Since its conception nearly 20 years ago, Logic Programming - the idea of using logic as a programming language - has been developed to the point where it now plays an important role in areas such as database theory, artificial intelligence and software engineering. However, there are still many challenging research issues to be addressed and the UK branch of the Association for Logic Programming was set up to provide a forum where the flourishing research community could discuss important issues (...) of Logic Programming which were often by-passed at the large international conferences. This volume contains the twelve papers which were presented at the ALPUK's 3rd conference which was held in Edinburgh, 10-12 April 1991. The aim of the conference was to give a broad but detailed technical insight into the work currently being done in this field, both in the UK and by researchers as far afield as Canada and Bulgaria. The breadth of interest in this area of Computer Science is reflected in the range of the papers which cover - amongst other areas - massively parallel implementation, constraint logic programming, circuit modelling, algebraic proof of program properties, deductive databases, specialised editors and standardisation. The resulting volume gives a good overview of the current progress being made in the field and will be of interest to researchers and students of any aspects of logic programming, parallel computing or database techniques and management. (shrink)

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, but (...) have been expanded by the development of sophisticated methods to study the properties of such systems using proof and model theory. In parallel with this evolution of logical formalisms as tools for articulating mathematical theories (broadly speaking), much progress has been made in the quest for a mechanization of logical inference and the investigation of its theoretical limits, culminating recently in the development of new foundational frameworks for mathematics with sophisticated computer-assisted proof systems. In addition, logical formalisms developed by logicians in mathematical and philosophical contexts have proved immensely useful in describing theories and systems of interest to computer scientists, and to some degree, vice versa. Three examples of the influence of logic in computer science are automated reasoning, computer verification, and type systems for programming languages. (shrink)

By reconciling the linguistic device and the linguistic person, his book argues for a Vygotskyan cognitive science.

This book constitutes the strictly refereed post-workshop proceedings of the 11th International Workshop on Computer Science Logic, CSL '97, held as the 1997 Annual Conference of the European Association on Computer Science Logic, EACSL, in Aarhus, Denmark, in August 1997. The volume presents 26 revised full papers selected after two rounds of refereeing from initially 92 submissions; also included are four invited papers. The book addresses all current aspects of computer science logics and its (...) applications and thus presents the state of the art in the area. (shrink)

Depending on what one means by the main connective of logic, the -if..., then... -, several systems of logic result: classic and modal logics, intuitionistic logic or relevance logic. This book presents the underlying ideas, the syntax and the semantics of these logics. Soundness and completeness are shown constructively and in a uniform way. Attention is paid to the interdisciplinary role of logic: its embedding in the foundations of mathematics and its intimate connection with philosophy, in particular the philosophy of (...) language. Set theory is presented both as a conditio sine qua non for logic and as a interesting exact ontology. The study of infinite sets yields perplexing results. Formalization of informal number theory results in formal number theory; Godel's incompleteness is treated. At appropriate places attention is paid to paradoxes, intuitionism, conditionals, the historical development of logic, to logic programming and automated theorem proving for classical logic.". (shrink)

Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 22nd Workshop on Logic, Language, Information and Computation, WoLLIC 2015, held in the campus of Indiana University, Bloomington, IN, USA in July 2015. The 14 contributed papers, presented together with 8 invited lectures and 4 tutorials, were carefully reviewed and selected from 44 submissions. The focus of the workshop was on interdisciplinary research involving formal logic, computing and programming theory, and (...) natural language and reasoning. (shrink)

