Discussion
Match each semantic notion with its definition.
List I
A. Valid
B. Satisfiable
C. Unsatisfiable
D. Entailed
List II
P. true in every model
Q. true in at least one model
R. true in no model
S. true in every model of the premises
Select the correct match.
Answer: B
All four notions are defined by quantifying over models in different ways, which is why they are so easily confused and so easily distinguished once that pattern is noticed. Entailment is validity relative to a set of premises, and validity is entailment from no premises at all, which connects the two ends of the list.
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