Sentence examples for material equivalence from inspiring English sources
That is, the connective of material equivalence divides sentences into two distinct collections.
Here again, Frege uses the identity sign to help state the material equivalence of two concepts.
The material equivalence of F and G does not imply the existence claim (D) as a matter of meaning, whatever notion of meaning is involved.
The other common boolean connectives '∧' (conjunction), '∨' (disjunction), and '↔' (material equivalence), the 'existential' quantifier '∃', and the possibility operator ◇ are all defined in the usual way.
Since the material equivalence of two concepts implies their equinumerosity (this was noted as Fact 1 in the subsection on Equinumerosity in the main part of the entry), it follows that Q ≈ R.
For example, note that the lemma only provides a (provable) material equivalence between D and A ⌈D⌉) (which states that both sides must have the same truth-value) and does not claim any sort of sameness of meaning.
McCall refers to a result by R. Meyer showing that the valid implications of CFL form a subset of the set of valid material equivalences and briefly discusses giving up the syntactic restriction to first-degree implication.
There are a number of reasons to conclude that, at least in general, Gödel sentences do not really say anything substantial about themselves (Milne 2007 is a careful analysis of such issues); for example, as was previously noted in the case of the Diagonalization Lemma, one is usually operating here with mere material equivalences.
Experimental investigations have been performed on the effects of flame holder geometry, material conductivity, equivalence ratio, and inlet Reynolds number on the combustor performance.
A key requirement for any reference material is the equivalence between the various units.
The dependence of velocity and pressure at the front of the detonation/shock wave on the thickness of the acoustically absorbing material and mixture composition (equivalence ratio) was presented.
