trek''s Data. By contrast, the editors of this book have assembled a panel of experts in neuroscience and artificial intelligence who have dared to tackle the issue of whether robots can have emotions from a purely scientific point of view. The study of the brain now usefully informs study of the social, communicative, adaptive, regulatory, and experimental aspects of emotion and offers support for the idea that we exploit our own psychological responses in order to feel others'' emotions. The contributors show the many ways in which the brain can be analyzed to shed light on emotions. Fear, reward, and punishment provide structuring concepts for a number of investigations. Neurochemistry reveals the ways in which different "neuromodulators" such as serotonin, dopamine, and opioids can affect the emotional valence of the brain. And studies of different regions such as the amygdala and orbitofrontal cortex provide a view of the brain as a network of interacting subsystems. Related studies in artificial intelligence and robotics are discussed and new multi-level architectures are proposed that make it possible for emotions to be implemented. It is now an accepted task in robotics to build robots that perceive human expressions of emotion and can "express" simulated emotions to ease interactions with humans. Looking towards future innovations, some scientists posit roles for emotion with our fellow humans. All of these issues are covered in this timely and stimulating book which is written for researchers and graduated students in neuroscience, cognitive science, psychology, robotics, and artificial intelligence.

This book explains how the human brain evolved to make language possible and how cultural evolution took over from biological evolution during the transition from basic forms of communication to fully fledged languages. Basing his argument on the latest research in neuroscience, linguistics, and primatology, Michael Arbib presents an up-to-the-minute version of a theory that offers insights into the evolutionary importance of the brain's mirror neurons that enable monkeys, chimps, and humans to recognize the actions of others. Only in humans have these evolved to allow the "complex imitation" which supports the breakthrough to language. This theory, he shows, lights the path from the simple manual gesture we share with apes, to the imitation of manual skills and pantomime, and to the development of sign language and speech. It also explains why we can learn sign languages as easily as we can learn to speak. The author looks at how the brain mechanisms that made the original emergence of fully-fledged languages possible are still active in the ways that children acquire language today and sign languages continue to emerge. He also shows their crucial role in the processes by which languages change on time scales from decades to centuries. This book explains how the brain evolved to make language Michael Arbib provides nonspecialist readers with all the necessary background in primatology, neuroscience, and linguistics. His compelling account of this fascinating subject is fully accessible to a general audience.

Unlike any other species, humans can learn and use language. This book explains how the brain evolved to make language possible, through what Michael Arbib calls the Mirror System Hypothesis. Because of mirror neurons, monkeys, chimps, and humans can learn by imitation, but only "complex imitation," which humans exhibit, is powerful enough to support the breakthrough to language. This theory provides a path from the openness of manual gesture, which we share with nonhuman primates, through the complex imitation of manual skills, pantomime, protosign (communication based on conventionalized manual gestures), and finally to protospeech. The theory explains why we humans are as capable of learning sign languages as we are of learning to speak. This fascinating book shows how cultural evolution took over from biological evolution for the transition from protolanguage to fully fledged languages. The author explains how the brain mechanisms that made the original emergence of languages possible, perhaps 100,000 years ago, are still operative today in the way children acquire language, in the way that new sign languages have emerged in recent decades, and in the historical processes of language change on a time scale from decades to centuries. Though the subject is complex, this book is highly readable, providing all the necessary background in primatology, neuroscience, and linguistics to make the book accessible to a general audience.

This collection of twenty-one essays explores the creative interaction among the cognitive neurosciences, philosophy, and theology. It is the result of the fourth of five international research conferences co-sponsored by the Vatican Observatory, Rome, and the Center for Theology and the Natural Sciences, Berkeley. The overarching goal of these conferences is to support the engagement of constructive theology with the natural sciences and to investigate the philosophical and theological elements in ongoing theoretical research in the natural sciences.This series of conferences builds on the initial Vatican Observatory conference and its resulting publication, Physics, Philosophy, and Theology: A Common Quest for Understanding (1988), and on previous jointly-sponsored conferences and their publications: Quantum Cosmology and the Laws of Nature (1993), Chaos and Complexity (1995); and Molecular and Evolutionary Biology (1998). A future conference will focus on quantum physics and quantum field theory.In Section One, essays on biblical accounts of human nature (Joel B. Green) and on the role of philosophical theories of human nature in recent theology (Fergus Kerr) are paired with "snapshots" of neuroscientific research (Joseph E. LeDoux, Peter Hagoort, Marc Jeannerod, and Leslie A. Brothers) to set the poles between which the volume's dialogue proceeds. In Section Two, essays of two types bridge the fields of cognitive neuroscience and philosophy of mind: the first begin with findings in science that raise philosophical issues (Michael A. Arbib, LeDoux, Jeannerod); the second type address current philosophical accounts of human nature, focusing especially on reductionism (William R. Stoeger, Nancey Murphy, Theo C. Meyering). Essays in Section Three proceed from neuroscientific or philosophical accounts of human nature to theological interpretations: three essays provide comprehensive accounts of human nature consistent with both theology and science (Philip Clayton, Arthur Peacocke, Ian G. Barbour); others relate findings and general trends in neuroscience to phenomenological and Thomistic accounts of human experience (Stephen Happel), to Christian teaching on life after death (Ted Peters), and to religious experience (Fraser Watts, Wesley J. Wildman, and Leslie Brothers). Section Four offers conflicting answers to the question whether or not a theistic account is needed to make sense of the various dimensions of human nature canvassed in this volume.

