Sentence examples for classical consequence from inspiring English sources

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].

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.

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}.

For example we define classical propositional consequence by means of truth valuations, first-order consequence relation by means of structures, the intuitionistic consequence relation by means of Kripke models, etc.

Moreover, we can define both a classical, monotonic consequence relation for this class of models and a defeasible, nonmonotonic relation (in fact, the nonmonotonic consequence relation can be defined in a variety of ways).

Classical clinical consequences of vitamin D deficiency include proximal myopathy and myalgia, which may in part explain the increased risk of functional limitations: falling and fractures in elderly patients who are vitamin D deficient [ 13– 15].

The characterization of the (classical first-order) consequence relation given above was semantic, in that we described it in terms of the consequence operation Th ○ Mod which invokes the structures for the language and what is true in them.