Bridges from Classical to Nonmonotonic Logic

Author: David Makinson
Publisher: College Publications
ISBN: 1904987001
Release Date: 2005
Genre: Computers

Imagine a robot trying to size up a difficult situation, to find a way of responding. Its sensors receive streams of information from which it tries to reach judgements. If it relies on deduction alone, it will not get far, no matter how fast its inference engines; for even the most massive information is still typically incomplete: there are relevant issues that it does not resolve one way or the other. The robot, or human agent for that matter, needs to go beyond these limits. It needs to `go supraclassical', inferring more than is authorised by classical logic alone. But such inferences are inherently uncertain. They are also nonmonotonic, in the sense that the acquisition of further information, even when consistent with the existing stock, may lead us to abondon as well as add conclusions. Nonmonotonic logic is the study of such reasoning and has been the subject of intensive research for more than two decades. But for the newcomer it is still a disconcerting affair, lacking unity with many systems going in different directions. The purpose of this book is to take the mystery out of the subject, giving a clear overall picture of what is going on. It makes the essential ideas and main approaches to nonmonotonic logic accessible, and meaningful, to anyone with a few basic tools of discrete mathematics and a minimal background in classical propositional logic. It is written as a textbook, with detailed explanations, examples, comments, exercises and answers. Students and instructors alike will find it an invaluable guide.

The Many Valued and Nonmonotonic Turn in Logic

Author: Dov M. Gabbay
Publisher: Elsevier
ISBN: 008054939X
Release Date: 2007-08-13
Genre: Mathematics

The present volume of the Handbook of the History of Logic brings together two of the most important developments in 20th century non-classical logic. These are many-valuedness and non-monotonicity. On the one approach, in deference to vagueness, temporal or quantum indeterminacy or reference-failure, sentences that are classically non-bivalent are allowed as inputs and outputs to consequence relations. Many-valued, dialetheic, fuzzy and quantum logics are, among other things, principled attempts to regulate the flow-through of sentences that are neither true nor false. On the second, or non-monotonic, approach, constraints are placed on inputs (and sometimes on outputs) of a classical consequence relation, with a view to producing a notion of consequence that serves in a more realistic way the requirements of real-life inference. Many-valued logics produce an interesting problem. Non-bivalent inputs produce classically valid consequence statements, for any choice of outputs. A major task of many-valued logics of all stripes is to fashion an appropriately non-classical relation of consequence. The chief preoccupation of non-monotonic (and default) logicians is how to constrain inputs and outputs of the consequence relation. In what is called “left non-monotonicity , it is forbidden to add new sentences to the inputs of true consequence-statements. The restriction takes notice of the fact that new information will sometimes override an antecedently (and reasonably) derived consequence. In what is called “right non-monotonicity , limitations are imposed on outputs of the consequence relation. Most notably, perhaps, is the requirement that the rule of or-introduction not be given free sway on outputs. Also prominent is the effort of paraconsistent logicians, both preservationist and dialetheic, to limit the outputs of inconsistent inputs, which in classical contexts are wholly unconstrained. In some instances, our two themes coincide. Dialetheic logics are a case in point. Dialetheic logics allow certain selected sentences to have, as a third truth value, the classical values of truth and falsity together. So such logics also admit classically inconsistent inputs. A central task is to construct a right non-monotonic consequence relation that allows for these many-valued, and inconsistent, inputs. The Many Valued and Non-Monotonic Turn in Logic is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics, computer science, AI, linguistics, cognitive science, argumentation theory, and the history of ideas. Detailed and comprehensive chapters covering the entire range of modal logic. Contains the latest scholarly discoveries and interprative insights that answers many questions in the field of logic.

Handbook of Philosophical Logic

Author: D.M. Gabbay
Publisher: Springer Science & Business Media
ISBN: 9781402030925
Release Date: 2006-01-17
Genre: Philosophy

A useful reference work to both students and researchers in formal philosophy, language and logic. This second edition is intended to comprise some 18 volumes and provides in-depth coverage of major topics in philosophical logic and its applications in many cutting-edge fields relating to computer science, language, argumentation, and others.

Logics in Artificial Intelligence

Author: Michael Fisher
Publisher: Springer Science & Business Media
ISBN: 9783540396253
Release Date: 2006-09-13
Genre: Computers

Logics provide a formal basis, and key descriptive notation, for the study and dev- opment of applications and systems in Arti'cial Intelligence (AI). With the depth and maturity of formalisms, methodologies,and systems today, such logics are increasingly important. The European Conference on Logics in Arti'cial Intelligence (or Journees ́ Europeennes ́ sur la Logique en Intelligence Arti'cielle -- JELIA) began back in 1988, as a workshop, in response to the need for a European forum for the discussion of emerging work in this ?eld. Since then, JELIA has been organised biennially, with - glish as of'cial language, and with proceedings published in Springer's Lecture Notes in Arti'cial Intelligence. Previousmeetingstookplace in Roscoff,France(1988),Ams- ́ terdam,Netherlands(1990),Berlin,Germany(1992),York,UK (1994),Evora,Portugal (1996), Dagstuhl, Germany (1998), Malaga, ́ Spain (2000), Cosenza, Italy (2002), and Lisbon, Portugal (2004). The increasing interest in this forum, its international level with growing parti- pation from researchers outside Europe, and the overall technical quality, has turned JELIA into a major forum for the discussion of logic-based approaches to AI. JELIA 2006constitutedtheTenthInternationalConferenceonLogicsinArti'cial Intelligence, and was held in Liverpool (UK) in September 2006. As with previous JELIA conf- ences, the aim of JELIA 2006 was to bring together active researchers interested in all aspects concerning the use of logics in AI to discuss current research, results, problems and applications of both a theoretical and practical nature. We received a total of 96 submissions, comprising 77 regular papers and 19 tool - scriptions.