Various brain areas of mammals can phyletically be traced back to homologous structures in amphibians. The amphibian brain may thus be regarded as a kind of "microcosm" of the highly complex primate brain, as far as certain homologous structures, sensory functions, and assigned ballistic (pre-planned and pre-pro­ grammed) motor and behavioral processes are concerned. A variety of fundamental operations that underlie perception, cognition, sensorimotor transformation and its modulation appear to proceed in primate's brain in a way understandable in terms of basic principles which can be investigated more easily by experiments in amphibians. We have learned that progress in the quantitative description and evaluation of these principles can be obtained with guidance from theory. Modeling - supported by simulation - is a process of transforming abstract theory derived from data into testable structures. Where empirical data are lacking or are difficult to obtain because of structural constraints, the modeler makes assumptions and approximations that, by themselves, are a source of hypotheses. If a neural model is then tied to empirical data, it can be used to predict results and hence again to become subject to experimental tests whose resulting data in tum will lead to further improvements of the model. By means of our present models of visuomotor coordination and its modulation by state-dependent inputs, we are just beginning to simulate and analyze how external information is represented within different brain structures and how these structures use these operations to control adaptive behavior.

This is an exciting time. The study of neural networks is enjoying a great renaissance, both in computational neuroscience - the development of information processing models of living brains - and in neural computing - the use of neurally inspired concepts in the construction of "intelligent" machines. Thus the title of this volume, Dynamic Interactions in Neural Networks: Models and Data can be given two interpretations. We present models and data on the dynamic interactions occurring in the brain, and we also exhibit the dynamic interactions between research in computational neuroscience and in neural computing, as scientists seek to find common principles that may guide us in the understanding of our own brains and in the design of artificial neural networks. In fact, the book title has yet a third interpretation. It is based on the U. S. -Japan Seminar on "Competition and Cooperation in Neural Nets" which we organized at the University of Southern California, Los Angeles, May 18-22, 1987, and is thus the record of interaction of scientists on both sides of the Pacific in advancing the frontiers of this dynamic, re-born field. The book focuses on three major aspects of neural network function: learning, perception, and action. More specifically, the chapters are grouped under three headings: "Development and Learning in Adaptive Networks," "Visual Function", and "Motor Control and the Cerebellum.

In this book, Michael Arbib, a researcher in artificial intelligence and brain theory, joins forces with Mary Hesse, a philosopher of science, to present an integrated account of how humans 'construct' reality through interaction with the social and physical world around them. The book is a major expansion of the Gifford Lectures delivered by the authors at the University of Edinburgh in the autumn of 1983. The authors reconcile a theory of the individual's construction of reality as a network of schemas 'in the head' with an account of the social construction of language, science, ideology and religion to provide an integrated schema-theoretic view of human knowledge. The authors still find scope for lively debate, particularly in their discussion of free will and of the reality of God. The book integrates an accessible exposition of background information with a cumulative marshalling of evidence to address fundamental questions concerning human action in the world and the nature of ultimate reality.

Mirror neurons may hold the brain's key to social interaction - each coding not only a particular action or emotion but also the recognition of that action or emotion in others. The Mirror System Hypothesis adds an evolutionary arrow to the story - from the mirror system for hand actions, shared with monkeys and chimpanzees, to the uniquely human mirror system for language. In this accessible volume, experts from child development, computer science, linguistics, neuroscience, primatology and robotics present and analyse the mirror system and show how studies of action and language can illuminate each other. Topics discussed in the fifteen chapters include: what do chimpanzees and humans have in common? Does the human capability for language rest on brain mechanisms shared with other animals? How do human infants acquire language? What can be learned from imaging the human brain? How are sign- and spoken-language related? Will robots learn to act and speak like humans?

