# Probabilities on finite models

```@article{Fagin1976ProbabilitiesOF,
title={Probabilities on finite models},
author={Ronald Fagin},
journal={Journal of Symbolic Logic},
year={1976},
volume={41},
pages={50 - 58}
}```
• Ronald Fagin
• Published 1 March 1976
• Mathematics
• Journal of Symbolic Logic
Let be a finite set of (nonlogical) predicate symbols. By an -structure, we mean a relational structure appropriate for . Let be the set of all -structures with universe {1, …, n}. For each first-order -sentence σ (with equality), let μn(σ) be the fraction of members of for which σ is true. We show that μn(σ) always converges to 0 or 1 as n → ∞, and that the rate of convergence is geometrically fast. In fact, if T is a certain complete, consistent set of first-order -sentences introduced by H…
429 Citations
• J. Lynch
• Mathematics
Random Struct. Algorithms
• 1994
If the stationary distribution is the same as the for random graphs with edg probability n−α, then the expected waiting time unitl σ holds is either bounded above by a polynomial in n, or it grows faster than any polynomical.
We begin with a rather easy random model which illustrates many of the concepts we shall deal with. We call it the simple unary predicate with parameters n, p and denote it by SU(n, p). The model is
The strong convergence law for formulas is defined, which carries over the ideas of the strong 0-1 law to formulas with free variables, and roughly states that for each formula x, the fraction of tuples a in , which satisfy the formula ϕ(x), almost surely has a limit as n tends to infinity.
In the present paper the results concerning the asymptotic behaviour of the fraction of satisfiability of formulae of a many-sorted language of the first order predicates are obtained. Let k sorts of
• Computer Science
ArXiv
• 2022
A (strict) partial order is described on the equivalence classes of some inference frameworks that seem natural in the context of machine learning and artiﬁcial intelligence.
th For any sentence φ of any logic and any n > 0, one may define the n probability of φ to be the fraction of structure for the vocabulary of φ with universe {0,1,...,n-1} th which satisfy φ. The the

## References

SHOWING 1-10 OF 10 REFERENCES

~0. Introduction. The idea of treating probability as a real valued function defined on sentences is an old one (see ['6] and [7], where other references can be found). Carnap's at tempt to set up a
• F. Harary
• Mathematics
Journal of Symbolic Logic
• 1958
The asymptotic results which are most useful here are either contained in, or are straight-forward extensions of, the formulas presented in Ford and Uhlenbeck [3], which in turn are based on unpublished work of G. Polya.
A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics.
Thank you for reading an introduction to probability theory and its applications vol 2. As you may know, people have look numerous times for their favorite novels like this an introduction to
Logical Foundations of ProbabilityBy Rudolf Carnap. Pp. xvii + 607. (London: Routledge and Kegan Paul, Ltd., 1951.) 42s. net.

• 1973