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Author: Lionel Daniel Publisher: ISBN: Category : Languages : en Pages : 52
Book Description
If we envisage delegating critical decisions to an autonomous computer, we should not only endow it with common sense, but also formally verify that such a machine is programmed to safely react in every situation, notably when the situation is depicted with uncertainty. In this thesis, I deem an uncertain situation to be a possibly inconsistent probabilistic propositional knowledge base, which is a possibly unsatisfiable multiset of constraints on a probability distribution over a propositional language, where each constraint can be given a reliability level. The main problem is to infer one probabilistic distribution that best represents the real world, with respect to a given knowledge base. The reactions of the computer, previously programmed then verified, will be determined by that distribution, which is the probabilistic model of the real world. J.B. Paris et al stated a set of seven commonsensical principles that characterises the inference from consistent knowledge bases. Following their approach, I suggest adhering to further principles intended to define common sense when reasoning from an inconsistent knowledge base. My contribution is thus the first principled framework of paraconsistent probabilistic reasoning that comprises not only an inference process, which coincides with J.B. Paris's one when dealing with consistent knowledge bases, but also several measures of dissimilarity, inconsistency, incoherence, and precision. Besides, I show that such an inference process is a solution to a problem originating from voting theory, namely reaching a consensus among conflicting opinions about a probability distribution; such a distribution can also represent a distribution of a financial investment. To conclude, this study enhances our understanding of common sense when dealing with inconsistencies; injecting common sense into decision systems should make them more trustworthy.
Author: Lionel Daniel Publisher: ISBN: Category : Languages : en Pages : 52
Book Description
If we envisage delegating critical decisions to an autonomous computer, we should not only endow it with common sense, but also formally verify that such a machine is programmed to safely react in every situation, notably when the situation is depicted with uncertainty. In this thesis, I deem an uncertain situation to be a possibly inconsistent probabilistic propositional knowledge base, which is a possibly unsatisfiable multiset of constraints on a probability distribution over a propositional language, where each constraint can be given a reliability level. The main problem is to infer one probabilistic distribution that best represents the real world, with respect to a given knowledge base. The reactions of the computer, previously programmed then verified, will be determined by that distribution, which is the probabilistic model of the real world. J.B. Paris et al stated a set of seven commonsensical principles that characterises the inference from consistent knowledge bases. Following their approach, I suggest adhering to further principles intended to define common sense when reasoning from an inconsistent knowledge base. My contribution is thus the first principled framework of paraconsistent probabilistic reasoning that comprises not only an inference process, which coincides with J.B. Paris's one when dealing with consistent knowledge bases, but also several measures of dissimilarity, inconsistency, incoherence, and precision. Besides, I show that such an inference process is a solution to a problem originating from voting theory, namely reaching a consensus among conflicting opinions about a probability distribution; such a distribution can also represent a distribution of a financial investment. To conclude, this study enhances our understanding of common sense when dealing with inconsistencies; injecting common sense into decision systems should make them more trustworthy.
Author: Egan J. Chernoff Publisher: Springer Science & Business Media ISBN: 940077155X Category : Education Languages : en Pages : 746
Book Description
This volume provides a necessary, current and extensive analysis of probabilistic thinking from a number of mathematicians, mathematics educators, and psychologists. The work of 58 contributing authors, investigating probabilistic thinking across the globe, is encapsulated in 6 prefaces, 29 chapters and 6 commentaries. Ultimately, the four main perspectives presented in this volume (Mathematics and Philosophy, Psychology, Stochastics and Mathematics Education) are designed to represent probabilistic thinking in a greater context.
Author: Raymond S. Nickerson Publisher: Psychology Press ISBN: 1135614628 Category : Business & Economics Languages : en Pages : 450
Book Description
This book presents an overview of the necessary information needed to make educational assumptions about the statistical or probable characteristics of a situation. The book can be used as a supplemental text in courses on probability, logic, statistics,
Author: Pei Wang Publisher: World Scientific ISBN: 9814440280 Category : Computers Languages : en Pages : 275
Book Description
This book provides a systematic and comprehensive description of Non-Axiomatic Logic, which is the result of the author''s research for about three decades.Non-Axiomatic Logic is designed to provide a uniform logical foundation for Artificial Intelligence, as well as an abstract description of the OC laws of thoughtOCO followed by the human mind. Different from OC mathematicalOCO logic, where the focus is the regularity required when demonstrating mathematical conclusions, Non-Axiomatic Logic is an attempt to return to the original aim of logic, that is, to formulate the regularity in actual human thinking. To achieve this goal, the logic is designed under the assumption that the system has insufficient knowledge and resources with respect to the problems to be solved, so that the OC logical conclusionsOCO are only valid with respect to the available knowledge and resources. Reasoning processes according to this logic covers cognitive functions like learning, planning, decision making, problem solving, This book is written for researchers and students in Artificial Intelligence and Cognitive Science, and can be used as a textbook for courses at graduate level, or upper-level undergraduate, on Non-Axiomatic Logic."
