Bücher veröffentlicht von College Publications

The Lambda Calculus, treated in this book mainly in its untyped version, consists of a collection of expressions, called lambda terms, together with ways how to rewrite and identify these. In the parts conversion, reduction, theories, and models the view is respectively 'algebraic', computational, with more ('coinductive') identifications, and finally set-theoretic.The lambda terms are built up from variables, using application and abstraction. Applying a term F to M has as intention that F is a function, M its argument, and FM the result of the application. This is only the intention: to actually obtain the result one has to rewrite the expression FM according tothe reduction rules. Abstraction provides a way to create functions according to the effect when applying them.The power of the theory comes from the fact that computations, both terminating and infinite, can be expressed by lambda terms at a 'comfortable' level of abstraction.

This book comprises a collection of 12 research articlespertaining to the infl uence of phenomenological analysison current issues of epistemology, this one meantas a philosophy of science. Ten of these articles havealready appeared in various research journals of thefi eld at large and have been to a considerable extentre-edited, updated and in certain respects reworked. Theremaining two are published originally for this book and naturallycomplement and invigorate the argumentation and the scope ofthe published articles. Overall, the content of the book can bedescribed as an original attempt to demonstrate the relevanceof Husserlian phenomenology with regard to theoreticalquestions arising from the contemporary evolution of suchdiverse scientifi c fi elds as the foundations of mathematics andthe interpretation of quantum mechanics."Stathis Livadas has pushed the investigation of the foundationsof mathematics and of present day physical theories out of astrictly analytic point of view, by considering a phenomenologicalapproach on these matters. According to him mathematicsand science present various ambiguous notions which cannotbe, in principle, resolved by analytical means only. Therefore, amore general approach is pursued. This book contains severalof his already published articles, and now they are put togetherfor a more general audience in the form of a book. I think thatthis line of investigation, facing current epistemological issuesunder a phenomenological point of view, is fruitful and relevant,and ought to be considered by a wide range of philosophers."Décio Krause. Universidad Federal de Santa Catarina, Brazil."Stathis Livadas' book embodies a masterly analysis of someimportant questions in the philosophy of mathematics andin Husserl's phenomenology. According to Livadas, non-Cantorian theories and intuitionistic ones are "trapped" in theimpredicativity of the continuum when they shift the boundariesbeyond naturally intuited countability in our witnesseduniverse. In this perspective, from a theoretical point of view,mathematical intuition is not eliminable. Hence the challengeto point out to the intuition of continuum in accordancewith a phenomenological point of view, i.e., making essentialreference to the existence of a categorial intuition based onthe intentionality of primary experience which is geneticallyconstituted in the unity of the fl ux of consciousness."Arturo Carsetti. University of Rome "Tor Vergata"

El razonamiento abductivo ha recibido una gran atención en los últimos años gracias a sus aplicaciones en diversas disciplinas, desde la epistemología hasta la lingüística o la inteligencia artificial. Este libro presentaalgunas de las aproximaciones a la abducción más populares dentro de la lógica clásica, tanto proposicional como de predicados.Dado el interés de la abducción dentro de la programación logica, el libro incluye un capítulo dedicado a las aplicaciones de la abducción en el razonamiento automático. Igualmente, se ofrece un razonador abductivo escritoen Prolog. En los apéndices se encuentra el código fuente, así como una pequeñaintroducción a la programación lógica.A lo largo del libro se incluyen numerosos ejemplos de problemas abductivos resueltos con cada uno de los sistemas que se presentan.

On 17-18 February 2011 the third installment of PhDs in Logic took place at the Academy Palace in Brussels, Belgium. Some forty European logicians gathered to discuss a diverse range of topics in mathematical and philosophical logic. PhDs in Logic is an annual series of graduate conferences/winter schools, run for and by PhD students. The winter school consists of tutorials taught by well established researchers; the graduate conference provides young logicians withan excellent opportunity to share their results with a large audience of peersand established logicians. This volume bundles thirteen of the papers presented at the graduate conference of PhDs in Logic III. These papers deal with a wide variety of topics, coming from subfields such as algebraic logic, set theory, and philosophical logic. All papers share the common goal of advancing the boundaries of research in logic and its applications, thus turning this volume into a unique overview of what's hot and upcoming in the field of logic.

Modal logic is a subject with ancient roots in the western logical tradition. Up until the last few generations, it was pursued mainly as a branch ofphilosophy. But in recent years, the subject has taken new directions with connections to topics in computer science and mathematics.This volume is the proceedings of the conference of record in its fi eld, Advances in Modal Logic. Its contributions are state-of-the-art papers. Thetopics include decidability and complexity results for specifi c modal logics, proof theory of modal logic, logics for reasoning about time and space,provability logic, dynamic epistemic logic, and the logic of evidence.

