Books published by College Publications

This book introduces elementary probability through its history, eschewing the usual drill in favour of a discussion of the problems that shaped the field's development. Numerous excerpts from the literature, both from the pioneers in the field and its commentators, some given new English translations, pepper the exposition. First, for the reader without a background in the Calculus, itoffers a brief intuitive explanation of some of the concepts behind the notation occasionally used in the text, and, for those with a stronger background, it gives more detailed presentations of some of the more technical results discussed in the text.Special features include two appendices on the graphing calculator and on mathematical topics. The former begins with a short course on the use of the calculator to raise the reader up from the beginner to a more advanced level, and then finishes with some simulations of probabilistic experimentson the the calculator. The mathematical appendix likewise serves a dual purpose.The book should be accessible to anyone taking or about to take a course in the Calculus, and certainly is accessible to anyone who has already had such acourse. It should be of special interest to teachers, statisticians, or anyone who uses probability or is interested in the history of mathematics or sciencein general.

This book is designed for readers who knowelementary mathematical logic and axiomatic settheory, and who want to learn more about set theory.The primary focus of the book is on the independenceproofs. Most famous among these is the independenceof the Continuum Hypothesis (CH); that is, there aremodels of the axioms of set theory (ZFC) in whichCH is true, and other models in which CH is false.More generally, cardinal exponentiation on the regularcardinals can consistently be anything not contradictingthe classical theorems of Cantor and König.The basic methods for the independence proofs arethe notion of constructibility, introduced by Gödel, andthe method of forcing, introduced by Cohen. This bookdescribes these methods in detail, verifi es the basicindependence results for cardinal exponentiation, andalso applies these methods to prove the independenceof various mathematical questions in measure theoryand general topology.Before the chapters on forcing, there is a fairly longchapter on "infi nitary combinatorics". This consistsof just mathematical theorems (not independenceresults), but it stresses the areas of mathematicswhere set-theoretic topics (such as cardinal arithmetic)are relevant.There is, in fact, an interplay between infi nitarycombinatorics and independence proofs. Infi nitarycombinatorics suggests many set-theoretic questionsthat turn out to be independent of ZFC, but it alsoprovides the basic tools used in forcing arguments. Inparticular, Martin's Axiom, which is one of the topicsunder infi nitary combinatorics, introduces many of thebasic ingredients of forcing.

La question de la fiction sous l'angle des normes représente un objet d'étude encore peu exploré par des chercheurs autres que les juristes. Notre objectif a été de réunir des collègues travaillant sur la fiction à partir de divers champs comme la littérature, la linguistique, le droit mais aussi la philosophie, afin de les inviter à réfléchir ensemble. Même si les résultats des analyses ne semblent pas toujours converger, chacun des textes porte sur un élément spécifique qui sert de détour fructueux dans le but de fournir une réponse à la question ultime de la signification et de l'usage des fictions normatives.Ce livre représente une tentative d'analyse de la notion de fiction normative comme objet d'une confrontation interdisciplinaire spécifique, une fois que le rapprochement entre les différents traitements de cette notion nous a permis de rechercher les motifs récurrents d'un champ à l'autre, mais aussi de mettre en relief les spécificités de chaque approche particulière. Le panorama réalisé dans ce volume sera certainement utile pour tous ceux qui abordent une recherche sur la fiction, ou encore pour les collègues qui, comme nous, aspirent à une étude systématique de la fiction de type normatif.

'Logic is not Mathematical' is a collection of the author's recently published papers. It traces a series of egregious errors that the founders of modern logic made, which have been uncorrected to this day largely because of the mathematical and empirical orientation of most of the main protagonists. Whether a piece of language is coherent or incoherent is independent of whether it has factual or fictional content, for one thing, but Logic is a literary subject, the author argues, in more ways than that. For this conclusion is defended in fine detail in a large number of areas by itemizing how the use of natural language features removes major difficulties that have beset the Fregean tradition, including Russell's Paradox, Berry's Paradox, and the Liar Paradox. Overlooking pragmatic features like the necessary contextuality of language is what has primarily given rise to these problems. But a whole range of other, patently wrong, linguistic confusions have been involved as well, such as confusing use with mention, reference with description, identity with equivalence, predicates with mathematical functions, predicates with their nominalizations, predicates with forms of sentences, and mentioned sentences with 'that'-clauses. The continued prevalence of these errors in what is now a very professional discipline is hard to comprehend, but it displays a major failure in the mental outlook of the mainline logicians who have followed on from, and developed Frege's advances without a second thought.

