附註:Includes bibliographical references (pages 288-300) and index.
Verity sequential logic -- Indefinite descriptions -- Unspecified truth values. Don't-care logic -- Don't-care conditions in logic design -- Elimination. Linear programming -- Leibnitz's vision -- Jakob Bernoulli : probability logic via the fates of gamblers -- Degree of certainty of an argument -- On combining two or more arguments -- J.H. Lambert : probabilistic syllogisms -- Bayes, and a problem " ... no less important than curious" -- John Michell on the distribution of the fixed stars -- Probability in Bolzano's Wissenschaftslehre 1837 -- De Morgan : testimony and argument -- Probable inference via six problems -- George Boole : claims for a general method -- Examination of Boole's general method -- On combining 'evidence' -- Peirce and macColl : conditional probability symbolized -- Confirmation from Keynes to Carnap -- Reichenbach : probability as multi-valued logic -- Probabilistic inference revived -- Bounds on probability : early history -- Best possible probability bounds -- Transmission of uncertainties in inferences -- Nilsson's probabilistic logic -- Probability logic of Scott and Krauss (1966) -- What is a logic?-- Probability functions on sentential languages -- Probability logic : the finite case -- Probability logic : the potential infinite case -- Interval probability logic -- Decision procedure for interval logic -- Set-theoretic versus logic-theoretic probability -- Conjunction and the multiplication of probabilities -- Independence : logical and stochastic -- Logical consequence with probability conditionals -- Logical consequence featuring intervals -- Boole's challenge problem -- Suppositional logic -- Probability on conditional events -- Other writers on conditional events -- A theorem of Rényi's and extensions -- Linear programming in probability/statistics -- Circuit fault testing. Fault trees -- Network reliability.
摘要: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.
