Temporalized Epistemic Default Logic

The nonmonotonic logic Epistemic Default Logic (EDL) [Meyer and van der Hoek, 1993] is based on the metaphore of a meta-level architecture. It has already been established [Meyer and van der Hoek, 1993] how upward reflection can be formalized by a nonmonotonic entailment based on epistemic states, and the meta-level process by a (monotonic) epistemic logic. The meta-level reasoning at a given state can be viewed as the part of the reasoning pattern where it is determined what the candidates are for default assumptions to be made, depending on the knowledge and ignorance at that state. The outcome at the meta-level concerns default conclusions of the form Pφ, where φ is an object-level formula. In EDL, default conclusions are kept separate from the object level knowledge (they remain at the meta-level), by means of this explicit default operator P. If one wants to draw further conclusions from them using object level knowledge this should be done at the meta-level. Compared to a meta-level architecture, what is still missing in EDL is the step where the default assumptions are actually made, i.e., where such formulas φ are added to the object level knowledge. Here we actually ‘jump (down) to conclusions’. This is what should be achieved by the downward reflection step. In the current paper we introduce a formalization of this downward reflection step. Thus a formalization, called TED L, is obtained of the reasoning pattern as a whole.