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Advances in Modal Logic is a unique international forum for presenting the latest results and new directions of research in Modal Logic broadly conceived. The topics dealt with are of interdisciplinary interest and range from mathematical, computational, and philosophical problems to applications in knowledge representation and formal linguistics. This volume contains invited and contributed papers from the seventh conference in the AiML series, held in Nancy, France, in September 2008. It reports on substantial advances, both in the foundations of modal logic and in a number of application areas. It includes papers on the metatheory of a variety of modal logics; on systems for spatial and temporal reasoning and interpreting natural language; on the emerging coalgebraic perspective; and on historical views of the nature of modality.

Algorithms are central to all areas of computer science, from compiler construction to numerical analysis to artificial intelligence. Throughout your academic and professional careers, you may be required to construct new algorithms, analyze existing algorithms, or modify algorithms to suit new purposes. How do we know that such algorithms are correct? One method involves making claims about how we expect our programs to operate, and then constructing code that carries out these tasks. The key component of such reasoning is the invariant, and is the topic of this book. In these pages, you will study how invariants are developed, how they are used to construct correct algorithms, and how they are helpful in analyzing existing programs. Along the way, you'll be introduced to some classic sorting, searching and mathematical algorithms, and even some solutions to games and logic puzzles. These examples, though, are only conduits for the loftier goal: understanding why algorithms work.

This monograph is an investigation into certain new logical structures implicit in the formalism of quantum mechanics.Its message rests on two pillars. The first pillar is the dynamic view of propositions. Propositions are viewed as acting on states of the world and changing them rather than just being true or false in them. The second pillar is a logical enquiry into the nature of the states of a dynamic framework in general and thus the nature of physical states in particular. It turns out that a physical state viewed as a logical entity must encode other states and also itself.The main logical structures under investigation are that of an M-algebra and that of a holistic logic. In a sense to be made precise the latter structures reflect the 'holistic' nature of quantum mechanics.

Prolog est un langage de programmation tout à fait original. «Prolog» est l'abréviation de «Programmation logique», et le lien qu'il entretient avec la logique est ce qui lui donne sa spécificité. Au coeur de Prolog, réside une idée surprenante : ne pas dire à l'ordinateur ce qu'il doit faire, mais lui décrire des situations, et lui faire faire des calculs en lui posant des questions. Prolog déduira alors logiquement de nouveaux faits concernant les situations, et donnera en réponse ses déductions.Pourquoi apprendre Prolog ? Tout d'abord, l'aspect «dis-moi quel est ton problème au lieu de me dire comment le résoudre» de son approche en fait un langage de très haut niveau, adapté aux applications riches en connaissances comme l'intelligence artificielle, la linguistique informatique, ou le web sémantique. En étudiant Prolog, on arrive à une meilleure compréhension de la façon dont des tâches sophistiquées peuvent être effectuées informatiquement. De plus, Prolog demande un état d'esprit différent : il nous apprend à penser déclarativement au lieu de procéduralement. Acquérir cette façon de réfléchir et apprendre à apprécier les liens entre la logique et la programmation font de l'apprentissage de Prolog à la fois un challenge et une récompense.Prolog tout de suite ! est une traduction de Learn Prolog Now!). Gratuitement accessible en ligne depuis 2001 (www.learnprolognow.org), le texte anglais est devenu l'une des introductions à la programmation en Prolog les plus populaires, grâce à sa clarté et son approche résolument concrète. Il est très largement utilisé comme manuel dans les universités du monde entier, et encore plus largement comme support d'auto-formation.College publications est fier de proposer la traduction française de ce classique du web. Préparée avec soin, et grâce aux remarques des lecteurs de la version anglaise, cette traduction ne présente que les implantations de Prolog compatibles avec la norme ISO. Elle présente aussi le système de modules de Prolog, et fournit toutes les réponses aux exercices. Que vous appreniez Prolog pour élargir votre compréhension de la logique et de l'informatique, ou pour vous ouvrir les portes de la riche littérature sur Prolog et le Traitement Automatique des Langues, vous trouverez certainement ici tout ce que vous souhaitiez pour apprendre Prolog... tout de suite !

