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

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

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