On the logic of acceptance and rejection (Q1577347)

Different extensions of classical logical formalisms have been proposed to model human thought. A very well-known nonmonotonic formalism is autoepistemic logic (AEL), introduced by \textit{R.~C. Moore} [Artif. Intell. 25, 75-94 (1985; Zbl 0569.68079)]. The present paper introduces the ``logic of acceptance and rejection'' (AEL2), extending Moore's AEL by the concept of uncertainty. This means that an agent may neither believe nor disbelieve a piece of information, or believe and disbelief it. For this aim, classical propositional logic is augmented by two operators \(B\) and \(D\) to express believe and disbelieve. Certain consequence operators are introduced and stability of theories is discussed. Also, similarly to Moore's AEL, AEL2 is shown to have a possible-worlds semantics. The article is a short presentation of results achieved in the author's Ph.~D.~thesis.