Ilkka Niiniluoto, a distinguished philosopher of science, has been a tirelesspokesman for scientific realism and reason more generally. Trained in the tradition of the Finnish school of inductive logic he has refined the notion of truthlikeness (verisimilitude) to make the realist idea scientific progress mathematically exact. Niiniluotös main technical works are included in his books Is Science Progressive? (1984) and Truthlikeness (1987), but his most recent general defense of scientific realism culminated in his Critical Scientific Realism (1999). Niiniluoto is, since 1981, Professor of Theoretical Philosophy at the University of Helsinki, and since 2003 the Rector of the University. He has for a long time been one of the most prominent public intellectuals in Finland.This Festschrift brings about a selection of philosophical essays on Niiniluotös philosophy by prominent member of the international community. The contributions are grouped around three themes. The first ones deal with philosophy of logic, the philosophy of language, and the philosophy of mathematics, and the second group consists of papers on induction, truthlikeness, and scientific progress. The third part collects essays on the history of logical empiricism, the ontology of social groups, and the dispute between theism and atheism. This book is a tribute to Ilkka Niiniluoto on his 60th birthday, and it also contains Niiniluoto's replies to comments, queries and criticisms.

Logic for Artificial Intelligence and Information Technology is based on student notes used to teach logic to second year undergraduates and Artificial Intelligence to graduate students at the University of London since1984, first at Imperial College and later at King's College.Logic has been applied to a wide variety of subjects such as theoretical computer science, software engineering, hardware design, logic programming, computational linguistics and artificial intelligence. In this way it has served to stimulate the research for clear conceptual foundations.Over the past 20 years many extensions of classical logic such as temporal, modal, relevance, fuzzy, probabilistic and non-monotoinic logics have been widely used in computer science and artificial intelligence, therefore requiring new formulations of classical logic, which can be modified to yield the effect of the new applied logics.The text introduces classical logic in a goal directed way which can easily deviate into discussing other applied logics. It defines the many types of logics and differences between them.Dov Gabbay, FRSC, FAvH, FRSA, FBCS, is Augustus De Morgan Professor of Logic at the University of London. He has written over 300 papers in logic and over 20 books. He is Editor-in-Chief of several leading journals and has published over 50 handbooks of logic volumes. He is a world authority on applied logics and is one of the directors and founder of the UK charity the International Federation of Computational Logic

"There is a principle in things, about which we cannot be deceived, but must always, on the contrary, recognize the truth - viz. that the same thing cannot at one and the same time be and not be": with these words of the Metaphysics, Aristotle introduced the Law of Non-Contradiction, which was to become the most authoritative principle in the history of Western thought. However, things have recently changed, and nowadays various philosophers, called dialetheists, claim that this Law does not hold unrestrictedly - that in peculiar circumstances the same thing may at the same time be and not be, and contradictions may obtain in the world.This book opens with an examination of the famous logical paradoxes that appear to speak on behalf of contradictions (e.g., the Liar paradox, the set-theoretic paradoxes such as Cantor's and Russell's), and of the reasons for the failure of the standard attempts to solve them. It provides, then, an introduction to paraconsistent logics - non-classical logics in which the admission of contradictions does not lead to logical chaos -, and their astonishing applications, going from inconsistent data base management to contradictory arithmetics capable of circumventing Gödel's celebrated Incompleteness Theorem. The final part of the book discusses the philosophical motivations and difficulties of dialetheism, and shows how to extract from Aristotle's ancient words a possible reply to the dialetheic challenge.How to Sell a Contradiction will appeal to anyone interested in non-classical logics, analytic metaphysics, and philosophy of mathematics, and especially to those who consider challenging our most entrenched beliefs the main duty of philosophical inquiry. Francesco Berto is Lecturer in Logic and Metaphysics at the University of Venice, Italy. He has published articles in American Philosophical Quarterly, The Australasian Journal of Philosophy, Dialectica, Logique et Analyse, The European Journal of Philosophy, and the books La dialettica della struttura originaria [The Dialectics of the Basic Structure, Padua 2003], Che cos'è la dialettica hegeliana [What is Hegel's Dialectics?, Padua 2005], Teorie dell'assurdo [Theories of the Absurd, Rome 2006] and Logica da zero a Gödel [Logic, from Zero to Gödel, Rome 2007].

