Some Remarks on Evaluations of the Primitive Logic
Hiroakira Ono · Nagoya Mathematical Journal · 1970
In [4], K. Ono introduced the notion of evaluations of the primitive logic LO and proved that any semi-evaluation E is an evaluation of LO if E satisfies the following conditions: (E1) p* → 0 = 0, (E2) p* → p* = 0, (E3) 0 → p* = p*, (E4) p* → (p* → q*) = p* → q*, (E5) p* → (q* → r*) = q* → (p* → r*), (E6) p* → q* = 0 implies (r* → p*) → (r* → q*) = 0, (E7) (x)p*(x) → p*(t) = 0 for any t, and (E8) if u* → p*(t) = 0 for any t, then u* → (x)p*(x) = 0.