J. M. E. McTaggart famously divided time into two time series, which he entitled A-series and B-series. Although he was proponent of neither of them, his division initiated a discussion as to which of the series is prior or real. This paper follows Clifford Williams’s claim that these series are not as distant as their proponents argue they are. It demonstrates their translatability in the case of examples from temporal logic and natural language. It argues that, if there are any (...) deep-rooted differences between these two series, they are only metaphysical. These metaphysical differences could be overcome by focusing on logic or natural language. These two series of time are also used in computer science and in the development of Artificial Intelligence. However, no attempt at unifying them has been suggested in these fields of study. J. M. E. McTaggart rozdělil čas na dvě časové série, A-série a B-série. Třebaže nebyl zastáncem žádné z nich, jeho rozdělení podnítilo diskuzi, která z těchto časových sérií je přednější nebo jediná skutečně reálná. Tento článek navazuje na názor Clifforda Williamse, že tyto časové série nejsou tak rozdílné, jak tvrdí jejich zastánci. V článku je demonstrována jejich přeložitelnost na příkladech z temporální logiky a přirozeného jazyka. Článek dále tvrdí, že jestliže je zde nějaký hluboce zakořeněný rozdíl mezi těmito dvěma sériemi, pak je pouze metafyzický. Tyto metafyzické rozdíly mohou být překonány, zaměříme-li se na logiku a přirozený jazyk. Tyto dvě časové série jsou také použity v informatice a rozvoji umělé inteligence, třebaže v těchto oborech dosud nebyly navrženy žádné pokusy o jejich propojení. (shrink)

We characterize abstraction in computer science by first comparing the fundamental nature of computer science with that of its cousin mathematics. We consider their primary products, use of formalism, and abstraction objectives, and find that the two disciplines are sharply distinguished. Mathematics, being primarily concerned with developing inference structures, has information neglect as its abstraction objective. Computer science, being primarily concerned with developing interaction patterns, has information hiding as its abstraction objective. We show that (...) abstraction through information hiding is a primary factor in computer science progress and success through an examination of the ubiquitous role of information hiding in programming languages, operating systems, network architecture, and design patterns. (shrink)

Computer science only became established as a field in the 1950s, growing out of theoretical and practical research begun in the previous two decades. The field has exhibited immense creativity, ranging from innovative hardware such as the early mainframes to software breakthroughs such as programming languages and the Internet. Martin Gardner worried that "it would be a sad day if human beings, adjusting to the Computer Revolution, became so intellectually lazy that they lost their power of creative (...) thinking" (Gardner, 1978, p. vi-viii). On the contrary, computers and the theory of computation have provided great opportunities for creative work. This chapter examines several key aspects of creativity in computer science, beginning with the question of how problems arise in computer science. We then discuss the use of analogies in solving key problems in the history of computer science. Our discussion in these sections is based on historical examples, but the following sections discuss the nature of creativity using information from a contemporary source, a set of interviews with practicing computer scientists collected by the Association of Computing Machinery’s on-line student magazine, Crossroads. We then provide a general comparison of creativity in computer science and in the natural sciences. (shrink)

This book looks at the ways in which conditionals, an integral part of philosophy and logic, can be of practical use in computer programming. It analyzes the different types of conditionals, including their applications and potential problems. Other topics include defeasible logics, the Ramsey test, and a unified view of consequence relation and belief revision. Its implications will be of interest to researchers in logic, philosophy, and computer science, particularly artificial intelligence.

Mathematical Logic for Computer Science is a mathematics textbook with theorems and proofs, but the choice of topics has been guided by the needs of computer science students. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and yet sufficiently elementary for undergraduates. To provide a balanced treatment of logic, tableaux are related to deductive proof systems.The logical systems presented are:- Propositional calculus (including binary decision diagrams);- Predicate calculus;- (...) Resolution;- Hoare logic;- Z;- Temporal logic.Answers to exercises (for instructors only) as well as Prolog source code for algorithms may be found via the Springer London web site: http://www.springer.com/978-1-85233-319-5 Mordechai Ben-Ari is an associate professor in the Department of Science Teaching of the Weizmann Institute of Science. He is the author of numerous textbooks on concurrency, programming languages and logic, and has developed software tools for teaching concurrency. In 2004, Ben-Ari received the ACM/SIGCSE Award for Outstanding Contributions to Computer Science Education. (shrink)

An excessive preoccupation with formalism is impeding the development of computer science. Form- content confusion is discussed relative to three areas: theory of computation, programming languages, and education.