Mathematics originates with intuition. But intuition alone can only go so far and formalism develops to handle the more difficult problems. Formalism, however, has its inherent dangers. There are three types of formalism. Type Iformalism, exemplified in the work of Euler, is basically heuristic reasoning, the use of familiar reasoning in areas where the reasoning might not or ought not apply. The results include startling successes, and also theorems admitting exceptions. Type II formalism, associated with names like Bolzano, Cauchy, and Weierstrass, attempts to clarify the situation by means of precise definitions of the terms used. Type III formalism, the axiomatic method, leaves the fundamental concepts undefined, but offers precise rules for their use. Such precision deserts intuition and one pays the price. Most dramatically, the formal definitions of Type II formalism allow for the construction of monsters -bizarre counterexamples that exhibit behaviour inconsistent with existing intuition. The initially repellant nature of these "monsters" leads to dissatisfaction that is only dispelled by their growing familiarity and applicability. The present book covers the history of formalism in mathematics from Euclid through the 20th century. It should be of interest to advancedmathematics students, anyone who teaches mathematics, and anyone generally interested in the foundation of mathematics.

Originating as an attempt to provide solid logical foundations for fuzzy set theory, and motivated also by philosophical and computational problems of vagueness and imprecision, Mathematical Fuzzy Logic (MFL) has become a significant subfield of mathematical logic. Research in this area focuseson many-valued logics with linearly ordered truth values and has yielded elegant and deep mathematical theories and challenging problems, thus continuing to attract an ever increasing number of researchers.This two-volume handbook provides an up-to-date systematic presentation of the best-developed areas of MFL. Its intended audience is researchers working on MFL or related fields, who may use the text as a reference book, and anyone looking for a comprehensive introduction to MFL. Despite being located in the realm of pure mathematical logic, this handbook will also be useful for readers interested in logical foundations of fuzzy set theory or in a mathematical apparatus suitable for dealing with some philosophical and linguistic issues related to vagueness.The first volume contains a gentle introduction to MFL, a presentation of an abstract algebraic framework for MFL, chapters on proof theory and algebraic semantics of fuzzy logics, and, finally, an algebraic study of Hájek's logic BL.The second volume is devoted to ¿ukasiewicz logic and MValgebras, Gödel-Dummett logic and its variants, fuzzy logics in expanded propositional languages, studies of functional representations for fuzzy logics and their free algebras,computational complexity of propositional logics, and arithmetical complexity of first-order logics.

Originating as an attempt to provide solid logical foundations for fuzzy set theory, and motivated also by philosophical and computational problems of vagueness and imprecision, Mathematical Fuzzy Logic (MFL) has become a significant subfield of mathematical logic. Research in this area focuses on many-valued logics with linearly ordered truth values and has yielded elegant and deep mathematical theories and challenging problems, thus continuing to attract an ever increasing number of researchers.This two-volume handbook provides an up-to-date systematic presentation of the best-developed areas of MFL. Its intended audience is researchers working on MFL or related fields, who may use the text as a reference book, and anyone looking for a comprehensive introduction to MFL. Despite being located in the realm of pure mathematical logic, this handbook will also be useful for readers interested in logical foundations of fuzzy set theory or in a mathematical apparatus suitable for dealing with some philosophical and linguistic issues related to vagueness.The first volume contains a gentle introduction to MFL, a presentation of an abstract algebraic framework for MFL, chapters on proof theory and algebraic semantics of fuzzy logics, and, fi nally, an algebraic study of Hájek's logic BL. The second volume is devoted to ¿ukasiewicz logic and MValgebras, Gödel-Dummett logic and its variants, fuzzy logics in expanded propositional languages, studies of functional representations for fuzzy logics and their free algebras, computational complexity of propositional logics, and arithmetical complexity of first-order logics.

Philosophy and sociology of science aim at understanding the workings of scientific endeavour. Despite their different emphasis and methodology,they deal with the same subject matter; and yet, they seem to be worlds apart. In the course of the last few decades, steps have been taken towardsa (partial) reconciliation. The conference FotFS VII was part of this process, bringing sociological aspects into philosophy of science and philosophicalaspects into sociology of science. Since the FotFS conference series focusses on the formal sciences, the conference had a certain, but non-exclusive focuson the role of mathematics as one of the sciences covered by philosophy and sociology. FotFS VII was organized by the research network PhiMSAMP Philosophy of Mathematics:Sociological Aspects and Mathematical Practice. A volume documenting the work of this network has already been published in the series Texts in Philosophy and covers specific questions linking philosophical issues in mathematics to mathematical practice. The present volume provides the generalmethodological background for the work done by the PhiMSAMP network. It contains fully refereed versions of papers presented at the seventhinstallment of the conference series Foundations of the Formal Sciences (FotFS).