Author: Van-Nam Huynh Publisher: Springer Science & Business Media ISBN: 3540776648 Category : Mathematics Languages : en Pages : 381
Book Description
This book contains the proceedings of the first International Workshop on Interval/Probabilistic Uncertainty and Non Classical Logics, Ishikawa, Japan, March 25-28, 2008. The workshop brought together researchers working on interval and probabilistic uncertainty and on non-classical logics. It is hoped this workshop will lead to a boost in the much-needed collaboration between the uncertainty analysis and non-classical logic communities, and thus, to better processing of uncertainty.
Author: Zoran Ognjanović Publisher: Springer ISBN: 3319470124 Category : Mathematics Languages : en Pages : 224
Book Description
The aim of this book is to provide an introduction to probability logic-based formalization of uncertain reasoning. The authors' primary interest is mathematical techniques for infinitary probability logics used to obtain results about proof-theoretical and model-theoretical issues such as axiomatizations, completeness, compactness, and decidability, including solutions of some problems from the literature. An extensive bibliography is provided to point to related work, and this book may serve as a basis for further research projects, as a reference for researchers using probability logic, and also as a textbook for graduate courses in logic.
Author: Theodore Hailperin Publisher: Lehigh University Press ISBN: 9780934223454 Category : Mathematics Languages : en Pages : 316
Book Description
This study presents a logic in which probability values play a semantic role comparable to that of truth values in conventional logic. The difference comes in with the semantic definition of logical consequence. It will be of interest to logicians, both philosophical and mathematical, and to investigators making use of logical inference under uncertainty, such as in operations research, risk analysis, artificial intelligence, and expert systems.
Author: David A. Schum Publisher: Northwestern University Press ISBN: 9780810118218 Category : History Languages : en Pages : 572
Book Description
In this work Schum develops a general theory of evidence as it is understood and applied across a broad range of disciplines and practical undertakings. He include insights from law, philosophy, logic, probability, semiotics, artificial intelligence, psychology and history.
Author: Walter Carnielli Publisher: Springer ISBN: 3319332058 Category : Philosophy Languages : en Pages : 417
Book Description
This book is the first in the field of paraconsistency to offer a comprehensive overview of the subject, including connections to other logics and applications in information processing, linguistics, reasoning and argumentation, and philosophy of science. It is recommended reading for anyone interested in the question of reasoning and argumentation in the presence of contradictions, in semantics, in the paradoxes of set theory and in the puzzling properties of negation in logic programming. Paraconsistent logic comprises a major logical theory and offers the broadest possible perspective on the debate of negation in logic and philosophy. It is a powerful tool for reasoning under contradictoriness as it investigates logic systems in which contradictory information does not lead to arbitrary conclusions. Reasoning under contradictions constitutes one of most important and creative achievements in contemporary logic, with deep roots in philosophical questions involving negation and consistency This book offers an invaluable introduction to a topic of central importance in logic and philosophy. It discusses (i) the history of paraconsistent logic; (ii) language, negation, contradiction, consistency and inconsistency; (iii) logics of formal inconsistency (LFIs) and the main paraconsistent propositional systems; (iv) many-valued companions, possible-translations semantics and non-deterministic semantics; (v) paraconsistent modal logics; (vi) first-order paraconsistent logics; (vii) applications to information processing, databases and quantum computation; and (viii) applications to deontic paradoxes, connections to Eastern thought and to dialogical reasoning.
Author: World Congress on Paraconsistency Publisher: ISBN: 9781280215216 Category : Electronic book Languages : en Pages : 577
Book Description
This title represents an integrated discussion of all major topics in the area of paraconsistent logic, highlighting philosophical and historical aspects, major developments and real-world applications.
Author: Lionel Daniel
Author: Lionel Daniel
Author: Egan J. Chernoff
Author: Raymond S. Nickerson
Author: Pei Wang
Author: Van-Nam Huynh
Author: Zoran Ognjanović
Author: Theodore Hailperin
Author: David A. Schum
Author: Walter Carnielli
Author: World Congress on Paraconsistency