Jeff Pelletier (Alberta)

MON FEB 19 — 15.00-17.00

Sala "Enzo Paci" — Direzione del Dipartimento (Via Festa del Perdono 7, Milano)

How to Make Some Many-Valued Logics be Useful

In 1976 Nuel Belnap published a (relatively) well-known paper “A Useful Four-Valued Logic: How a Computer Should Think” in which he argued for a four-valued logic that could accommodate knowledge bases that had been given conflicting data, or incomplete data, relevant to a query in some field of knowledge. More of the formal background was presented in Michael Dunn’s “Intuitive Semantics for First Degree Entailment” that same year. The logic became known as FDE. A serious problem with FDE (and some related logics) is that you can’t do any reasoning with them!! They do not contain a conditional connective that would allow for a normal modus ponens inference, nor from any other rule of inference that is equivalent to modus ponens, such as (unit) resolution and the like. One cannot do sustained reasoning of the “chaining one result with the result of a different inference” form. The present talk proposes a conditional connective for FDE that will work, and furthermore has interesting (and surprising) extensions to certain 3-valued logics, such as Lukasiewicz-3, Kleene-3, RM3, and LP (Priest’s “logic of paradox”).