The publication of the seminal special issue on nonmonotonic logics bythe Artificial Intelligence Journal in 1980 resulted in a new area ofresearch in knowledge representation and changed the mainstream paradigmof logic that originated in antiquity. It led to discoveries of connections between logic, knowledge representation and computation, and attracted not only computer scientists but also logicians, mathematicians and philosophers.Nonmonotonic reasoning concerns situations when information is incomplete or uncertain. Thus, conclusions drawn lack iron-cladcertainty that comes with classical logic reasoning. New information,even if the original one is retained, may change conclusions. Formalways to capture mechanisms involved in nonmonotonic reasoning, andto exploit them for computation as in the answer set programming paradigm are at the heart of this research area. The conference NonMon@30 - Thirty Years of Nonmonotonic Reasoning,held in Lexington, KY, USA, October 22-25, 2010, aimed to sum up the experience of the first 30 years of nonmonotonic logics and to map paths into the future. It comprised eighteen invited talks and several technical presentations. The present volume consists of the texts based on twelve of the invited presentations. These papers offer unique insights into the key questions that have been driving the development of nonmonotonicreasoning and suggest problems worthy of consideration in the future. They paint the picture of the field that has a well-established tradition, and remains vibrant and relevant to long-term goals of artificial intelligence.

This collection of papers, published in honour of Hector J. Levesque on theoccasion of his 60th birthday, addresses a number of core areas in the field ofknowledge representation and reasoning. In a broad sense, the book is aboutknowledge and belief, tractable reasoning, and reasoning about action andchange. More specifically, the book contains contributions to DescriptionLogics, the expressiveness of knowledge representation languages, limited formsof inference, satisfiablity (SAT), the logical foundations of BDI architectures, only-knowing,belief revision, planning, causation, the situation calculus, the actionlanguage Golog, and cognitive robotics.

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 3 (2010) contains two research papers by outstanding mathematicians.

A hundred years ago, October 18th 1911, young Wittgenstein invaded Russell's room to start studying with him. Seven years later he had finished the Tractatus Logico-Philosophicus; a highly original ethical deed that involved presenting a logical system in literary fashion. The current book sets out to show that despite its condensed literary presentation the Tractatus has a strong interpretation, both philosophically and in its technical fine-structure. It makes clear how Wittgenstein's early views on ethics and logic are related to his symbolic turn. To this end, the symbolic nature of contingent propositions in logical space is charted in detail, while logical propositions are characterized as empty forms about nothing. Not only the finite system is covered but also a natural infinite generalization that Wittgenstein's text just hints at. As it turns out, Wittgenstein's early philosophy gives the sign of a symbol center stage in a way that anticipates the elegant tableaux methods developed much later. Also, Wittgenstein's injective treatment of quantification is shown to be correct.

In a wide-ranging series of papers, researchers from Poland, Slovakia and the Czech Republic and from the UK, Denmark and Germany offer perspectives on social work interventions in adult services in the European Union. Topics include: adult care policies in Europe and the UK, including personalisation, end-of-life care, care homes for older people, drug abuse, Roma people, care leavers and foster care recruitment and management, peoplewith disabilities, homelessness and unemployment, multi-problem families and universities of the Third Age.The papers draw on research and practice in a wide range of social work agencies in many different European countries.The papers are from a conference organised by Opole University, Poland of participants in an EU Leonardo da Vinci programme.The volume is edited by: Professor Józefa Br¿giel and Dr Iwona D¿browska-Jab¿öska (Faculty of Pedagogical Sciences, Opole University, Poland) and Professor Malcolm Payne (St Christopher's Hospice, and Kingston University, UK, and Opole University, Poland).

This volume contains selected papers presented by students atURC* 2010 (Undergraduate Research in Computer Science - Theory andApplications).The papers cover a wide range of topics, including algorithm design (inparticular, the design of heuristic algorithms for the maximum-leaf spanning tree problem, and the analysis of speed scaling algorithms), programming language design (in particular, language based security, the use of effect systems for automating model extraction, and results on adaptation languages using visual environments) and applications to ray tracing optical phenomena and pattern matching in MIDI ¿les.The URC* 2010 conference took place at King's College London, 24-26 March2010, in association with a Spring School on Information and Software Security.URC*2010 brought together undergraduate students, postgraduate students andleading scientists, with the goal of promoting research in computer science andinterdisciplinary topics amongst undergraduate students. By introducing students to new research results and techniques, it encouraged them to startconducting research and producing research results already during theirundergraduate studies.

