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The two volumes in this advanced textbook present results, proof methods, and translations of motivational and philosophical considerations to formal constructions. In the associated Vol. I the author explains preferential structures and abstract size. In this Vol. II he presents chapters on theory revision and sums, defeasible inheritance theory, interpolation, neighbourhood semantics and deontic logic, abstract independence, and various aspects of nonmonotonic and other logics. In both volumes the text contains many exercises and some solutions, and the author limits the discussion of motivation and general context throughout, offering this only when it aids understanding of the formal material, in particular to illustrate the path from intuition to formalisation. Together these books are a suitable compendium for graduate students and researchers in the area of computer science and mathematical logic.
Nonmonotonic reasoning provides formal methods that enable intelligent systems to operate adequately when faced with incomplete or changing information. In particular, it provides rigorous mechanisms for taking back conclusions that, in the presence of new information, turn out to be wrong and for deriving new, alternative conclusions instead. Nonmonotonic reasoning methods provide rigor similar to that of classical reasoning; they form a base for validation and verification and therefore increase confidence in intelligent systems that work with incomplete and changing information. Following a brief introduction to the concepts of predicate logic that are needed in the subsequent chapters, this book presents an in depth treatment of default logic. Other subjects covered include the major approaches of autoepistemic logic and circumscription, belief revision and its relationship to nonmonotonic inference, and briefly, the stable and well-founded semantics of logic programs.
The two volumes in this advanced textbook present results, proof methods, and translations of motivational and philosophical considerations to formal constructions. In this Vol. I the author explains preferential structures and abstract size. In the associated Vol. II he presents chapters on theory revision and sums, defeasible inheritance theory, interpolation, neighbourhood semantics and deontic logic, abstract independence, and various aspects of nonmonotonic and other logics. In both volumes the text contains many exercises and some solutions, and the author limits the discussion of motivation and general context throughout, offering this only when it aids understanding of the formal material, in particular to illustrate the path from intuition to formalisation. Together these books are a suitable compendium for graduate students and researchers in the area of computer science and mathematical logic.
This volume contains the refereed proceedings of the 13th International Conference on Logic Programming and Nonmonotonic Reasoning, LPNMR 2015, held in September 2015 in Lexington, KY, USA. The 290long and 11 short papers presented together with 3 invited talks, the paper reporting on the Answer Set Programming competition, and four papers presented by LPNMR student attendees at the doctoral consortium were carefully reviewed and selected from 60 submissions. LPNMR is a forum for exchanging ideas on declarative logic programming, nonmonotonic reasoning, and knowledge representation. The aim of the LPNMR conferences is to facilitate interactions between researchers interested in the design and implementation of logic-based programming languages and database systems, and researchers who work in the areas of knowledge representation and nonmonotonic reasoning.
The two volumes in this advanced textbook present results, proof methods, and translations of motivational and philosophical considerations to formal constructions. In this Vol. I the author explains preferential structures and abstract size. In the associated Vol. II he presents chapters on theory revision and sums, defeasible inheritance theory, interpolation, neighbourhood semantics and deontic logic, abstract independence, and various aspects of nonmonotonic and other logics. In both volumes the text contains many exercises and some solutions, and the author limits the discussion of motivation and general context throughout, offering this only when it aids understanding of the formal material, in particular to illustrate the path from intuition to formalisation. Together these books are a suitable compendium for graduate students and researchers in the area of computer science and mathematical logic.
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.
This volume contains the proceedings of FORTE 2008, 28th IFIP WG6.1 - ternational Conference on Formal Techniques for Networked and Distributed Systems. FORTE 2008 was held at the Campus Innovation Center in Tokyo, Japan during June 10–13, 2008. FORTE denotes a series of international wo- ing conferences on formal description techniques applied to computer networks and distributed systems. The conference series started in 1981 under the name PSTV. In 1988 a second series under the name FORTE was set up. Both - ries were united to FORTE/PSTV in 1996. In 2001 the conference changed the name to its current form. Recent conferences of this long series were held in Berlin (2003), Madrid(2004), Taipei(2005), Paris(2006), and Tallinn(2007). As in the previous year, FORTE 2008 was collocated with TESTCOM/ FATES 2008: the 20th IFIP International Conference on Testing of Com- nicating Systems (TESTCOM) and the 8th International Workshop on Formal Approaches to Testing of Software (FATES). The co-location of FORTE and TESTCOM/FATES fostered the collaboration between their communities. The commonspiritofboth conferenceswasunderpinnedby jointopening andclosing sessions, invited talks, as well as joint social events.
Informatics and the Foundations of Legal Reasoning represents a close collaboration between a wide range of disciplines and countries. Fourteen papers, together with a long analytical introduction by the editors, were selected from the contributions of legal theorists, computer scientists, philosophers and logicians who were members of an International Working Group supported by the European Commission. The Group was mandated to work towards determining how far the law is amenable to formal modeling, and in what ways computers might assist legal thinking and practice. The book is the result of discussions held by the Group over two and half years. It will help students and researchers from different backgrounds to focus on a common set of topics of increasing general interest. It embodies the results of work in progress and suggests many issues for further discussion. A stimulating text for undergraduate and graduate courses in law, philosophy and computer science departments, as well as for those interested in the place of computers in legal practice, especially at the international level.
Conditional structures lie at the heart of the sciences, humanities, and everyday reasoning. This is why conditional logics – logics specifically designed to account for natural language conditionals – are an active, interdisciplinary area. Discussing a wide range of topics, this book gives a formal and a philosophical account of indicative and counterfactual conditionals in terms of Chellas-Segerberg semantics.
What Is Non Monotonic Logic A formal logic is said to be non-monotonic if its conclusion connection does not follow a monotonic pattern. In other words, the purpose of non-monotonic logics is to capture and represent defeasible inferences. This refers to a type of inference in which reasoners form tentative conclusions, which allows reasoners to retract their conclusion(s) based on future data. Non-monotonic logics are designed to do this.The vast majority of formal logics that have been examined have a monotonic entailment relation, which indicates that the addition of a formula to a theory does not result in the trimming of its set of conclusions. Intuitively, the concept of monotonicity suggests that acquiring new information does not have the potential to narrow the scope of what is already known. A monotonic logic is incapable of handling a variety of reasoning tasks, including reasoning by default, abductive reasoning, key approaches to reasoning about knowledge, and belief revision. How You Will Benefit (I) Insights, and validations about the following topics: Chapter 1: Non-monotonic logic Chapter 2: Abductive reasoning Chapter 3: Deductive reasoning Chapter 4: Inductive reasoning Chapter 5: Default logic Chapter 6: Belief revision Chapter 7: Defeasible reasoning Chapter 8: Defeasible logic Chapter 9: Abductive logic programming Chapter 10: Logic (II) Answering the public top questions about non monotonic logic. (III) Real world examples for the usage of non monotonic logic in many fields. (IV) 17 appendices to explain, briefly, 266 emerging technologies in each industry to have 360-degree full understanding of non monotonic logic' technologies. Who This Book Is For Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of non monotonic logic.