Sentence examples for logically entails from inspiring English sources
Theorem (Conditional Certainty for Logical Consequences) When \(A\) logically entails \(B\), \(p(B\mid A =1\).
All we need to do is consider a person who infers P from E where E logically entails P, but where the entailment is far too complex for the person to see or even understand.
This suggests a stronger requirement on a formal system of logic namely, that p be derivable from X by the system whenever X logically entails p. The usual systems of logic satisfy this requirement because, besides the completeness theorem, there is also a compactness theorem: A theory X has a model if every finite subset of X has a model.
It follows because, in classical first-order predicate logic, universal sentences have existential import: '∀x φ(x)' logically entails '∃x φ(x)'.
However, in order to work as an argument against increased legal immigration, Friedman required a further, false assumption: that legal residency logically entails eligibility for free money.
In particular, p is valid if the empty set, defined as having no members, logically entails p for this is just another way of saying that p is true in every model.
In deductive logic the syntactic structure of the sentences involved completely determines whether premises logically entail a conclusion.
He did not intend harm, nor did his statements logically entail harm; therefore, her sense of harm is on her.
In addition to defending our basic beliefs against objections, we frequently need to clarify what our basic beliefs mean or logically entail.
Early exponents of the view that observation reports provide an indubitably certain foundation for knowledge held that verifiability requires that a statement be logically entailed by some finite set of observation reports.
"I do not wonder that some commentators have considered this a matter of ultimate importance, although the breaking of the law -- if that is what happened -- does not logically entail a particular penalty such as impeachment.
