The logic of lost Lingens (Q750408)

This paper presents a doxastic logic, LB, designed to treat problems involving identity substitution with respect to the subject of the belief operator (the believer). Such problems arise especially when there are multiple belief operators, and in the representation of situations like that of lost Lingens and other cases of belief requiring the believer's self-representation. Lingens is lost in the ultimate library where every fact is recorded and Lingens thus has access to every fact, including the fact that Lingens is lost in the ultimate library. Nevertheless, Lingens may not know or believe that he is lost in the library, because he may not believe that he is Lingens. In order to represent such personal self- representation (or its failure), LB contains a class of individual quasi- indexical terms which, unlike names, are supposed to carry no information. Substitution of identicals in belief contexts is restricted to cases where both terms are such quasi-indexicals. The system LB is defined first axiomatically and then semantically, with a possible-worlds type model structure. The calculus LB is proved sound and complete with respect to its semantics. The completeness proof follows the familiar Henkin-style method.