In this book, Michael Arbib, a researcher in artificial intelligence and brain theory, joins forces with Mary Hesse, a philosopher of science, to present an integrated account of how humans 'construct' reality through interaction with the social and physical world around them. The book is a major expansion of the Gifford Lectures delivered by the authors at the University of Edinburgh in the autumn of 1983. The authors reconcile a theory of the individual's construction of reality as a network of schemas 'in the head' with an account of the social construction of language, science, ideology and religion to provide an integrated schema-theoretic view of human knowledge. The authors still find scope for lively debate, particularly in their discussion of free will and of the reality of God. The book integrates an accessible exposition of background information with a cumulative marshalling of evidence to address fundamental questions concerning human action in the world and the nature of ultimate reality.

Mirror neurons may hold the brain's key to social interaction - each coding not only a particular action or emotion but also the recognition of that action or emotion in others. The Mirror System Hypothesis adds an evolutionary arrow to the story - from the mirror system for hand actions, shared with monkeys and chimpanzees, to the uniquely human mirror system for language. In this accessible volume, experts from child development, computer science, linguistics, neuroscience, primatology and robotics present and analyse the mirror system and show how studies of action and language can illuminate each other. Topics discussed in the fifteen chapters include: what do chimpanzees and humans have in common? Does the human capability for language rest on brain mechanisms shared with other animals? How do human infants acquire language? What can be learned from imaging the human brain? How are sign- and spoken-language related? Will robots learn to act and speak like humans?

This is an exciting time. The study of neural networks is enjoying a great renaissance, both in computational neuroscience - the development of information processing models of living brains - and in neural computing - the use of neurally inspired concepts in the construction of "intelligent" machines. Thus the title of this volume, Dynamic Interactions in Neural Networks: Models and Data can be given two interpretations. We present models and data on the dynamic interactions occurring in the brain, and we also exhibit the dynamic interactions between research in computational neuroscience and in neural computing, as scientists seek to find common principles that may guide us in the understanding of our own brains and in the design of artificial neural networks. In fact, the book title has yet a third interpretation. It is based on the U. S. -Japan Seminar on "Competition and Cooperation in Neural Nets" which we organized at the University of Southern California, Los Angeles, May 18-22, 1987, and is thus the record of interaction of scientists on both sides of the Pacific in advancing the frontiers of this dynamic, re-born field. The book focuses on three major aspects of neural network function: learning, perception, and action. More specifically, the chapters are grouped under three headings: "Development and Learning in Adaptive Networks," "Visual Function", and "Motor Control and the Cerebellum.

This is a book whose time has come-again. The first edition (published by McGraw-Hill in 1964) was written in 1962, and it celebrated a number of approaches to developing an automata theory that could provide insights into the processing of information in brainlike machines, making it accessible to readers with no more than a college freshman''s knowledge of mathematics. The book introduced many readers to aspects of cybernetics-the study of computation and control in animal and machine. But by the mid-1960s, many workers abandoned the integrated study of brains and machines to pursue artificial intelligence (AI) as an end in itself-the programming of computers to exhibit some aspects of human intelligence, but with the emphasis on achieving some benchmark of performance rather than on capturing the mechanisms by which humans were themselves intelligent. Some workers tried to use concepts from AI to model human cognition using computer programs, but were so dominated by the metaphor "the mind is a computer" that many argued that the mind must share with the computers of the 1960s the property of being serial, of executing a series of operations one at a time. As the 1960s became the 1970s, this trend continued. Meanwhile, experi­ mental neuroscience saw an exploration of new data on the anatomy and physiology of neural circuitry, but little of this research placed these circuits in the context of overall behavior, and little was informed by theoretical con­ cepts beyond feedback mechanisms and feature detectors.

In the 1930s, mathematical logicians studied the notion of "effective comput­ ability" using such notions as recursive functions, A-calculus, and Turing machines. The 1940s saw the construction of the first electronic computers, and the next 20 years saw the evolution of higher-level programming languages in which programs could be written in a convenient fashion independent (thanks to compilers and interpreters) of the architecture of any specific machine. The development of such languages led in turn to the general analysis of questions of syntax, structuring strings of symbols which could count as legal programs, and semantics, determining the "meaning" of a program, for example, as the function it computes in transforming input data to output results. An important approach to semantics, pioneered by Floyd, Hoare, and Wirth, is called assertion semantics: given a specification of which assertions (preconditions) on input data should guarantee that the results satisfy desired assertions (postconditions) on output data, one seeks a logical proof that the program satisfies its specification. An alternative approach, pioneered by Scott and Strachey, is called denotational semantics: it offers algebraic techniques for characterizing the denotation of (i. e. , the function computed by) a program-the properties of the program can then be checked by direct comparison of the denotation with the specification. This book is an introduction to denotational semantics. More specifically, we introduce the reader to two approaches to denotational semantics: the order semantics of Scott and Strachey and our own partially additive semantics.

