In logic a designated value is a valuation of sentences in the logic that is preserved by entailments. In other words, if we define a logic L=⟨P,F,⊢⟩ with atomic sentences in P and operations in F, then the entailment relation ⊢ takes (a set of) sentences to another (set of) sentence(s) in the language with the following condition: If the input sentences all have the designated value, then the output sentence will too. When the designated value isn’t “preserved” in this way, then the entailment relation doesn’t obtain between the sentences.
Designated Values
Designated Values
Designated Values
In logic a designated value is a valuation of sentences in the logic that is preserved by entailments. In other words, if we define a logic L=⟨P,F,⊢⟩ with atomic sentences in P and operations in F, then the entailment relation ⊢ takes (a set of) sentences to another (set of) sentence(s) in the language with the following condition: If the input sentences all have the designated value, then the output sentence will too. When the designated value isn’t “preserved” in this way, then the entailment relation doesn’t obtain between the sentences.