This volume is dedicated to a distinguished logician, Walter Alexandre Carnielli, celebrating his 60th birthday.The honoree's contributions to contemporary logic range from innovative tableaux techniques, to the development of the foundations and applications of paraconsistent logics, to the invention of creative semantical apparatus.In this book the reader will find brilliant contributions by prominent logicians and philosophers that discourse over a broad repertoire of topics related to the outstanding work of Walter Carnielli.

Larry Powers' Non-contradiction is an engaging, innovative,and delightful book. It re-tells the story of Greek philosophyfrom the novel starting point that Parmenides, Plato andAristotle took their primary philosophical task to be thedefence of the principle of non-contradiction.In the course of nine chapters devoted to ancient Westernphilosophy we see Powers as the ally of the Greeks, and weget the impression that he sees their project even moreclearly than they did.The book also includes a substantial chapter that takes onthe challenge of explaining the importance of Hegel to modernanalytical philosophers, and another chapter that comparesour logical ways with those of ancient Indian and Chinesethinkers, such as Dignaga and Chuang Tsu.Interwoven with Powers' exposition of the history of philosophyis a primer on his own meta-philosophy, a theory devoted to theanalysis and resolution of philosophical disagreements.Especially those with an interest in logic and metaphysics willwant to study this book: throughout, the argumentation isoriginal, insightful, provocative, persistent and stimulating.

Hilbert and Bernays' 'Grundlagen der Mathematik'appeared in two volumes in 1934 and 1939, asecond edition in 1968 and 1970. It offers afoundation for proof theory and is a major source onDavid Hilbert's formalist programme, Paul Bernays'philosophy, the epsilon operator, and much more.It has been a profound infl uence on mathematics,logic, and philosophy, and it covers formal groundand philosophical perspectives beyond the scope ofWhitehead and Russell's 'Principia Mathematica' andFrege's 'Grundlagen der Arithmetik'.This book is not only essential to any scholar of thehistory and philosophy of modern mathematics, but italso contains formal research - on the epsilon and iotaoperators - of contemporary relevance to logicians,mathematicians and computer science. For us, it isone of the most fascinating books ever written.This a bilingual German-English, commented editionof the 'Grundlagen'. It is the fi rst English publicationof these texts and shows the facsimile of the Germanoriginal text on the left-hand side of a double page,and its English translation on the right-hand side.In addition to extensive comments on the historyand the interpretation of the text's mathematicaland philosophical content, there are also carefulannotations regarding the differences between thetwo German editions (1934/39,1968/1970) of thistwo volume monograph.

Vague language and corresponding models of inference and information processing is an important and challenging topic as witnessed by a number of recent monographs and collections of essays devoted to the topic.This volume collects fifteen papers, the majority of which originated with talks presented at the conference "Logical Models of Reasoning with VagueInformation (LoMoReVI)", September 14-17, 2009, in ¿ejkovice, that initiated a EUROCORES/LogICCC project with the same title.At least two features set the current volume apart from other texts: first, the interdisciplinary nature of the topic is nicely reflected by the wide range ofinterests of the authors, who include philosophers, linguists, logicians, as well as mathematicians and computer scientists. Secondly, all the papers areaccompanied by comments written by other authors and a few outside experts. These comments and corresponding replies by the authors document the very lively ongoing debate on adequate models of vague language.

Hao Wang (1921-1995) was a prolific researcher andwriter in mathematical logic, computer science, andphilosophy. He is known for the close relation hedeveloped with Kurt G├╢del during the last decade of thelatter''s life and the two books about G├╢del that hepublished after G├╢del''s death. This volume of essayscovers to some extent each of these fields of Wang''sactivity but with greatest emphasis on philosophy.Wang spent the first twenty-five years of his life in Chinaand continued to identify himself as Chinese, and in lateryears he returned to China several times. The volumeadds to the picture of the Chinese side of Wang and hisengagement with the intellectual life of his own countryduring a turbulent period. Wang''s writings in Chineseare surveyed, and two translations are included of shortessays on two Chinese scholars, his teacher Jin Yuelinand his friend from student days He Zhaowu, as well asa short memoir of Wang by He, written shortly afterWang''s death.Another writing of Wang published for the first time isan edition with introduction of an exposition by Wang ofG├╢del''s views on sets and concepts. Essays on Wangand his work include a memoir of collaboration with himon G├╢del''s philosophy by Eckehart K├╢hler, an account oftwo classic contributions to computer science and logicby Martin Davis, and essays by Abner Shimony on hisdistinctive view of the nature and method of philosophyand by Juliet Floyd on his reflections on the philosophyof Wittgenstein, who fascinated Wang partly because ofthe contrast between his views and G├╢del''s.

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.

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).