scholarly journals A logic with conditional probability operators

2010 ◽  
Vol 87 (101) ◽  
pp. 85-96 ◽  
Author(s):  
Dragan Doder ◽  
Bojan Marinkovic ◽  
Petar Maksimovic ◽  
Aleksandar Perovic
Keyword(s):  
Conditional Probability ◽  
Decision Procedure ◽  
Conditional Probabilities ◽  
Linear Combinations ◽  
Complete Axiomatization ◽  
Probability Operators

We present a sound and strongly complete axiomatization of a reasoning about linear combinations of conditional probabilities, including comparative statements. The developed logic is decidable, with a PSPACE containment for the decision procedure.

scholarly journals A logic with higher order conditional probabilities

2007 ◽  
pp. 141-154 ◽  
Author(s):  
Zoran Ognjanovic ◽  
Nebojsa Ikodinovic
Keyword(s):  
Conditional Probability ◽  
Probability Space ◽  
Possible Worlds ◽  
Axiomatic System ◽  
Probability Logic ◽  
Conditional Probabilities ◽  
Unconditional Probability ◽  
Possible World ◽  
Intended Meaning ◽  
Probability Operators

We investigate probability logic with the conditional probability operators This logic, denoted LCP, allows making statements such as: P?s?, CP?s(? | ?) CP?0(? | ?) with the intended meaning "the probability of ? is at least s" "the conditional probability of ? given ? is at least s", "the conditional probability of ? given ? at most 0". A possible-world approach is proposed to give semantics to such formulas. Every world of a given set of worlds is equipped with a probability space and conditional probability is derived in the usual way: P(? | ?) = P(?^?)/P(?), P(?) > 0, by the (unconditional) probability measure that is defined on an algebra of subsets of possible worlds. Infinitary axiomatic system for our logic which is sound and complete with respect to the mentioned class of models is given. Decidability of the presented logic is proved.

The dependence of the majority voting decision-making probabilities on a multi-expert binary system experts number

2020 ◽  
pp. 7-14
Author(s):  
E. D. Avedyan ◽  
Le Thi Trang Linh
Keyword(s):  
Decision Making ◽  
Binary System ◽  
Conditional Probability ◽  
Majority Voting ◽  
Correct Solution ◽  
Conditional Probabilities ◽  
Analytical Results ◽  
Independent Expert ◽  
Mutually Independent

The article presents the analytical results of the decision-making by the majority voting algorithm (MVA). Particular attention is paid to the case of an even number of experts. The conditional probabilities of the MVA for two hypotheses are given for an even number of experts and their properties are investigated depending on the conditional probability of decision-making by independent experts of equal qualifications and on their number. An approach to calculating the probabilities of the correct solution of the MVA with unequal values of the conditional probabilities of accepting hypotheses of each statistically mutually independent expert is proposed. The findings are illustrated by numerical and graphical calculations.

scholarly journals NONCONGLOMERABILITY FOR COUNTABLY ADDITIVE MEASURES THAT ARE NOT κ-ADDITIVE

2016 ◽  
Vol 10 (2) ◽  
pp. 284-300 ◽  
Author(s):  
MARK J. SCHERVISH ◽  
TEDDY SEIDENFELD ◽  
JOSEPH B. KADANE
Keyword(s):  
Conditional Probability ◽  
Inaccessible Cardinal ◽  
Conditional Probabilities ◽  
Uncountable Cardinal ◽  
Additive Probability ◽  
De Finetti ◽  
Additive Measures

AbstractLet κ be an uncountable cardinal. Using the theory of conditional probability associated with de Finetti (1974) and Dubins (1975), subject to several structural assumptions for creating sufficiently many measurable sets, and assuming that κ is not a weakly inaccessible cardinal, we show that each probability that is not κ-additive has conditional probabilities that fail to be conglomerable in a partition of cardinality no greater than κ. This generalizes a result of Schervish, Seidenfeld, & Kadane (1984), which established that each finite but not countably additive probability has conditional probabilities that fail to be conglomerable in some countable partition.

Conditional Probability

2017 ◽  
Author(s):  
Kenny Easwaran
Keyword(s):  
Conditional Probability ◽  
Conditional Probabilities ◽  
Unconditional Probability

Conditional probability has been put to many uses in philosophy, and several proposals have been made regarding its relation to unconditional probability, especially in cases involving infinitely many alternatives that may have probability 0. This chapter briefly summarizes some of the literature connecting conditional probabilities to probabilities of conditionals and to Humphreys' Paradox for chances, and then investigates in greater depth the issues around probability 0. Approaches due to Popper, Rényi, and Kolmogorov are considered. Some of the limitations and alternative formulations of each are discussed, in particular the issues arising around the property of “conglomerability” and the idea that conditional probabilities may depend on a conditioning algebra rather than just an event.

scholarly journals Disintegration and Bayesian inversion via string diagrams

2019 ◽  
Vol 29 (7) ◽  
pp. 938-971 ◽  
Author(s):  
Kenta Cho ◽  
Bart Jacobs
Keyword(s):  
Probability Theory ◽  
Conditional Probability ◽  
Opposite Direction ◽  
Bayesian Inversion ◽  
Conditional Probabilities ◽  
Discrete Probability ◽  
Joint State

AbstractThe notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These notions exist in the literature, in concrete situations, but are presented here in abstract graphical formulations. The resulting abstract descriptions are used for proving basic results in conditional probability theory. The existence of disintegration and Bayesian inversion is discussed for discrete probability, and also for measure-theoretic probability – via standard Borel spaces and via likelihoods. Finally, the usefulness of disintegration and Bayesian inversion is illustrated in several examples.

