Formal Semantics of Temporal Epistemic Reflection

Meta-level architectures often are used either to model dynamic control of the object level inferences, or to extend the inference relation of the object level. In [Treur, 1992] we introduced formal semantics for meta-level architectures of the first kind based on temporal models. It may be considered quite natural that for such a dynamic type of reasoning system the temporal element of the reasoning should be made explicit in the formal semantics. For the use of meta-level architectures to extend the object level inference relation the situation looks different. In principle one may work out formal semantics in terms of (the logic behind) this extended, non-classical inference relation; e.g., as in the literature for nonmonotonic logics. However, much discussion is possible about this case. Some papers argue that also in the case of a non-monotonic logic the semantics have to make the inherent temporal element explicit; approaches are described in, e.g., [Gabbay, 1982], [Engelfriet and Treur, 1993]. In the current paper we adopt this line.