Sentence examples for probabilistic formula from inspiring English sources

Given a formula ϕ with nested probabilities, construct ϕ ′ by substituting a new atomic proposition B for a basic probabilistic formula P i ⋈α, that is subformula of another basic probabilistic formula P j ⋈′ α ′, with 1≤i,j≤N and ⋈,⋈′∈.

This leads to our probabilistic formula for the weighting function: w ij ( 2 ) = ∫ E min ( i, j ) E max ( i, j ) f E | z E i z ij d E i = Pr E min ( i, j ) < E i < E max ( i, j ) z ij (32).

We can then formulate the probabilistic formula as P≥0.5{ P(C(B n), T i) = True }

Essentially, this procedure draws samples until it can assert or reject a probabilistic formula with statistical guarantees on the error rates.

OSM is able to determine the number of simulation runs required to prove whether a stochastic model satisfies a probabilistic formula, P≥ θ where θ represents the threshold probability and ψ represents the property.

AI is based on probabilistic formulas, while blockchain is more deterministic in nature.

The resulting language can be viewed as the closure of probabilistic formulas with respect to Boolean and probabilistic operators.

This paper studies the generalized probabilistic satisfiability (GPSAT) problem, where the probabilistic satisfiability (PSAT) problem is extended by allowing Boolean combinations of probabilistic assertions and nested probabilistic formulas.

Its probabilistic semantics is similar to ours because the probabilistic formulas have truth value in specific states (worlds), but they introduce a probability distribution for each set of indistinguishable possible worlds (states).

To prove that, we depart from formulas (phi in mathcal {L}_{N}) without nesting, as it can be eliminated with a slight modification of Lemma 6: For every (phi in mathcal {L}_{N}), for a fixed (Nin mathbb {N}), there exists a θ∈L N in which all probabilistic formulas are not subformulas of another probabilistic formulas, such that ϕ is satisfiable if, and only if, θ is.

We can move to an even more expressive language by allowing probabilistic formulas to be nested; that is, by allowing a subformula of ϕ in P=α to be P=α ′.