Semantics for Default Reasoning

摘要

We present a bi-valued semantics for default logic appealing to maximal sets, instead of a fixed point of an operator as it is done by its creator Raymond Reiler. It has the advantage of precluding incoherent theories (theories with no extension), and it fixes many drawbacks of Reiter's original formalism, This approach is then generalized, using a many-valued logic (the. logic FOUR of Belnap) as the underlining semantics, to construct a paraconsistent and nonmonotonic logic. Besides, we introduce a new notation for defaults which represents them as formulae and not as (pseudo) inference rules. The resulting formalism is both simples and powerful.