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About 10,000 papers for “probability rules”

Probability Rules

Probability Involves Functions, Probability Rules · 2007

(1) The Addition Rule. For two events A 1 , A 2 , A 1 can occur with or without A 2 , and vice versa. Thus the probability that at least one of them will occur is the same as the probability that A 1 occurs, plus the probability that A 2 occurs, less the probability that neither occurs: 1 For continuous data, various simplifying assumptions are made, e.g., to define P for intervals only. The mathematics are then more straightforward, and the conclusions apply to events in this new space of discrete intervals. 1 Mar. 27 CS W4999 Probability Topics PfA 1 [ A 2 g = PfA 1 g + PfA 2 g \\Gamma PfA 1 " A 2 g<

Cited by 0

Inference rules for probability logic

Marija Boričić · Publications de l Institut Mathematique · 2016

Gentzen?s and Prawitz?s approach to deductive systems, and Carnap?s and Popper?s treatment of probability in logic were two fruitful ideas of logic in the mid-twentieth century. By combining these two concepts, the notion of sentence probability, and the deduction relation formalized by means of inference rules, we introduce a system of inference rules based on the traditional proof-theoretic principles enabling to work with each form of probabilized propositional formulae. Namely, for each propositional connective, we define at least one introduction and one elimination rule, over the formulae of the form A[a,b] with the intended meaning that ?the probability c of truthfulness of a sentence A belongs to the interval [a,b] ?[0,1]?. It is shown that our system is sound and complete with respect to the Carnap-Poper-type probability models.

Cited by 9Open access

Probability propagation rules for Aristotelian syllogisms

Niki Pfeifer, Giuseppe Sanfilippo · Annals of Pure and Applied Logic · 2023

We present a coherence-based probability semantics and probability propagation rules for (categorical) Aristotelian syllogisms. For framing the Aristotelian syllogisms as probabilistic inferences, we interpret basic syllogistic sentence types A, E, I, O by suitable precise and imprecise conditional probability assessments. Then, we define validity of probabilistic inferences and probabilistic notions of the existential import which is required, for the validity of the syllogisms. Based on a generalization of de Finetti's fundamental theorem to conditional probability, we investigate the coherent probability propagation rules of argument forms of the syllogistic Figures I, II, and III, respectively. These results allow to show, for all three figures, that each traditionally valid syllogism is also valid in our coherence-based probability semantics. Moreover, we interpret the basic syllogistic sentence types by suitable defaults and negated defaults. Thereby, we build a bridge from our probability semantics of Aristotelian syllogisms to nonmonotonic reasoning. Then we show that reductio by conversion does not work while reductio ad impossibile can be applied in our approach. Finally, we show how the proposed probability propagation rules can be used to analyze syllogisms involving generalized quantifiers (like Most).

Cited by 2Open access

Brief Communication: Probability and the Westgard Rules

Tomás A Carroll, Heather A Pinnick, Wallace E Carroll · 2002

Abstract. Shewhart introduced industry to the concept of three standard deviation (3S) limits for quality control and Levey, Jennings, Henry, and Westgard adapted this idea to clinical laboratory medicine. Westgard ultimately formulated a system of rules to enable clinical laboratory scientists to decide whether the tests they were doing were “in control ” and reportable, or “out of control. ” The present communication explains mathematically how Shewhart’s “beyond 3S ” (ie,>1 chance in 370) is an indication for corrective laboratory

Cited by 1

Probability sum rules and consistent quantum histories

Jordan, Thomas F., Chisolm, Eric D. · arXiv (Cornell University) · 2008

An example shows that weak decoherence is more restrictive than the minimal logical decoherence structure that allows probabilities to be used consistently for quantum histories. The probabilities in the sum rules that define minimal decoherence are all calculated by using a projection operator to describe each possibility for the state at each time. Weak decoherence requires more sum rules. They bring in additional variables, that require different measurements and a different way to calculate probabilities, and raise questions of operational meaning. The example shows that extending the linearly positive probability formula from weak to minimal decoherence gives probabilities that are different from those calculated in the usual way using the Born and von Neumann rules and a projection operator at each time.

Cited by 0Open access

Understanding Probability: Chance Rules in Everyday Life

Henk Tijms · 2004

In this fully revised second edition of Understanding Probability, the reader can learn about the world of probability in an informal way. The author demystifies the law of large numbers, betting systems, random walks, the bootstrap, rare events, the central limit theorem, the Bayesian approach and more. This second edition has wider coverage, more explanations and examples and exercises, and a new chapter introducing Markov chains, making it a great choice for a first probability course. But its easy-going style makes it just as valuable if you want to learn about the subject on your own, and high school algebra is really all the mathematical background you need.

Cited by 140

Scoring Rules and the Inevitability of Probability

D. V. Lindley · 1981

Abstract : Let a person express his uncertainty about an event E, conditional upon an event F, by a number x and let him be given, as a result, a score which depends on x and the truth or falsity of E when F is true. It is shown that if the scores are additive for different events and if the person chooses admissible values only, then there exists a known transform of the values x to values which are probabilities. In particular, it follows that values x derived by significance tests, confidence intervals or by the rules of fuzzy logic are inadmissible. Only probability is a sensible description of uncertainty.

Cited by 11