Representation of symmetric probability models

This paper is a sequel to the joint publication of Scott and Krauss [8] in which the first aspects of a mathematical theory are developed which might be called “First Order Probability Logic”. No attempt will be made to present this additional material in a self-contained form. We will use the same notation and terminology as introduced and explained in Scott and Krauss [8], and we will frequently refer to the theorems stated and proved in the preceding paper.

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Using First-Order Probability Logic for the Construction of Bayesian Networks

Uncertainty in Artificial Intelligence ◽

10.1016/b978-1-4832-1451-1.50031-7 ◽

1993 ◽

pp. 219-226 ◽

Cited By ~ 11

Author(s):

Fahiem Bacchus

Keyword(s):

Bayesian Networks ◽

Probability Logic ◽

First Order ◽

Order Probability

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Probability logic: A model-theoretic perspective

Journal of Logic and Computation ◽

10.1093/logcom/exaa066 ◽

2020 ◽

Author(s):

M Pourmahdian ◽

R Zoghifard

Keyword(s):

Characterization Theorem ◽

Expressive Power ◽

Probability Logic ◽

Theoretic Analysis ◽

Compactness Property ◽

Probability Models ◽

Finitely Additive Probability ◽

Additive Probability ◽

Basic Probability ◽

Abstract Logics

Abstract This paper provides some model-theoretic analysis for probability (modal) logic ($PL$). It is known that this logic does not enjoy the compactness property. However, by passing into the sublogic of $PL$, namely basic probability logic ($BPL$), it is shown that this logic satisfies the compactness property. Furthermore, by drawing some special attention to some essential model-theoretic properties of $PL$, a version of Lindström characterization theorem is investigated. In fact, it is verified that probability logic has the maximal expressive power among those abstract logics extending $PL$ and satisfying both the filtration and disjoint unions properties. Finally, by alternating the semantics to the finitely additive probability models ($\mathcal{F}\mathcal{P}\mathcal{M}$) and introducing positive sublogic of $PL$ including $BPL$, it is proved that this sublogic possesses the compactness property with respect to $\mathcal{F}\mathcal{P}\mathcal{M}$.

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A first-order conditional probability logic

Logic Journal of IGPL ◽

10.1093/jigpal/jzr033 ◽

2011 ◽

Vol 20 (1) ◽

pp. 235-253 ◽

Cited By ~ 11

Author(s):

M. Milosevic ◽

Z. Ognjanovic

Keyword(s):

Conditional Probability ◽

Probability Logic ◽

First Order

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Vibration Fatigue Reliability of Lead and Lead-Free Solder Joint by FORM/SORM

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.345-346.1393 ◽

2007 ◽

Vol 345-346 ◽

pp. 1393-1396

Author(s):

Ouk Sub Lee ◽

Man Jae Hur ◽

Yeon Chang Park ◽

Dong Hyeok Kim

Keyword(s):

Solder Joint ◽

Failure Probability ◽

Lead Free ◽

Lead Free Solder ◽

Fatigue Reliability ◽

Probability Models ◽

First Order ◽

Reliability Method ◽

Vibration Fatigue ◽

Free Solder

It is well-known that the vibration significantly affect the life of solder joint. In this paper, the effects of the vibration on the failure probability of the solder joint are studied by using the failure probability models such as the First Order Reliability Method (FORM) and the Second Order Reliability Method (SORM). The accuracies of the results are estimated by a help of the Monte Carlo Simulation (MCS). The reliability of the lead and the lead-free solder joint was also evaluated. The reliability of lead-free solder joint is found to be higher than that of lead solder joint.

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Intertextual Precision Expectations

Probability Designs ◽

10.1093/oso/9780190050955.003.0009 ◽

2019 ◽

pp. 107-116

Author(s):

Karin Kukkonen

Keyword(s):

Third Order ◽

Structural Patterns ◽

First Order ◽

The Third ◽

Order Probability

In the chapters that follow, the third-order probability design is developed. The third-order probability design revolves around how expectations about second- and first-order predictions are developed through structural patterns yielded by genre (III.1), textual gaps and shadow stories (III.2), and intertextual references to unfamiliar texts (III.3). The final chapter of the section, then, traces the tension between flexibility and constraint in probability designs.

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Many-valued logics of extended Gentzen style II

Journal of Symbolic Logic ◽

10.2307/2271438 ◽

1970 ◽

Vol 35 (4) ◽

pp. 493-528 ◽

Cited By ~ 8

Author(s):

Moto-o Takahashi

Keyword(s):

Topological Space ◽

Model Theory ◽

Natural Extension ◽

Preceding Paper ◽

Considerable Extent ◽

Continuous Logic ◽

First Order ◽

Natural Extensions ◽

Fundamental Theorems ◽

Order Continuous

In the monograph [1] of Chang and Keisler, a considerable extent of model theory of the first order continuous logic (that is, roughly speaking, many-valued logic with truth values from a topological space) is ingeniously developed without using any notion of provability.In this paper we shall define the notion of provability in continuous logic as well as the notion of matrix, which is a natural extension of one in finite-valued logic in [2], and develop the syntax and semantics of it mostly along the line in the preceding paper [2]. Fundamental theorems of model theory in continuous logic, which have been proved with purely model-theoretic proofs (i.e. those proofs which do not use any proof-theoretic notions) in [1], will be proved with proofs which are natural extensions of those in two-valued logic.

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