Modus ponens is a classically valid inference pattern. Its classical truth table shows that there is no case in which the premises are true and the conclusion is untrue. (Note the use of the word 'untrue' here rather than 'false.' In classical logic, the only value that is untrue is false, but that is not the case in multi-valued logic.)
Task: Draw complete truth tables for modus ponens for both Bochvar's and Kleene's versions of three-valued logic (in the slides, policy 1 and policy 2 respectively.) Then answer the following questions:
1. Do either of these systems preserve the validity of modus ponens as defined above?
2. What does your answer suggest about the relative desirability of these systems?