A useful logic in which to specify normative system behaviour, deontic logic has a broad spectrum of possible applications within the field: from legal expert systems to natural language processing, database integrity to electronic contracting and the specification of fault-tolerant software.

An understanding of logic is essential to computer science. This book provides a highly accessible account of the logical basis required for reasoning about computer programs and applying logic in fields like artificial intelligence. The text contains extended examples, algorithms, and programs written in Standard ML and Prolog. No prior knowledge of either language is required. The book contains a clear account of classical first-order logic, one of the basic tools for program verification, as well as an (...) introductory survey of modal and temporal logics and possible world semantics. An introduction to intuitionistic logic as a basis for an important style of program specification is also featured in the book. (shrink)

This festschrift volume is dedicated to Boris (Boaz) Trakhtenbrot on the occasion of his 85th birthday. For over half a century, Trakhtenbrot has been making seminal contributions to virtually all of the central areas of theoretical computer science. He is universally admired as a founding father and long-standing pillar of the discipline of computer science. On Friday, 28 April 2006, the School of Computer Science at Tel Aviv University held a “Computation Day Celebrating Boaz (...) (Boris) Trakhtenbrot's Eighty-Fifth Birthday”. As a follow-up to that event, his students and colleagues were asked to contribute to a volume in his honor and in recognition of his grand contributions to the field. The book opens with two historical overviews and a bibliography. These are followed by 33 thoroughly reviewed technical contributions. The broad range of topics covered include mathematical logic, logics for computer science, mathematics for computer science, automata and formal languages, asynchronous computation, semantics of programming languages, verification, and software engineering. This tapestry of subjects stands as testimony to the vast scope of Trakhtenbrot's achievements and the profound influence he has had on the field. (shrink)

Internationally recognized logicians present current thinking on the understanding of the role of deduction in human reasoning.

Alfred Tarski’s influence on computer science was indirect but significant in a number of directions and was in certain respects fundamental. Here surveyed is Tarski’s work on the decision procedure for algebra and geometry, the method of elimination of quantifiers, the semantics of formal languages, model-theoretic preservation theorems, and algebraic logic; various connections of each with computer science are taken up.

The Interpolation Theorem, first formulated and proved by W. Craig fifty years ago for predicate logic, has been extended to many other logical frameworks and is being applied in several areas of computer science. We give a short overview, and focus on the theory of software systems and modules. An algebra of theories TA is presented, with a nonstandard interpretation of the existential quantifier . In TA, the interpolation property of the underlying logic corresponds with the quantifier combination (...) property . It is shown how the Modularization Theorem, the Factorization Lemma and the Normal Form Theorem for module expressions can be proved in TA. (shrink)

Abstract: Laws of computer science are prescriptive in nature but can have descriptive analogs in the physical sciences. Here, we describe a law of conservation of information in network programming, and various laws of computational motion (invariants) for programming in general, along with their pedagogical utility. Invariants specify constraints on objects in abstract computational worlds, so we describe language and data abstraction employed by software developers and compare them to Floridi's concept of levels of abstraction. We also consider (...) Floridi's structural account of reality and its fit for describing abstract computational worlds. Being abstract, such worlds are products of programmers' creative imaginations, so any "laws" in these worlds are easily broken. The worlds of computational objects need laws in the form of self-prescribed invariants, but the suspension of these laws might be creative acts. Bending the rules of abstract reality facilitates algorithm design, as we demonstrate through the example of search trees. (shrink)

Types now play an essential role in computer science; their ascent originates from Principia Mathematica. Type checking and type inference algorithms are used to prevent semantic errors in programs, and type theories are the native language of several major interactive theorem provers. Some of these trace key features back to Principia.

