Sentence examples for classical consequences from inspiring English sources

For example, in Moore's case, a set Δ is a stable expansion of a theory Γ just in case Δ is the set of classical consequences of the set Γ ∪ {¬Mp: p ∈ Δ} ∪ {Mp: p ∉ Δ}.

Let ⊢ be the classical consequence relation.

We shall use a classical consequence of Mawhin's continuation theorem [16], Theorem 7.2 to prove Lemma 2.1.

Whereas the classical consequence relation preserves truth in all logically possible worlds, nonmonotonic consequence relations preserve truth in all least abnormal worlds.

Then we say that A is a consequence of Σ iff A is a classical consequence of Σ′ for some maximally consistent subset Σ′.

The following reverse Hölder inequality is also a classical consequence that originated from the famous Gehring-Giaquinta-Modica lemma, also see [13].

Moreover, as we have seen, nonmonotonic consequence relations (especially the preferential ones) share a number of very significant formal properties with classical consequence, warranting the inclusion of them all in a larger family of logics.

Let ⊢C be the classical consequence (or derivability) relation and express the consistency of the set of formulas Γ such that if A and B then (A * B) where * is any two place logical connective.

Both Cautious Monotony and the stronger principle of Rational Monotony are special cases of Monotony, and are therefore not in the foreground as long as we restrict ourselves to the classical consequence relation ⊨ of CL.

Σ [⊢ A iff l = ∞, or l = n and for every covering of size n there is a j ∈ I such that Σj ⊢ A. If l = 1 or ∞ then the forcing relation coincides with classical consequence relation.

In this approach, the first level is represented by the components seismically damaged, whereas the following levels are treated through a classical consequence analysis, including propagation of multiple simultaneous and interacting chains of accidents.