Abstract
In this paper, we contribute to a series of results on the family of many-valued modal logics which as been recently introduced by M. Fitting in [8, 9, 10, 12]. In this family, the underlying propositional logics employ finite Heyting algebras for the space of truth values and the monotonic modal logics correspond to possible-worlds models with many-valued accessibility relations. There exist also modal non-monotonic counterparts in the McDermott & Doyle fashion. In [10], M. Fitting provided a many-valued generalization of Moore's autoepistemic logic and proved that, for logics with linear truth spaces, the important theorem of G. Schwarz for the equivalence of K45 and autoepistemic logic from [31], extends to the many-valued case. Here, we define and investigate a many-valued generalization of Schwarz's reflexive autoepistemic logic from [28] with an intended interpretation of □ as 'true and known'. We prove several interesting properties of many-valued reflexive expansions and show that - under the same linearity restriction - Schwarz's relevant theorem extends also in the many-valued setting, i.e., our many-valued reflexive autoepistemic logic coincides with many-valued non-monotonic Sw5