THREE-WAY GOVERNMENT DECISION ANALYSIS WITH DECISION-THEORETIC ROUGH SETS

2012 ◽  
Vol 20 (supp01) ◽  
pp. 119-132 ◽  
Author(s):  
DUN LIU ◽  
TIANRUI LI ◽  
DECUI LIANG
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Decision Procedure ◽  
Loss Functions ◽  
Conditional Probabilities ◽  
Bayesian Decision ◽  
Government Decision ◽  
Risk Investment ◽  
Negative Rule

By considering the risks in policy making procedure, a three-way decision approach based on the decision-theoretic rough set model is adopted to risk government decision-making. A three-way decision is made based on a pair of thresholds on conditional probabilities. A positive rule makes a decision of executing, a negative rule makes a decision of non-executing, and a boundary rule makes a decision of deferment. The loss functions are used to calculate the required two thresholds to describe the decision risk with the Bayesian decision procedure. A case study of government petroleum risk investment demonstrates the proposed method.

scholarly journals N-gram probability effects in a cloze task

2014 ◽  
Vol 9 (3) ◽  
pp. 437-472 ◽  
Author(s):  
Cyrus Shaoul ◽  
R. Harald Baayen ◽  
Chris F. Westbury
Keyword(s):  
Conditional Probability ◽  
Language Processing ◽  
Implicit Knowledge ◽  
Empirical Measure ◽  
Word Choice ◽  
Conditional Probabilities ◽  
Linguistic Context ◽  
Specific Context ◽  
Probabilistic Information ◽  
N Gram

What knowledge influences our choice of words when we write or speak? Predicting which word a person will produce next is not easy, even when the linguistic context is known. One task that has been used to assess context dependent word choice is the fill-in-the-blank task, also called the cloze task. The cloze probability of specific context is an empirical measure found by asking many people to fill in the blank. In this paper we harness the power of large corpora to look at the influence of corpus-derived probabilistic information from a word’s micro-context on word choice. We asked young adults to complete short phrases called n-grams with up to 20 responses per phrase. The probability of the responded word and the conditional probability of the response given the context were predictive of the frequency with which each response was produced. Furthermore the order in which the participants generated multiple completions of the same context was predicted by the conditional probability as well. These results suggest that word choice in cloze tasks taps into implicit knowledge of a person’s past experience with that word in various contexts. Furthermore, the importance of n-gram conditional probabilities in our analysis is further evidence of implicit knowledge about multi-word sequences and support theories of language processing that involve anticipating or predicting based on context.

scholarly journals The Challenge of Diagnostic Inferences From Implicit Measures: The Case of Non-Evaluative Influences in the Evaluative Priming Paradigm

2020 ◽  
Vol 38 (Supplement) ◽  
pp. s208-s222
Author(s):  
Christian Unkelbach ◽  
Klaus Fiedler
Keyword(s):  
Conditional Probability ◽  
Implicit Association Test ◽  
Diagnostic Tools ◽  
Implicit Association ◽  
Implicit Measures ◽  
Conditional Probabilities ◽  
Evaluative Priming ◽  
Causal Influence ◽  
Priming Paradigm ◽  
Prime Target

Implicit measures are diagnostic tools to assess attitudes and evaluations that people cannot or may not want to report. Diagnostic inferences from such tools are subject to asymmetries. We argue that (causal) conditional probabilities p(AM+|A+) of implicitly measured attitudes AM+ given the causal influence of existing attitudes A+ is typically higher than the reverse (diagnostic) conditional probability p(A+|AM+), due to non-evaluative influences on implicit measures. We substantiate this argument with evidence for non-evaluative influences on evaluative priming—specifically, similarity effects reflecting the higher similarity of positive than negative prime-target pairs; integrativity effects based on primes and targets’ potential to form meaningful semantic compounds; and congruity proportion effects that originate in individuals’ decisional strategies. We also cursorily discuss non-evaluative influences in the Implicit Association Test (IAT). These influences not only have implications for the evaluative priming paradigm in particular, but also highlight the intricacies of diagnostic inferences from implicit measures in general.

Towards a New Model for Causal Reasoning in Expert Systems

2017 ◽  
Vol 7 (1) ◽  
pp. 32-63 ◽  
Author(s):  
M. Keith Wright
Keyword(s):  
Expert Systems ◽  
Conditional Probability ◽  
Causal Reasoning ◽  
Causal Theory ◽  
Probability Judgment ◽  
Probability Assessment ◽  
Conditional Probabilities ◽  
Long Run ◽  
Causal Strength ◽  
As If

This paper presents ideas for improved conditional probability assessment and improved expert systems consultations. It cautions that knowledge engineers may sometimes be imprecise when capturing causal information from experts: their elicitation questions may not distinguish between causal and correlational expertise. This paper shows why and how such models cannot support normative inferencing over conditional probabilities as if they were all based on frequencies in the long run. In some cases, these probabilities are instead causal theory-based judgments, and therefore are not traditional conditional probabilities. This paper argues that these should be processed as if they were causal strength probabilities or causal propensity probabilities. This paper reviews the literature on causal and probability judgment, and then presents a probabilistic inferencing model that integrates theory-based causal probabilities with frequency-based conditional probabilities. The paper also proposes guidelines for elicitation questions that knowledge engineers may use to avoid conflating causal theory-based judgment with frequency based judgment.

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