Many mathematical and computational concepts can be represented in a natural way using higher-order logic. Consequently, higher-order logic has become an important topic of research. /Automated Reasoning in Higher-Order Logic/ presents both a theoretical analysis of fragments of higher-order logic as well as a complete automated search procedure for an extensional form ofhigher-order logic.The first part of the book provides a detailed presentation of the theory (syntax and semantics) of fragments of higher-order logic. The fragments differ in the amount of extensionality and set comprehension principles included. Three families of sequent calculi are defined and proven sound and complete with respect to appropriate model classes. Using the model constructions in the book, different versions of Cantor's theorem are determined to not be provable in certain fragments. In fact, some versions of Cantor's theorem are independent of other versions (in sufficiently weak fragments).In the second part of the book, an automated proof procedure for extensional type theory is described. Proving completeness of such a higher-order search procedure is a nontrivial task. The book provides such a completeness proof by first proving completeness of the ground case and then proving appropriate lifting results./Automated Reasoning in Higher-Order Logic/ is an essential document for researchers in higher-order logic and higher-order theorem proving. The book is also essential reading for programmers implementing or extending higher-order search procedures. Users of higher-order theorem provers can use the book to improve their understanding of the underlying logical systems.

Paraconsistent logics are logics which allow solid deductivereasoning under contradictions by offering a mathematical andphilosophical support to contradictory yet non-trivial theories.Due to its role in models of scientific reasoning and to itsphilosophical implications, as well as to its connections totopics such as abduction, automated reasoning, logic programming,and belief revision, paraconsistency has becoming a fast growingarea.During the III World Congress onParaconsistency (WCP3) held in Toulouse, France, in July, 2003, it became apparent that there is a need for a Handbook covering the most recent results on several aspects of paraconsistent logic, including philosophical debates onparaconsistency and its connections to philosophy of language,argumentation theory, computer science, information theory, andartificial intelligence.This book is a basic tool for those who want to know more about paraconsistent logic, its history and philosophy, the various systems of paraconsistent logic and their applications.The present volume is edited by Jean-Yves Beziau, Walter Carnielli and Dov Gabbay, expert logicians versed in a variety of logics.

The realism/anti-realism debate is one of the traditional central themes in the philosophy of mathematics. The controversies about the existence of the irrational numbers, the complex numbers, the infintesimals, etc. will be familiar to all who are acquainted with the history of mathematics.This book aims mainly at presenting and defending a non-Platonist form of mathematical structural realism which, in the respect of the history of mathematics, harmonizes with a plausible epistemology that naturally arises from it."Gianluigi Oliveri's book embodies a masterly survey of salient questions in the philosophy of mathematics, and propounds a challenging, if controversial, theory of the subject." Michael Dummett

This volume takes a reflective position with respect to the conferenceseries "Foundations of the Formal Sciences" (FotFS) and asks:* What are the Formal Sciences?* Can we develop a theoretical classification of the sciences thatjuxtaposes the formal sciences to the natural sciences, social sciences,and humanities? Can we do this solely by identifying common methodologicalfeatures?* Can we identify changes of the notion of formal sciences over time?How were the areas that we now conceived as the "Foundations of the FormalSciences" classified throughout history?Investigating the "History of the Concept of the Formal Sciences" to findanswers to an array of questions with this wide scope, you need anenthusiastic group of researchers interested in going beyond thetraditional boundaries of their subjects covering at once thephilosophical, historical and logical issues at hand, like the authors ofthis volume.The papers in this volume stand witness to our success in touching thementioned questions. It will be of interest to philosophers,sociologists, historians, and logicians, and covers many aspects of thehistory of the formal sciences from the Bronze Age to the early XXIstcentury.

Russell's paradox arises when we consider those sets that do not belong to themselves. The collection of such sets cannot constitute a set. Step back a bit. Logical formulas define sets (in a standard model). Formulas, being mathematical objects, can be thought of as sets themselves-mathematics reduces to set theory. Consider those formulas that do not belong to the set they define. The collection of such formulas is not definable by a formula, by the same argument that Russell used. This quickly gives Tarski's result on the undefinability of truth. Variations on the same idea yield the famous results of Gödel, Church, Rosser, and Post.This book gives a full presentation of the basic incompleteness and undecidability theorems of mathematical logic in the framework of set theory. Corresponding results for arithmetic follow easily, and are also given. Gödel numbering is generally avoided, except when an explicit connection is made between set theory and arithmetic. The book assumes little technical background from the reader. One needs mathematical ability, a general familiarity with formal logic, and an understanding of the completeness theorem, though not its proof. All else is developed and formally proved, from Tarski's Theorem to Gödel's Second Incompleteness Theorem. Exercises are scattered throughout.

