Logichard
0:00.0

In a 3-valued Post logic with truth values V={0,1,2}V = \{0, 1, 2\}, we define the operations as follows:

  • Conjunction: xy=min(x,y)x \land y = \min(x, y)
  • Disjunction: xy=max(x,y)x \lor y = \max(x, y)
  • Negation: ¬x=2x\neg x = 2 - x
  • Cyclic shift: x=(x+1)(mod3)\vec{x} = (x + 1) \pmod 3

Given the truth assignments v(P)=1v(P) = 1, v(Q)=2v(Q) = 2, and v(R)=0v(R) = 0, evaluate the truth value of the formula: ϕ=(PQ)¬(QR)\phi = \vec{(P \land Q)} \lor \neg(Q \lor \vec{R})