En Paradojas, Paradojas y más Paradojas se analiza de modo claro y precisoun problema fundamental: ¿Qué es una paradoja y cuál es su importancia en lafilosofía contemporánea? El libro pone al alcance del lector no especializadouna selección de las paradojas más conocidas e inquietantes, y realiza unanálisis y discusión que permite que el lector pueda tener una comprensiónprofunda de ellas y de las alternativas que surgen frente a ellas. Las paradojasson un fenómeno multidisciplinario: la verdad, la racionalidad, elconocimiento, la justificación y el infinito son algunos de los conceptos que endiferentes campos del saber han sido afectados por ellas.

The novel use of symbolism in early modern mathematics poses both philosophical and historical questions. How can we trace its development and transmission through manuscript sources? Is it intrinsically related to the emergence of symbolic algebra? How does symbolism relate to the use of diagrams? What are the consequences of symbolic reasoning on our understanding of nature? Can a symbolic language enable new forms of reasoning? Does a universal symbolic language exists which enables us to express all knowledge?This book brings together a collection of papers that address all these and related questions ? which were initially posed on a conference held in Ghent (Belgium) in August 2009. Scholars working on philosophy of science, history of philosophy and history of mathematics provide an insight into the role and function of symbolic representations in the development of early modern mathematics. The papers cover the period from early abbaco arithmetic and algebra (14th century) up to Leibniz (early 18th century).

In this book we study the Deontic Logic of the Talmud. We find the system is different from the formal deontic logical system currently used in the general scientific community, both in its ethical aspects as well as in its legal aspects. We show that the Talmudic distinctions between Obligations and Prohibitions are not based on the manner of execution of actions (positive action or lack of action) and offer a suitable model for such distinctions.Our model distinguishes between the normative and practical aspects of the Talmudic legal and ethical argumentation and discusses several applications and clarifications to current so called paradoxes of Deontic Logic as related to Contrary to Duties and to legal and ethical practical decision making.

Logique Dynamique de la Fiction is a masterly piece of work and a substantial contribution to a disciplined understanding of human thought and discourse about the unreal. It is, in that very respect, a logic working at the very heart of les sciences humaines. M. Redmond's command of the literature - actually of the several literatures associated with each of the constituent parts of his synthesis - is not only substantial and comprehensive; it is also rather breath-taking. Equally impressive is the technical assurance displayed by the formal development of the constituent logics, and the virtuosity with which they are adapted to the purposes of his project. [...] On the other hand, I find myself rather captivated by the insight that the practices of fiction - its writing and its reading - possess an inherently dialogical structure, and with it, the idea that to get the semantics of fiction right it will be necessary to dynamize the underlying logic. John Woods Bien que la logique de la non - existence a été développée dès les débuts de la philosophie analytique, il a fallu attendre les travaux de John Woods en 1974, afin que les relations entre logique et littérature, notamment sur la question de la fictionalité, commencent à être considérées. Le développement de ces liens entre logique et littérature sera-t-il fructueux à la fois pour la philosophie de la logique, pour l'analyse philosophique de la littérature et, plus généralement, pour l'analyse de la fictionalité? C'est à cette question que le présent ouvrage propose d'apporter des éléments de réponse. Shahid Rahman

The Mathematics of the Models of Reference is a detailed exposition of the modeling of physical and informational reality pursued by iLabs Milan ( www.ilabs.it ), a private research lab in applied Artificial Intelligence. Based on an original approach to cellular automata theory, this book includes an array of axiomatic formal theories, ranging from a discrete, mereological model of the structure of space-time, to non-standard computation and recursion theory. The appendices to the volume explain the applications of the theory in the algorithmic recapture of a variety of physical, biological, and cognitive phenomena.Francesco BertoLogic & Formal Modeling @ iLabsPhD in Philosophy, has studied at the University of Notre Dame (Indiana, USA), at the Sorbonne-Ecole Normale Supérieure of Paris, and is currently lecturer at the University of Aberdeen. He has published various papers and monographs in ontology and the philosophy of logic.Gabriele RossiDirector of iLabs A.I. Department @ iLabsHas a degree in Economic and Social Disciplines at the Bocconi University in Milan and is CEO of Diagramma, a leading company in insurance software applications. Expert in Artificial Intelligence, in 2007 he has co-authored with Antonella Canonico the book Semi-Immortality, a manifesto of European transhumanism.Jacopo TagliabueChief Scientist for Qualitative Modeling @ iLabsA PhD student with a degree in Philosophy at the University San Raffaele of Milan, has studied Economics at LSE, Statistics at New York University, and Complex Systems at the Santa Fe Institute. He has published papers in ontology and non-standard computation.