Tbilisi Mathematical Journal (TMJ) is a fully refereed international journal, publishing original research papers in all areas of mathematics. Papers should satisfy the high standards and only works of high quality will be recommended for publication. The Management Committee may occasionally decide to invite the submission of survey and expository papers of the highest quality. Unsolicited submissions of survey and expository papers will not be considered for publication. Volume 1 (2008) contains eight research papers by outstanding mathematicians in areas ranging from functional analysis to mathematical logic.

The International Directory of Logicians is a listing of over 260 of the world's most foremost living logicians, representing the most important and influential developments of our day. It provides a compact summary of each entrant's eduction, professional appointments, honours and awards, principal publications, as well as a description of the nature and significance of his or her contributions to logic, and a "vision statement" concerning logic's future prospects. Logic here is understood in its broad sense, encompassing all branches of mathematical logic, philosophical logic and the history of logic.Inclusion in the Directory is by invitation only, following a rigorous selection process guided by a distinguished Advisory Board. The Directory is designed to meet the needs of students and professional logicians alike. It is the most informative single-volume record of logic's present state and will serve as an invaluable historical reference for future generations of scholarship.

Causal inference is perhaps the most important form ofreasoning in the sciences. A panoply of disciplines, ranging fromepidemiology to biology, from econometrics to physics, makeuse of probability and statistics in order to infer causalrelationships. However, the very foundations of causal inferenceare up in the air; it is by no means clear which methods of causalinference should be used, nor why they work when they do.This book brings philosophers and scientists together to tackle these important questions. The papers in this volume shed light on the relationship between causality and probability and the application of these concepts within the sciences. With its interdisciplinary perspective and its careful analysis, "Causality and Probability in the Sciences" heralds the transition of causal inference from an art to a science.

Advances in Modal Logic is a unique international forum for presenting the latest results and new directions of research in modal logic broadly conceived. The topics dealt with are of interdisciplinary interest and range from mathematical, computational, and philosophical problems to applications in knowledge representation and formal linguistics.This volume contains invited and contributed papers from the sixth conference in the series, held for the first time outside Europe, in Noosa, Queensland, Australia, in September 2006. It reports on considerable progress, both in the foundations of modal logic and in a number of application areas. It includes papers on the theory of modal logic itself, on process theory, multi-agent systems and spatial reasoning, and work on quantified modal logic, modal reasoning methods, and philosophical issues.

The study of creative, 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. Several of the papers in this volume aim at increasing epistemological knowledge about the role of model-based reasoning in various scientific tasks, other papers address fundamental cognitive issues related to model-based reasoning and illustrate novel analyses of cognitive "logical" models of model-based reasoning and of the interplay abduction/model-based reasoning/creative inferences.The volume is based on the papers that were presented at the International Conference Model-Based Reasoning in Science and Engineering: Abduction, Visualization, Simulation (MBR'04), held at the Collegio Ghislieri, University of Pavia, Pavia, Italy, in December 2004.

This volume is both a tribute to Ulrich Felgner's research inalgebra, logic, and set theory and a strong researchcontribution to these areas. Felgner's former students, friendsand collaborators have contributed sixteen papers to thisvolume that highlight the unity of these three fields in the spiritof Ulrich Felgner's own research. The interested reader will find excellent original research surveys and papers that span the field from set theory without the axiom of choice via model-theoretic algebra to the mathematics of intonation.

The key-terms "language", "knowledge" and "metaphysics" arguably shapemost of the recent researches in analytic philosophy. This volume aim toaddress some of the currently debated issues revolving around thesethree fundamental areas and, in particular: can the notion of"descriptive name" be extended to names of natural kinds? What does itmean for a belief to be justified? Is there a principled way to draw thedistinction between causal and non causal relations? Do futurecontingent claims require us to employ a notion of relative truth? Inwhat sense analytic sentences could be taken to be known a posteriori?The twelve papers collected in this volume arise from a selection ofthose presented during the First Graduate Conference of the ItalianSociety for Analytic Philosophy (SIFA) held at the University of Paduain September 2007. The authors are all young and brilliant scholarscoming from some of the most prestigious universities in the world:University College (London), Nottingham, Princeton, Kentucky, Stanford,Eastern Piedmont, St. Andrews, Hebrew University of Jerusalem, Duhram,Catholic University of Leuven, London School of Economics.

