Many-Vawed Modal Logics II

Article type: Research Article

Authors: Fitting, Melvin^{; *}

Affiliations: Dept. Mathematics and Computer Science, Lehman College (CUNY), Bronx, NY 10468, Depts. Computer Science, Philosophy, Mathematics, Graduate Center (CUNY), 33 West 42nd Street, NYC. NY 10036, E-mail: [email protected]

Note: [*] Research partly supported by NSF Grants CCR-8901489 and CCR-9104015.

Abstract: Suppose there are several experts, with some dominating others (expert A dominates expert B if B says something is true whenever A says it is). Suppose, further, that each of the experts has his or her own view of what is possible – in other words each of the experts has their own Kripke model in mind (subject, of course, to the dominance relation that may hold between experts). How will they assign truth values to sentences in a common modal language, and on what sentences will they agree? This problem can be reformulated as one about many-valued Kripke models, allowing many-valued accessibility relations. This is a natural generalization of conventional Kripke models that has only recently been looked at. The equivalence between the many-valued version and the multiple expert one will be formally established. Finally we will axiomatize many-valued modal logics, and sketch a proof of completeness.

DOI: 10.3233/FI-1992-171-205

Journal: Fundamenta Informaticae, vol. 17, no. 1-2, pp. 55-73, 1992