Probabilistic Logic in a Coherent SettingThe 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. |
Contents
Events as Propositions | 17 |
Finitely Additive Probability | 25 |
Betting Interpretation of Coherence | 37 |
Coherent Extensions of Probability Assessments | 43 |
Random Quantities | 49 |
To Be or not To Be Compositional? | 57 |
Coherent Conditional Probability | 73 |
ZeroLayers | 99 |
Lower and Upper Conditional Probabilities | 127 |
Inference | 137 |
Stochastic Independence in a Coherent Setting 163 | 164 |
A Random Walk in the Midst of Paradigmatic | 191 |
Fuzzy Sets and Possibility as Coherent Conditional | 215 |
Coherent Conditional Probability and Default | 241 |
A Short Account of Decomposable Measures | 257 |
Bibliography | 271 |
Other editions - View all
Probabilistic Logic in a Coherent Setting Giulianella Coletti,R. Scozzafava No preview available - 2002 |
Common terms and phrases
additive agreeing algebra approach arbitrary assessment assignment assuming atoms belief called Chapter choice classic clearly coherent conditional probability concept concerning conclusion conditional events consider contained corresponding defined Definition denote dependent discussed distribution easily element entails equal equations essentially evaluation example exists expressed extension fact Finally Finetti finite framework function fuzzy given gives hand holds implies independence interpretation introduced latter likelihood logical looked lower means measure Moreover natural necessarily Notice obtained obviously operations particular partition positive possible prior prob probabilistic problem proof properties propositions prove random recall refer relations relative relevant Remark represented requirement resorting respect restriction result role rules satisfying sense situation solution stochastic subjective subset suitable T-norm Theorem theory tion trivially true unique unknowns updating usual zero-layer