This book provides an invaluable overview of the reach of logic. It provides reference to some of the most important, well-established results in logic, while at the same time offering insight into the lattest research issues in the area. It also has a balance of theory and practice, containing essays in the areas of Modal Logic, Intuitionistic Logic, Logic and Language, Non-monotonic Logic and Logic Programming, Temporal Logic, Logic and Learning, Combination of Logics, Practical Reasoning, Logic and Artificial Intelligence, Abduction, Theorem Proving, and Goal-Directed Reasoning. It will be invaluable reading for researchers and graduate students in Logic and Computer Science, and a fabulous source of inspiration for research students in search of a topic for a PhD in logic or theoretical computer science.

This book provides an invaluable overview of the reach of logic. It provides reference to some of the most important, well-established results in logic, while at the same time offering insight into the latest research issues in the area. It also has a balance of theory and practice, containing essays in the areas of Modal Logic, Intuitionistic Logic, Logic and Language, Non-monotonic Logic and Logic Programming, Temporal Logic, Logic and Learning, Combination of Logics, Practical Reasoning, Logic and Artificial Intelligence, Abduction, Theorem Proving, and Goal-Directed Reasoning. It will be invaluable reading for researchers and graduate students in Logic and Computer Science, and a fabulous source of inspiration for research students in search of a topic for a PhD in logic and theoretical computer science.

Automata and Dictionaries is aimed at students and specialists in natural language processing and related disciplines where efficient text analysis plays a role. Large linguistic resources, in particular lexica, are now recognized as a fundamental pre-requisite for all natural language processing tasks. Specialists in this domain cannot afford to be ignorant of the state-of-the-art lexicon-management algorithms. This monograph, which is also intended be used as an advanced text book in computational linguistics, fills a gap in natural language processing monographs and is complementary to other publications in this area.This book is also a source of examples, exercises and problems for software engineering in general. The algorithms that are presented are excellent examples of non-trivial problems of graph construction, graph handling and graph traversal. Even though published in scientific journals, they have not been presented in an easily accessible form so far to teachers and students. These algorithms will also be of interest for the training of software engineers.Chapter 1 of Automata and Dictionaries provides the application-oriented motivation for solving the problems studied in the rest of the book. It introduces and exemplifies several key notions of lexicon-based natural language processing in a way accessible to any computer science student. Chapter 2 surveys the main solutions of the problem, using as an example a very small toy lexicon. Chapter 3 defines the underlying mathematical notions, immediately illustrating theory with practical examples, which makes this part quite readable.Chapters 4 and 5 are dedicated to the two central notions of lexicon construction: the algorithms of determinization and minimization. The standard form of both algorithms is presented, but also their variants and some special cases that occur frequently in practice. The operation of the algorithms is described step by step in examples, introducing the beginner into the world of epsilon-transitions, state heights and reverse automata.Chapter 6 goes a step further into complexity. It is based on algorithms published by scholars from 1998 to now. They are presented here with the same clarity as the preceding, more classical, algorithms. This remarkable achievement owes much to the rigorous structuration of this chapter. These algorithms have variants for transducers, which are presented in Chapter 7 with the same pedagogical skill.The last chapter studies time and space complexity of the algorithms and explains several tricks useful to speed up their operation.

This volume is a collection of papers that explore various areas of common interest between philosophy, computing, and cognition. The book illustrates the rich intrigue of this fascinating recent intellectual story. It begins by providing a new analysis of the ideas related to computer ethics, such as the role in information technology of the so-called moral mediators, the relationship between intelligent machines and warfare, and the new opportunities offered by telepresnece, for example in teaching and learning. The book also ties together the concerns of epistemology and logic, showing, for example, the connections between computers, bio-robotics, and scientific research and between computational programs and scientific discovery. Important results coming from recent computational models of deduction, the dynamic nature of meaning, and the role of reasoning and learning in spatial, visual and exemplar-based compuational frameworks are also addressed. Some stimulating papers carefully study how the interplay between computing and philosophy has also shed new light on the role of rational acceptance in the logic of belief and on the status of old philosophical topics like embodiment and consciousness, the role of information and the problem of realism in the new digital world. Finally, a considerable part of the book addresses the role of intenal and external representations in scientific reasoning and creative inferences as well as the place of manipulation of objects and artifacts in human cognition. Taking these topics together this book describes an aspect of an emerging agenda which is likely to carry the interaction between philosophy, cognition and computing forward into the twenty-first century. The volume is based on the papers that were presented at the International European Conference Computing and Philosophy, E-CAP2004, Italy, held at the University of Paiva, Paiv, Italy in June 2004, chaired by Lorenzo Magnani.