Taking Brian Cantwell Smith’s study, “Limits of Correctness in Computers,” as its point of departure, this article explores the role of models in computer science. Smith identifies two kinds of models that play an important role, where specifications are models of problems and programs are models of possible solutions. Both presuppose the existence of conceptualizations as ways of conceiving the world “in certain delimited ways.” But high-level programming languages also function as models of virtual (or abstract) machines, while (...) low-level programming languages function as models of causal (or physical) machines. The resulting account suggests that sets of models embedded within models are indispensable for computer programming. (shrink)

Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and (...) first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time. Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings. Gives an exceptionally broad view of logic. Treats traditional logic in a modern format. Presents relevance logic with applications. Provides an ideal text for a variety of one-semester upper-level undergraduate courses. (shrink)

Samson Abramsky’s wide-ranging contributions to logical and structural aspects of Computer Science have had a major influence on the field. This book is a rich collection of papers, inspired by and extending Abramsky’s work. It contains both survey material and new results, organised around six major themes: domains and duality, game semantics, contextuality and quantum computation, comonads and descriptive complexity, categorical and logical semantics, and probabilistic computation. These relate to different stages and aspects of Abramsky’s work, reflecting its (...) exceptionally broad scope and his ability to illuminate and unify diverse topics. Chapters in the volume include a review of his entire body of work, spanning from philosophical aspects to logic, programming language theory, quantum theory, economics and psychology, and relating it to a theory of unification of sciences using dual adjunctions. The section on game semantics shows how Abramsky’s work has led to a powerful new paradigm for the semantics of computation. The work on contextuality and categorical quantum mechanics has been highly influential, and provides the foundation for increasingly widely used methods in quantum computing. The work on comonads and descriptive complexity is building bridges between currently disjoint research areas in computer science, relating Structure to Power. The volume also includes a scientific autobiography, and an overview of the contributions. The outstanding set of contributors to this volume, including both senior and early career academics, serve as testament to Samson Abramsky’s enduring influence. It will provide an invaluable and unique resource for both students and established researchers. (shrink)

In 1960, E. P. Wigner, a joint winner of the 1963 Nobel Prize for Physics, published a paper titled On the Unreasonable Effectiveness of Mathematics in the Natural Sciences [61]. This paper can be construed as an examination and affirmation of Galileo's tenet that “The book of nature is written in the language of mathematics”. To this effect, Wigner presented a large number of examples that demonstrate the effectiveness of mathematics in accurately describing physical phenomena. Wigner viewed these examples as (...) illustrations of what he called the empirical law of epistemology, which asserts that the mathematical formulation of the laws of nature is both appropriate and accurate, and that mathematics is actually the correct language for formulating the laws of nature. At the same time, Wigner pointed out that the reasons for the success of mathematics in the natural sciences are not completely understood; in fact, he went as far as asserting that “… the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation for it.”. (shrink)

Tylman has recently pointed out some striking conceptual and methodological analogies between philosophy and computer science. In this paper, I focus on one of Tylman’s most convincing cases, viz. the similarity between Plato’s theory of Ideas and the object-oriented programming paradigm, and analyze it in some more detail. In particular, I argue that the platonic doctrine of the Porphyrian tree corresponds to the fact that most object-oriented programming languages do not support multiple inheritance. This analysis further reinforces Tylman’s (...) point regarding the conceptual continuity between classical metaphysical theorizing and contemporary computer science. (shrink)

Dialogue theory, although it has ancient roots, was put forward in the 1970s in logic as astructure that can be useful for helping to evaluate argumentation and informal fallacies.Recently, however, it has been taken up as a broader subject of investigation in computerscience. This paper surveys both the historical and philosophical background of dialoguetheory and the latest research initiatives on dialogue theory in computer science. The main components of dialogue theory are briefly explained. Included is a classification of (...) the main types of dialogue that, it is argued, should provide the central focus for studying many important dialogue contexts in specific cases. Following these three surveys, a concluding prediction is made about the direction dialogue theory is likely to take in the next century, especially in relation to the growing field of communication studies. (shrink)