Logic Programming and Nonmonotonic Reasoning

Author: Pedro Cabalar
Publisher: Springer
ISBN: 9783642405648
Release Date: 2013-09-12
Genre: Computers

This volume contains the refereed proceedings of the 12th International Conference on Logic Programming and Nonmonotonic Reasoning, LPNMR 2013, held in September 2013 in Corunna, Spain. The 34 revised full papers (22 technical papers, 9 application description, and 3 system descriptions) and 19 short papers (11 technical papers, 3 application descriptions, and 5 system descriptions) presented together with 2 invited talks, were carefully reviewed and selected from 91 submissions. Being a forum for exchanging ideas on declarative logic programming, nonmonotonic reasoning, and knowledge representation, the conference aims to facilitate interactions between those researchers and practitioners interested in the design and implementation of logic-based programming languages and database systems, and those who work in the area of knowledge representation and nonmonotonic reasoning.

Towards Mathematical Philosophy

Author: David Makinson
Publisher: Springer Science & Business Media
ISBN: 9781402090844
Release Date: 2008-11-09
Genre: Mathematics

area and in applications to linguistics, formal epistemology, and the study of norms. The second contains papers on non-classical and many-valued logics, with an eye on applications in computer science and through it to engineering. The third concerns the logic of belief management,whichis likewise closely connected with recent work in computer science but also links directly with epistemology, the philosophy of science, the study of legal and other normative systems, and cognitive science. The grouping is of course rough, for there are contributions to the volume that lie astride a boundary; at least one of them is relevant, from a very abstract perspective, to all three areas. We say a few words about each of the individual chapters, to relate them to each other and the general outlook of the volume. Modal Logics The ?rst bundle of papers in this volume contains contribution to modal logic. Three of them examine general problems that arise for all kinds of modal logics. The ?rst paper is essentially semantical in its approach, the second proof-theoretic, the third semantical again: • Commutativity of quanti?ers in varying-domain Kripke models,by R. Goldblatt and I. Hodkinson, investigates the possibility of com- tation (i.e. reversing the order) for quanti?ers in ?rst-order modal logics interpreted over relational models with varying domains. The authors study a possible-worlds style structural model theory that does not v- idate commutation, but satis?es all the axioms originally presented by Kripke for his familiar semantics for ?rst-order modal logic.

The Many Sides of Logic

Author: Walter Carnielli
Publisher:
ISBN: STANFORD:36105215300687
Release Date: 2009-10
Genre: Computers

The Many Sides of Logic'' is a volume containing a selection of the papers delivered at three simultaneous events held between 11-17 May 2008 in Paraty, RJ, Brazil, continuing a tradition of three decades of Brazilian and Latin-American meetings and celebrating the 30th anniversary of an institution congenital with the mature interest for logic, epistemology and history of sciences in Brazil: CLE 30 - 30th Anniversary of the Centre for Logic, Epistemology and the History of Science at the State University of Campinas (UNICAMP) XV EBL -15th Brazilian Logic Conference XIV SLALM - 14th Latin-American Symposium on Mathematical Logic Several renowned logicians, philosophers and mathematicians gathered in colonial Paraty, a historic village on the Brazilian coast founded in the 17th Century and surrounded by the luscious Atlantic rain forest to deliver lectures and talks celebrating the many sides of logic: the philosophical, the mathematical, the computational, the historical, and the multiple facets therein. The topics of the joint conferences, well represented here, included philosophical and mathematical Logic and applications with emphasis on model theory and proof theory, set theory, non-classical logics and applications, history and philosophy of logic, philosophy of the formal sciences and issues on the foundations of mathematics. The events have been preceded by a Logic School planned for students and young researchers held at the UNICAMP campus in Campinas, SP.

Evolving Knowledge Bases

Author: João Alexandre Leite
Publisher:
ISBN: UCSD:31822033087941
Release Date: 2003
Genre: Electronic books

An Evolving Knowledge Base (EKB) is capable of self evolution by means of its internally specified behaviour. In this thesis the author incrementally specifies, semantically characterizes and illustrates with examples, the concepts and tools necessary to the development of EKBs.

Inductive Logic

Author: Dov M. Gabbay
Publisher: Elsevier
ISBN: 9780080931692
Release Date: 2011-05-27
Genre: Mathematics

This volume is number ten in the 11-volume Handbook of the History of Logic. While there are many examples were a science split from philosophy and became autonomous (such as physics with Newton and biology with Darwin), and while there are, perhaps, topics that are of exclusively philosophical interest, inductive logic — as this handbook attests — is a research field where philosophers and scientists fruitfully and constructively interact. This handbook covers the rich history of scientific turning points in Inductive Logic, including probability theory and decision theory. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration. • Chapter on the Port Royal contributions to probability theory and decision theory • Serves as a singular contribution to the intellectual history of the 20th century • Contains the latest scholarly discoveries and interpretative insights

Handbook of the History of Logic Inductive logic

Author: Dov M. Gabbay
Publisher: Elsevier
ISBN: 9780444529367
Release Date: 2004
Genre: Induction (Logic)

In designing the Handbook of the History of Logic, the Editors have taken the view that the history of logic holds more than an antiquarian interest, and that a knowledge of logic's rich and sophisticated development is, in various respects, relevant to the research programmes of the present day. Ancient logic is no exception. The present volume attests to the distant origins of some of modern logic's most important features, such as can be found in the claim by the authors of the chapter on Aristotle's early logic that, from its infancy, the theory of the syllogism is an example of an intuitionistic, non-monotonic, relevantly paraconsistent logic. Similarly, in addition to its comparative earliness, what is striking about the best of the Megarian and Stoic traditions is their sophistication and originality.