Probability Logic and F

1976 ◽  
Vol 43 (2) ◽  
pp. 254-265
Author(s):  
A. I. Dale
Keyword(s):  
Probability Logic

scholarly journals Probability logic: A model-theoretic perspective

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 $\mathcal{F}\mathcal{P}\mathcal{M}$.

scholarly journals On Basic Probability Logic Inequalities

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1409
Author(s):  
Marija Boričić Joksimović
Keyword(s):  
Probability Theory ◽  
Inference Rule ◽  
Modus Ponens ◽  
Probability Logic ◽  
Modus Tollens ◽  
Short Overview ◽  
Basic Probability ◽  
Probabilistic Version ◽  
Hypothetical Syllogism

We give some simple examples of applying some of the well-known elementary probability theory inequalities and properties in the field of logical argumentation. A probabilistic version of the hypothetical syllogism inference rule is as follows: if propositions A, B, C, A→B, and B→C have probabilities a, b, c, r, and s, respectively, then for probability p of A→C, we have f(a,b,c,r,s)≤p≤g(a,b,c,r,s), for some functions f and g of given parameters. In this paper, after a short overview of known rules related to conjunction and disjunction, we proposed some probabilized forms of the hypothetical syllogism inference rule, with the best possible bounds for the probability of conclusion, covering simultaneously the probabilistic versions of both modus ponens and modus tollens rules, as already considered by Suppes, Hailperin, and Wagner.

scholarly journals QUANTUM TEAM LOGIC AND BELL’S INEQUALITIES

2015 ◽  
Vol 8 (4) ◽  
pp. 722-742 ◽  
Author(s):  
TAPANI HYTTINEN ◽  
GIANLUCA PAOLINI ◽  
JOUKO VÄÄNÄNEN
Keyword(s):  
Quantum Mechanics ◽  
Completeness Theorem ◽  
Probability Logic ◽  
Bell’S Inequalities ◽  
Dependence Logic ◽  
Logical Approach ◽  
Team Semantics ◽  
Bell's Inequalities

AbstractA logical approach to Bell’s Inequalities of quantum mechanics has been introduced by Abramsky and Hardy (Abramsky & Hardy, 2012). We point out that the logical Bell’s Inequalities of Abramsky & Hardy (2012) are provable in the probability logic of Fagin, Halpern and Megiddo (Fagin et al., 1990). Since it is now considered empirically established that quantum mechanics violates Bell’s Inequalities, we introduce a modified probability logic, that we call quantum team logic, in which Bell’s Inequalities are not provable, and prove a Completeness theorem for this logic. For this end we generalise the team semantics of dependence logic (Väänänen, 2007) first to probabilistic team semantics, and then to what we call quantum team semantics.

Representation of symmetric probability models

1969 ◽  
Vol 34 (2) ◽  
pp. 183-193 ◽  
Author(s):  
Peter H. Krauss
Keyword(s):  
Mathematical Theory ◽  
Preceding Paper ◽  
Probability Logic ◽  
Probability Models ◽  
Additional Material ◽  
First Order ◽  
Order Probability ◽  
Joint Publication

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.

A first-order conditional probability logic

2011 ◽  
Vol 20 (1) ◽  
pp. 235-253 ◽  
Author(s):  
M. Milosevic ◽  
Z. Ognjanovic
Keyword(s):  
Conditional Probability ◽  
Probability Logic ◽  
First Order

Probability Logic

1968 ◽  
pp. 182-195
Author(s):  
Nicholas Rescher
Keyword(s):  
Probability Logic

Quantifying over events in probability logic: an introduction

2016 ◽  
Vol 27 (8) ◽  
pp. 1581-1600
Author(s):  
STANISLAV O. SPERANSKI
Keyword(s):  
Computational Complexity ◽  
Boolean Algebras ◽  
Probability Logic ◽  
Discrete Probability ◽  
Complexity Results ◽  
Probability Spaces

In this article we describe a bunch of probability logics with quantifiers over events, and develop primary techniques for proving computational complexity results (in terms of m-degrees) about these logics, mainly over discrete probability spaces. Also the article contains a comparison with some other probability logics and a discussion of interesting analogies with research in the metamathematics of Boolean algebras, demonstrating a number of attractive features and intuitive advantages of the present proposal.

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