Computability theory is at the heart of theoretical computer science. Yet, ironically, many of its basic results were discovered by mathematical logicians prior to the development of the first stored-program computer. As a result, many texts on computability theory strike today''s computer science students as far removed from their concerns. To remedy this, we base our approach to computability on the language of while-programs, a lean subset of PASCAL, and postpone consideration of such classic models as Turing machines, string-rewriting systems, and p. -recursive functions till the final chapter. Moreover, we balance the presentation of un solvability results such as the unsolvability of the Halting Problem with a presentation of the positive results of modern programming methodology, including the use of proof rules, and the denotational semantics of programs. Computer science seeks to provide a scientific basis for the study of information processing, the solution of problems by algorithms, and the design and programming of computers. The last 40 years have seen increasing sophistication in the science, in the microelectronics which has made machines of staggering complexity economically feasible, in the advances in programming methodology which allow immense programs to be designed with increasing speed and reduced error, and in the develop­ ment of mathematical techniques to allow the rigorous specification of program, process, and machine.

Computability theory is at the heart of theoretical computer science. Yet, ironically, many of its basic results were discovered by mathematical logicians prior to the development of the first stored-program computer. As a result, many texts on computability theory strike today's computer science students as far removed from their concerns. To remedy this, we base our approach to computability on the language of while-programs, a lean subset of PASCAL, and postpone consideration of such classic models as Turing machines, string-rewriting systems, and p. -recursive functions till the final chapter. Moreover, we balance the presentation of un solvability results such as the unsolvability of the Halting Problem with a presentation of the positive results of modern programming methodology, including the use of proof rules, and the denotational semantics of programs. Computer science seeks to provide a scientific basis for the study of information processing, the solution of problems by algorithms, and the design and programming of computers. The last 40 years have seen increasing sophistication in the science, in the microelectronics which has made machines of staggering complexity economically feasible, in the advances in programming methodology which allow immense programs to be designed with increasing speed and reduced error, and in the develop­ ment of mathematical techniques to allow the rigorous specification of program, process, and machine.

The major goal of this book is to present the techniques of top-down program design and verification of program correctness hand-in-hand. It thus aims to give readers a new way of looking at algorithms and their design, synthesizing ten years of research in the process. It provides many examples of program and proof development with the aid of a formal and informal treatment of Hoare''s method of invariants. Modem widely accepted control structures and data structures are explained in detail, together with their formal definitions, as a basis for their use in the design of correct algorithms. We provide and apply proof rules for a wide range of program structures, including conditionals, loops, procedures and recur­ sion. We analyze situations in which the restricted use of gotos can be justified, providing a new approach to proof rules for such situations. We study several important techniques of data structuring, including arrays, files, records and linked structures. The secondary goal of this book is to teach the reader how to use the programming language Pascal. This is the first text to teach Pascal pro­ gramming in a fashion which not only includes advanced algorithms which operate on advanced data structures, but also provides the full axiomatic definition of Pascal due to Wirth and Hoare. Our approach to the language is very different from that of a conventional programming text.

The major goal of this book is to present the techniques of top-down program design and verification of program correctness hand-in-hand. It thus aims to give readers a new way of looking at algorithms and their design, synthesizing ten years of research in the process. It provides many examples of program and proof development with the aid of a formal and informal treatment of Hoare's method of invariants. Modem widely accepted control structures and data structures are explained in detail, together with their formal definitions, as a basis for their use in the design of correct algorithms. We provide and apply proof rules for a wide range of program structures, including conditionals, loops, procedures and recur­ sion. We analyze situations in which the restricted use of gotos can be justified, providing a new approach to proof rules for such situations. We study several important techniques of data structuring, including arrays, files, records and linked structures. The secondary goal of this book is to teach the reader how to use the programming language Pascal. This is the first text to teach Pascal pro­ gramming in a fashion which not only includes advanced algorithms which operate on advanced data structures, but also provides the full axiomatic definition of Pascal due to Wirth and Hoare. Our approach to the language is very different from that of a conventional programming text.

