Propositional Logic Flashcards
(13 cards)
[[P]]
Semantics of P, given by assignment
Valid/Tautology
A proposition π such that all assignments make [[π]] T
Unsatisfiable/Contradiction
A proposition π such that all assignments make [[π]] F
Satisfiable
A proposition π such that at least one assignment makes [[π]] T
Invalid
A proposition π such that at least one assignment makes [[π]] F
Complete Set of Operators
Operators in terms of which we can define everything else (construct any truth table)
π β π
(π β§ π) β¨ (Β¬π β§ Β¬π)
π β π
Β¬π β¨ π
π β¨ (π β§ π )
(π β¨ π) β§ (π β¨ π )
π β¨ (π β§ π)
P
π β§ (π β¨ π)
P
Assumption Rule
Ξ β’ π
Modus Ponens
If we can prove π β π and π, then we can use that to
prove π
