[1] MANY-VALUED EPISTEMIC STATES. AN APPLICATION TO A REFLECTIVE ARCHITECTURE: MILORD-II *† Lluís Godo 1‡ , Wiebe van der Hoek 2 , John-Jules Ch. Meyer 2 , Carles Sierra 1‡ 1 Institut d'Investigació en Intel . ligència Artificial, (IIIA) Spanish Council for Scientific Research, (CSIC) Camí de Sta. Bàrbara s/n, 17300 Blanes, Catalonia, Spain e-mails: {godo,sierra}@ceab.es 2 Department of Computer Science, Utrecht University P.O. BOX 80.089, 3508 TB Utrecht, The Netherlands e-mails: {jj,wiebe}@cs.ruu.nl ABSTRACT Halpern and Moses [Halpern & Moses, 84] define and characterize what a minimal epistemic state associated to a set of premises is, using the notions of stable set and S5- Kripke models. Based on such epistemic states, Halpern and Moses define an entailment relation with which one can infer what is known and, more importantly, what is unknown by an agent. In this paper we formulate an extension of these ideas to the many-valued case. As an application example we study the logical foundation of a core fragment of the MILORD II architecture [Sierra & Godo, 92,93], focusing in particular on giving a modal interpretation of MILORD II meta-predicates. This paper has to be understood as a preliminary report on the relationship between special meta-predicates in meta-level architectures for non-monotonic reasoning such as MILORD II or BMS [Tan & Treur, 91], [Tan, 92] and modal operators in non-monotonic epistemic logics. Keywords: Epistemic logic, Many-valued logic, Reflective architectures 1. INTRODUCTION The knowledge states of a rational and introspective agent are usually modelled as ‘stable sets’ of epistemic formulas. Epistemic formulas are formulas in a language with a standard pair of epistemic (modal) operators standing for knowledge and possibility. In [Halpern & Moses, 84], Halpern and Moses define and characterize what a minimal epistemic state associated to a set of premises is, using the notions of stable set and S5-Kripke models. Based on such epistemic states, Halpern and Moses define an entailment relation with which one can infer what is known and, more importantly, what is unknown by an agent. This entailment relation is obviously non- monotonic, and provides the link of this epistemic theory to logical meta-level architectures. Namely, the entailment relation can be used to derive ‘meta-knowledge’ about what is known and what is not from object formulas represented by non-modal formulas. Moreover, in [Meyer & van der Hoek, 93a, 93b], a default logic based on epistemic notions is introduced where the above mentioned meta-knowledge is used as input to derive default beliefs. All this has been used up to now in a classical two-valued framework. However, many times we want to model agent states coping with fuzzy knowledge, in the sense that an agent’s knowledge can incorporate propositions which can be assigned partial degrees of truth. To do this an extension of the formalism is necessary. First of all, we extend the epistemic framework to the many-valued case. Then we apply this extension to a meta-level architecture MILORD II based on many-valued logics. MILORD II is an architecture for Knowledge Base Systems (KBS) that combines reflection and modularization techniques, together with an approximate reasoning * Research supported by the ESPRIT III Basic Research Action nº 6156 DRUMS II ‡ Research also supported by the Spanish CICYT project ARREL TIC92-0579-c02-01 †Proofs are omitted: they can be found in [Godo et al, 1993].