PHI 112 SYMBOL LOGIC TEST
RECENTLY UPDATED
validity definition - ANSWER *A* is a validity iff *A* is true in every
interpretation (i.e. ⊨ *A*)
contradiction definition - ANSWER *A* is a contradiction iff *A* is false in
every interpretation (i.e. ⊨ ~*A*)
valid in FOL definition - ANSWER *A1, A2, . . , An* ∴ *C* is valid in FOL
iff there is no interpretation in which all the premises are true and the
conclusion is false (i.e. *A1, A2, . . , An* ⊨ *C*)
invalid in FOL definition - ANSWER *A1, A2, . . , An* ∴ *C* is invalid in
FOL iff there there is an interpretation in which all the premises are true and the
conclusion is false
equivalent definition - ANSWER Two FOL sentences *A* and *B* are
equivalent iff they are true in exactly the same interpretations as each other (i.e.
*A* ⊨ *B* and *B* ⊨ *A*)
jointly satisfiable definition - ANSWER The FOL sentences *A1, A2, . . , An*
are jointly satisfiable iff some interpretation makes all of them true
jointly unsatisfiable definition - ANSWER The FOL sentences *A1, A2, . . ,
An* are jointly unsatisfiable iff there is not an interpretation that makes all of
them true
To show *A* is not a validity: - ANSWER Find an interpretation where *A* is
false
