Three-valued logic: computational problems 1. In a trivalent interpretation in which every sentence letter is #, what is the Łukasiewicz-value of the formula (P ^Q) → (R ^ S)? What is its Kleene-value? What is its supervaluational truth value? 2. Write out the complete three-valued Łukasiewicz truth-table for the formula (PQ)V(P →~Q). Then write out the complete three-valued Kleene truth-table for that same formula. (These tables should each have nine rows, since there are nine possible combinations of 1, 0, and # for the two sentence letters P and Q. 3. Is the formula P · →>> (PVQ) valid in…… (a)...Łukasiewicz's system? (b) ...Kleene's? (c) ...the logic of paradox? (d) ……the system of supervaluations? In each case, justify your answer: if the answer is yes, give a metalogic proof; if the answer is no, give a counterexample. 4. Do the formulas P and P Q in... →>> Qtogether semantically imply the formula (a) ...Łukasiewicz's system? (b) ... Kleene's? (c) ...the logic of paradox? (d) ...the system of supervaluations? Again, justify your answer in each case.

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