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It interprets only if as expressing in the metalanguage that the sentences in the database represent the only knowledge that should be considered when drawing conclusions from the database. In first-order logic (FOL) with the standard semantics, the same English sentence would need to be represented, using if and only if , with only if ...
Venn diagram of (true part in red) In logic and mathematics, the logical biconditional, also known as material biconditional or equivalence or biimplication or bientailment, is the logical connective used to conjoin two statements and to form the statement "if and only if" (often abbreviated as "iff " [1]), where is known as the antecedent, and the consequent.
Also, the section "Distinction from 'if' and 'only if'" is valiant but ultimately unsuccessful. As proved by the comments above, the meanings of "if" and of "only if" in common English are inconsistent and malleable, so trying to use ordinary sentences to explain the mathematical meanings of those words is doomed from the start.
The first of these sentences is a basic zero conditional with both clauses in the present tense. The fourth is an example of the use of will in a condition clause [4] (for more such cases, see below). The use of verb tenses, moods and aspects in the parts of such sentences follows general principles, as described in Uses of English verb forms.
(5) "∀x(Fx)" is true if, and only if, for all objects x, "Fx" is true. (6) "∃x(Fx)" is true if, and only if, there is an object x for which "Fx" is true. These explain how the truth conditions of complex sentences (built up from connectives and quantifiers) can be reduced to the truth conditions of their constituents.
Only after Trump's hush-money sentencing can NJ officials move to revoke his liquor licenses. A revocation hearing is still pending, officials said.
Hunter, whose sentence ended in 2021, said he spent his first year at Red Onion in solitary confinement. The Virginia DOC told NBC News that it does not deploy solitary confinement but a program ...
A conditional sentence is a sentence in a natural language that expresses that one thing is contingent on another, e.g., "If it rains, the picnic will be cancelled." They are so called because the impact of the sentence’s main clause is conditional on a subordinate clause.