This is a book whose time has come-again. The first edition (published by McGraw-Hill in 1964) was written in 1962, and it celebrated a number of approaches to developing an automata theory that could provide insights into the processing of information in brainlike machines, making it accessible to readers with no more than a college freshman's knowledge of mathematics. The book introduced many readers to aspects of cybernetics-the study of computation and control in animal and machine. But by the mid-1960s, many workers abandoned the integrated study of brains and machines to pursue artificial intelligence (AI) as an end in itself-the programming of computers to exhibit some aspects of human intelligence, but with the emphasis on achieving some benchmark of performance rather than on capturing the mechanisms by which humans were themselves intelligent. Some workers tried to use concepts from AI to model human cognition using computer programs, but were so dominated by the metaphor "the mind is a computer" that many argued that the mind must share with the computers of the 1960s the property of being serial, of executing a series of operations one at a time. As the 1960s became the 1970s, this trend continued. Meanwhile, experi­ mental neuroscience saw an exploration of new data on the anatomy and physiology of neural circuitry, but little of this research placed these circuits in the context of overall behavior, and little was informed by theoretical con­ cepts beyond feedback mechanisms and feature detectors.

In the 1930s, mathematical logicians studied the notion of "effective comput­ ability" using such notions as recursive functions, A-calculus, and Turing machines. The 1940s saw the construction of the first electronic computers, and the next 20 years saw the evolution of higher-level programming languages in which programs could be written in a convenient fashion independent (thanks to compilers and interpreters) of the architecture of any specific machine. The development of such languages led in turn to the general analysis of questions of syntax, structuring strings of symbols which could count as legal programs, and semantics, determining the "meaning" of a program, for example, as the function it computes in transforming input data to output results. An important approach to semantics, pioneered by Floyd, Hoare, and Wirth, is called assertion semantics: given a specification of which assertions (preconditions) on input data should guarantee that the results satisfy desired assertions (postconditions) on output data, one seeks a logical proof that the program satisfies its specification. An alternative approach, pioneered by Scott and Strachey, is called denotational semantics: it offers algebraic techniques for characterizing the denotation of (i. e. , the function computed by) a program-the properties of the program can then be checked by direct comparison of the denotation with the specification. This book is an introduction to denotational semantics. More specifically, we introduce the reader to two approaches to denotational semantics: the order semantics of Scott and Strachey and our own partially additive semantics.

The study of formal languages and of related families of automata has long been at the core of theoretical computer science. Until recently, the main reasons for this centrality were connected with the specification and analy­ sis of programming languages, which led naturally to the following ques­ tions. How might a grammar be written for such a language? How could we check whether a text were or were not a well-formed program generated by that grammar? How could we parse a program to provide the structural analysis needed by a compiler? How could we check for ambiguity to en­ sure that a program has a unique analysis to be passed to the computer? This focus on programming languages has now been broadened by the in­ creasing concern of computer scientists with designing interfaces which allow humans to communicate with computers in a natural language, at least concerning problems in some well-delimited domain of discourse. The necessary work in computational linguistics draws on studies both within linguistics (the analysis of human languages) and within artificial intelligence. The present volume is the first textbook to combine the topics of formal language theory traditionally taught in the context of program­ ming languages with an introduction to issues in computational linguistics. It is one of a series, The AKM Series in Theoretical Computer Science, designed to make key mathematical developments in computer science readily accessible to undergraduate and beginning graduate students.

The study of formal languages and of related families of automata has long been at the core of theoretical computer science. Until recently, the main reasons for this centrality were connected with the specification and analy­ sis of programming languages, which led naturally to the following ques­ tions. How might a grammar be written for such a language? How could we check whether a text were or were not a well-formed program generated by that grammar? How could we parse a program to provide the structural analysis needed by a compiler? How could we check for ambiguity to en­ sure that a program has a unique analysis to be passed to the computer? This focus on programming languages has now been broadened by the in­ creasing concern of computer scientists with designing interfaces which allow humans to communicate with computers in a natural language, at least concerning problems in some well-delimited domain of discourse. The necessary work in computational linguistics draws on studies both within linguistics (the analysis of human languages) and within artificial intelligence. The present volume is the first textbook to combine the topics of formal language theory traditionally taught in the context of program­ ming languages with an introduction to issues in computational linguistics. It is one of a series, The AKM Series in Theoretical Computer Science, designed to make key mathematical developments in computer science readily accessible to undergraduate and beginning graduate students.