Probability Operators

2010 ◽  
Vol 5 (11) ◽  
pp. 916-937 ◽  
Author(s):  
Seth Yalcin
Keyword(s):  
Probability Operators

Some New Probability Operators

2020 ◽  
pp. 143-163
Author(s):  
Zoran Marković ◽  
Miodrag Rašković
Keyword(s):  
Probability Operators

scholarly journals Triangular Surface Patch Based on Bivariate Meyer-König-Zeller Operator

2019 ◽  
Vol 17 (1) ◽  
pp. 282-296 ◽  
Author(s):  
Guorong Zhou ◽  
Qing-Bo Cai
Keyword(s):  
Convex Hull ◽  
Curve Surface ◽  
Surface Modeling ◽  
Modeling Method ◽  
Basis Functions ◽  
Surface Patch ◽  
Affine Invariance ◽  
Triangular Domain ◽  
Probability Operators ◽  
The Relationship

Abstract Based on the relationship between probability operators and curve/surface modeling, a new kind of surface modeling method is introduced in this paper. According to a kind of bivariate Meyer-König-Zeller operator, we study the corresponding basis functions called triangular Meyer-König-Zeller basis functions which are defined over a triangular domain. The main properties of the basis functions are studied, which guarantee that the basis functions are suitable for surface modeling. Then, the corresponding triangular surface patch called a triangular Meyer-König-Zeller surface patch is constructed. We prove that the new surface patch has the important properties of surface modeling, such as affine invariance, convex hull property and so on. Finally, based on given control vertices, whose number is finite, a truncated triangular Meyer-König-Zeller surface and a redistributed triangular Meyer-König-Zeller surface are constructed and studied.

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.

scholarly journals Probabilistic language in indicative and counterfactual conditionals

2017 ◽  
Vol 27 ◽  
pp. 525
Author(s):  
Daniel Lassiter
Keyword(s):  
Structural Equation ◽  
Structural Equation Models ◽  
Compositional Semantics ◽  
Direct Role ◽  
Revision Procedure ◽  
Counterfactual Conditionals ◽  
Bayes Nets ◽  
Causal Bayes Nets ◽  
Probability Operators

This paper analyzes indicative and counterfactual conditionals that have in their consequents probability operators: probable, likely, more likely than not, 50% chance and so on. I provide and motivate a unified compositional semantics for both kinds of probabilistic conditionals using a Kratzerian syntax for conditionals and a representation of information based on Causal Bayes Nets. On this account, the only difference between probabilistic indicatives and counterfactuals lies in the distinction between conditioning and intervening. This proposal explains why causal (ir)relevance is crucial for probabilistic counterfactuals, and why it plays no direct role in probabilistic indicatives. I conclude with some complexities related to the treatment of backtracking counterfactuals and subtleties revealed by probabilistic language in the revision procedure used to create counterfactual scenarios. In particular, I argue that certain facts about the interaction between probability operators and counterfactuals motivate the use of Structural Equation Models (Pearl 2000) rather than the more general formalism of Causal Bayes Nets.

If-Clauses and Probability Operators

Topoi ◽  
2011 ◽  
Vol 30 (1) ◽  
pp. 17-29 ◽  
Author(s):  
Paul Égré ◽  
Mikaël Cozic
Keyword(s):  
Probability Operators
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