Sentence examples for the classical consequence from inspiring English sources

Let ⊢ be the classical consequence relation.

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

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.

In accord with a principle of least mutilation, Dummett (1975), Fine (1975) and Keefe (2000) adapt Van Fraassen's supervaluation semantics to the sorites paradox, and vagueness more generally, resulting in a non-bivalent logic that, initially at least, retains the classical consequence relation and classical laws whilst admitting truth-value gaps.

The classical consequence relation ⊢ (conceived of as a relation between two sentences rather than as a relation between a set of sentences, the premises, and a sentence, the conclusion) is non-ampliative in the sense that the conclusion of a classically valid argument does not convey information that goes beyond the information contained in the premise.

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.

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

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.

An extension of a default theory is a fixed point of a particular inferential process: an extension E must be a consistent theory (a consistent set closed under classical consequence) that contains all of the facts of the default theory T, and, in addition, for each normal default (p ⇒ q), if p belongs to E, and q is consistent with E, then q must belong to E also.