Probabilistic Logic in a Coherent Setting
“Probabilistic Logic in a Coherent Setting” by Giulianella Coletti, published by Springer Netherlands on October 31, 2002, is a softcover reprint of the original first edition, comprising 291 pages. This book presents a unique approach to probability theory, characterizing probability as a linear operator rather than a measure. It is based on the concept of coherence and offers a flexible framework for addressing partial probability assessments and conditional independence, diverging from traditional measure-theoretic methods.
Readers will find that the book provides a self-contained exploration of probabilistic logic, suitable for those familiar with basic propositional calculus, linear algebra, and analysis. It discusses how this coherent approach can unify various methods of uncertain reasoning, including fuzziness and possibility functions. The content aims to address inconsistencies related to logical dependence and extends to graphical models beyond typical Bayesian networks, making it relevant for those interested in the intersections of philosophy, logic, mathematics, and artificial intelligence.
Official synopsis Publisher
The approach to probability theory followed in this book (which differs radically from the usual one, based on a measure-theoretic framework) characterizes probability as a linear operator rather than as a measure, and is based on the concept of coherence, which can be framed in the most general view of conditional probability. It is a `flexible’ and unifying tool suited for handling, e.g., partial probability assessments (not requiring that the set of all possible `outcomes’ be endowed with a previously given algebraic structure, such as a Boolean algebra), and conditional independence, in a way that avoids all the inconsistencies related to logical dependence (so that a theory referring to graphical models more general than those usually considered in bayesian networks can be derived). Moreover, it is possible to encompass other approaches to uncertain reasoning, such as fuzziness, possibility functions, and default reasoning.
The book is kept self-contained, provided the reader is familiar with the elementary aspects of propositional calculus, linear algebra, and analysis.
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