Abstract
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.
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