This book bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos. This highly active branch of combinatorics is deeply rooted in and between many fields of mathematics and logic, including proof theory, commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics and subrecursive hierarchies. As a unifying concept for slick finiteness or termination proofs, wqos have been rediscovered in diverse contexts, and proven (...) to be extremely useful in computer science. The book introduces readers to the many facets of, and recent developments in, wqos through chapters contributed by scholars from various fields. As such, it offers a valuable asset for logicians, mathematicians and computer scientists, as well as scholars and students. (shrink)

This volume brings together a collection of papers covering a wide range of topics in computer and cognitive science. Topics included are: the foundational relevance of logic to computer science, with particular reference to tense logic, constructive logic, and Horn clause logic; logic as the theoretical underpinnings of the engineering discipline of expert systems; a discussion of the evolution of computational linguistics into functionally distinct task levels; and current issues in the implementation of speech act theory.

The purpose of this paper is to explore three alternative frameworks for understanding the nature of language and mentality, which accent syntactical, semantical, and pragmatical aspects of the phenomena with which they are concerned, respectively. Although the computational conception currently exerts considerable appeal, its defensibility appears to hinge upon an extremely implausible theory of the relation of form to content. Similarly, while the representational approach has much to recommend it, its range is essentially restricted to those units of language that (...) can be understood in terms of undefined units. Thus, the only alternative among these three that can account for the meaning of primitive units of language is one emphasizing the basic role of skills, habits, and tendencies in relating signs and dispositions. (shrink)

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. One very striking feature of the application of logic to language and to computation is that it requires the combination, the integration and the use of many diverse systems and methodologies - all in the same single application. The papers in this volume will give the reader a glimpse into the problems (...) of this active frontier of logic. The Editors CONTENTS Preface IX 1. S. AKAMA Recent Issues in Logic, Language and Computation 1 2. M. J. CRESSWELL Restricted Quantification 27 3. B. H. SLATER The Epsilon Calculus' Problematic 39 4. K. VON HEUSINGER Definite Descriptions and Choice Functions 61 5. N. ASHER Spatio-Temporal Structure in Text 93 6. Y. NAKAYAMA DRT and Many-Valued Logics 131 7. S. AKAMA On Constructive Modality 143 8. H. W ANSING Displaying as Temporalizing: Sequent Systems for Subintuitionistic Logics 159 9. L. FARINAS DEL CERRO AND V. LUGARDON 179 Quantification and Dependence Logics 10. R. SYLVAN Relevant Conditionals, and Relevant Application Thereof 191 Index 245 Preface This is a collection of papers by distinguished researchers on Logic, Lin guistics, Philosophy and Computer Science. The aim of this book is to address a broad picture of the recent research on related areas. In particular, the contributions focus on natural language semantics and non-classical logics from different viewpoints. (shrink)

One of the most important contributions of A. Church to logic is his invention of the lambda calculus. We present the genesis of this theory and its two major areas of application: the representation of computations and the resulting functional programming languages on the one hand and the representation of reasoning and the resulting systems of computer mathematics on the other hand.

Second-language learners rarely arrive at native proficiency in a number of linguistic domains, including morphological and syntactic processing. Previous approaches to understanding the different outcomes of first- versus second-language learning have focused on cognitive and neural factors. In contrast, we explore the possibility that children and adults may rely on different linguistic units throughout the course of language learning, with specific focus on the granularity of those units. Following recent psycholinguistic evidence for the role of multiword chunks in online language (...) processing, we explore the hypothesis that children rely more heavily on multiword units in language learning than do adults learning a second language. To this end, we take an initial step toward using large-scale, corpus-based computational modeling as a tool for exploring the granularity of speakers' linguistic units. Employing a computational model of language learning, the Chunk-Based Learner, we compare the usefulness of chunk-based knowledge in accounting for the speech of second-language learners versus children and adults speaking their first language. Our findings suggest that while multiword units are likely to play a role in second-language learning, adults may learn less useful chunks, rely on them to a lesser extent, and arrive at them through different means than children learning a first language. (shrink)