Affiliations: Computer Engineering Program, Faculty of Engineering, Istanbul Aydin University, Istanbul, Turkey. [email protected]
Correspondence:
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Address for correspondence: Florya Yerle.skesi (Halit Ayd.n Yerle.skesi), Be.syol Mahallesi, Inonu Caddesi, No: 38 Sefakoy.Ku.cuk.cekmece / Istanbul, Turkey. First and foremost, I sincerely thank the anonymous reviewers for their useful comments and suggestions which have helped me improve the earlier drafts of the paper substantially. I also thank the FI guest editors, Dario Della Monica, Aniello Murano and Luigi Sauro for all the effort they put on the paper. This work was supported in part by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) in project number 389792660 (TRR 248, Center for Perspicuous Systems).
Abstract: This paper presents a general strategy, bringing together some major types of nonmonotonic reasoning under a monotonic bimodal setting. Such formalisms are also of interest to the fields of knowledge representation and declarative programming. We exemplify the methodology, capturing minimal model reasoning that underlies nonmonotonicity over S4F first, but then we also show how to apply the technique to other nonmonotonic logics respectively based on the modal logics KD45 and SW5. We naturally succeed it, by modifying only the axioms of the underlying modal logic and show that it successfully works. The last two formalisms are also known as autoepistemic logic (AEL) and its reflexive extension (RAEL) in the given order: AEL is an important form of nonmonotonic reasoning, introduced by Robert C. Moore in order to allow an agent to reason about his own knowledge. Equilibrium logic (EL) is a general-purpose nonmonotonic reasoning formalism, proposed more recently by David Pearce as a semantical framework for answer set programming (ASP). The latter is an efficient declarative problem solving approach with lots of applications to science and technology. Fariñas et al. have embedded EL (and so ASP) into a monotonic bimodal logic. We take this work as an initiative and successfully apply a similar methodology to closely aligned nonmonotonic modal logics. We finally discuss the potential capability to subsume the epistemic extensions of ASP within our unified paradigm.
Keywords: nonmonotonic reasoning, minimal model semantics, (autoepistemic) equilibrium logic, answer set programming, epistemic specifications, monotonic modal logic, Kripke model
