Sentence examples for a relation of logical from inspiring English sources

Let ⊨ be a relation of logical consequence, defined either semantically or proof-theoretically.

They are in a relation of logical dependence with the phenomena of which they form a part.

Pluralists do not need to hold that every conceivable precisification of the GTT defines a relation of logical consequence.

To a contemporary reader, this might sound like a relation of logical entailment, but Spinoza clearly understands it to be a causal relation (e.g., Ip16c, Ip28d).

To give just a few simple examples, suppose that I am directly aware of a red triangle in my visual field, and also aware of a relation of logical exclusion or incompatibility (or, if you like, non-correspondence) between the figure's being a red triangle and the proposition that it is green, that it is a circle, or that it has five sides.

Hence having its extension given by a precisification of the GTT is only a necessary condition on being a genuine relation of logical consequence (Beall & Restall 2006, 26 35).

A concept more general than validity is that of the relation of logical entailment or implication between a possibly infinite set X of sentences and a single sentence p that holds if and only if p is true in every model of X.

Carnap's logical probability generalized the metalinguistic relation of logical implication to a numerical function, c(h, e), that expresses the extent to which an evidence sentence e confirms a hypothesis h.

Quine's criterion (as he understood it) avoids this problem by focusing on the formal relation of logical entailment between sentences, a relation that is well understood.

Hence, as was to be desired, if the defined relation of logical

For such reasons, many have taken the relation of logical consequence to pair an arbitrary (possibly infinite) collection of premises with a single conclusion.