Grigori Mints is one the most distinguished proof theorists ofour time. He has contributed significantly not only to thesubject in general but also to most of its applications.This collection of papers by a number of Mints' colleaguesworldwide are both a personal tribute and a testimony to hisbreadth and importance by dealing with all areas in whichMints has worked: from proof-theoretical reductions throughnon-classical logics and category theory to automatedtheorem proving and proof mining, i.e., the extraction ofmathematical information from formal proofs.The collection itself is significant for another reason: it bridgesthe two logical worlds in which Mints has worked, the world ofthe former Soviet Union and that of the West.

This Festschrift is published on the occasion of Gerhard Heinzmann's 60th birthday. Its title "Construction" refers to Heinzmann's philosophical options (intuitionism, dialogical pragmatism, constructivism), as well as to his exceptional involvement in the building of many scientific enterprises and new scientific institutions.Sixty authors contributed to the volume, and the gathered essays witness the various centers of interest and intellectual achievements of Heinzmann. They are organised in five sections: (1) Henri Poincare; (2) History and Philosophy of Mathematics; (3) History and Philosophy of Logic; (4) Pragmatism; and (5) Miscellaneous.

We analyse the Klal uPrat family of textual rules in the Talmud. We view them as common-sense practical rules for defining sets. Such methods do not exist in general common-sense logical systems, and they complement the existing common-sense (non-monotonic) deductive logics.

Homotopy is a basic discipline of mathematics having fundamental and various applications to important fields of mathematics. The Journal has a wide scope which ranges from homotopical algebra and algebraic number theory and functional analysis. Diverse algebraic, geometric, topological and categorical structures are closely related to homotopy and the influence of homotopy is found in many fundamental areas of mathematics such as general algebra, algebraic topology, algebraic geometry, category theory, differential geometry, computer science, K-theory, functional analysis, Galois theory ad in physical sciences as well. The J. Homotopy and Related Structures intends to develop its vision on the determining role of homotopy in mathematics. the aim of the Journal is to show the importance, merit and diversity of homotopy in mathematical sciences. The J. Homotopy and Related structures is primarily concerned with publishing carefully refereed significant and original research papers. However a limited number of carefully selected survey and expository papers are also included, and special issues devoted to Proceedings of meetings in the field as well as to Festschrifts.

From Leibniz, through Kant, Frege and the "Booleans" to Husserl, this book is offered as a contribution to the conceptual understanding of symbolic knowledge, the kind of knowledge obtained by means of symbols. Some traditionalproblems of logic, philosophy of formal sciences, epistemology, philosophy of language, metaphysics and philosophical methodology are also dealt with here; among them, problems concerning content and form, signs and representation,structural knowledge and isomorphism, language and calculus, and real and ideal elements. Despite its multiple authorship, the book has stylistic and thematic unity, and can be of interest to a potentially large philosophical audience.The authors teach in Brazilian and Argentinean universities, conducting their researches mainly in the philosophy of formal sciences.

Eis um livro-texto atualizado de teoria de modelos levando o leitor das primeiras defi nições até o teorema de Morley e as partes elementares dateoria da estabilidade. Além dos resultados padrão tais como os teoremas da compacidade e da omissão de tipos, o livro também descreve várias conexõescom a álgebra, incluindo o método de eliminação de quantifi cadores de Skolem-Tarski, modelocompletude, grupos de automorfi smos e omegacategoricidade,ultraprodutos, O-minimalidade e estruturas de posto de Morley finito. O materialsobre equivalências vai-e-vem, interpretações e leis zero-um pode servir como introdução a aplicações de teoria de modelos à ciência da computação. Cadacapítulo termina com um breve comentário sobre a literatura e sugestões de leitura adicional.

Os trabalhos aqui reunidos foram originalmente apresentados no XIII Colóquio Conesul de Filosofia das Ciências Formais Visualização, realizado 2008. Desde 1997, os Colóquios reúnem um grupo estável de pesquisadores de filosofia da lógica e da matemática do Brasil, Argentina e Uruguai, juntamente com convidados especiais de outros países.  O leitor encontrará nas páginas que seguem desde análises conceituais e/ou estudos históricos dos problemas envolvidos na representação diagramática até estudos técnicos de sistemas diagramáticos.Dedicamos esta obra ao Professor Emérito Oswaldo Chateaubriand Filho.

This book returns to the discussion in volume 1 on analogy and induction,and analyses their substance. The first part distinguishes between twokinds of logic: One kind based on union of the common features, and theother kind based on synthesis of different features. In the second part ofthe book we propose a formal scheme for synthesis of concepts. The thirdpart analyses various mechanisms for kidushin and kinyan, which form amathematical group.