Abstract
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.
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Bibliography
P. Doherty. NM3–A Three-Valued Cumulative Non-Monotonic Formalism. In: Logics in AI, J. van Eijck(ed.), LNCS 478, Springer, Berlin, 196–211, 1991.
J. Engelfriet and J. Treur. A Temporal Model Theory for Default Logic. In: M. Clarke, R. Kruse and S. Moral (eds.), Proc. ECSQARU ‘83, Springer Verlag, 91–96, 1993.
M. Finger and D. Gabbay. Adding a temporal dimension to a logic system. Journal of Logic, Language and Computation, 1, 203–233, 1992.
D.M. Gabbay. Intuitionistic basis for non-monotonic logic. In: G. Goos and J. Hartmanis (eds.), 6th Conference on Automated Deduction, LNCS 138, Springer Verlag, 260–273, 1982.
Giunchiglia et al.,1993] E. Giunchiglia, P. Traverso and F. Giunchiglia. Multi-Context Systems as a Specification Framework for Complex Reasoning Systems. In: J. Treur and Th. Wetter (eds.), Formal Specification of Complex Reasoning Systems,Ellis Horwood, 45–72, 1993.
Halpern and Moses, 1984 ] J.Y. Halpern and Y.O. Moses. Towards a Theory of Knowledge and Ignorance. Proc. Workshop on Non-Monotonic Reasoning, 125–143, 1984.
van der Hoek et al.,1994a] W. van der Hoek, J.-J. Ch. Meyer and J. Treur. Temporal epistemic default logic. Journal of Logic, Language and Information,7, 341–367, 1998.
van der Hoek et al.,1994b] W. van der Hoek, J.-J. Ch. Meyer and J. Treur. Formal Semantics of Temporal Epistemic Reflection. Techn. Report, Free University Amsterdam, 1994.
J.-J.Ch. Meyer and W. van der Hoek. Non-Monotonic Reasoning by Monotonic Means. In: J. van Eijck (ed.), Logics in Al (Proc. JEL1A ‘80), LNCS 478, Springer, 399–411, 1991.
J.-J.Ch. Meyer and W. van der Hoek. A Modal Logic for Nonmonotonic Reasoning. In: W. van der Hoek, J.-J. Ch. Meyer, Y.H. Tan and C. Witteveen (eds.), Non-Monotonic Reasoning and Partial Semantics, Ellis Horwood, Chichester, 37–77, 1992.
J.-J. Ch. Meyer and W. van der Hoek. An Epistemic Logic for Defeasible Reasoning using a Meta-Level Architecture Metaphor. Techn. Report IR-329, Free University, Amsterdam, 1993.
J.-J. Ch. Meyer and W. van der Hoek. A default logic based on epistemic states. Fundamenta Informaticae, 23, 33–65, 1995.
J.-J. Ch. Meyer and W. van der Hoek. Counterfactual reasoning by (means of) defaults. In: Annals of Mathematics and Artificial Intelligence, 9, III-IV, 345–360, 1993.
J.-J. Ch. Meyer and W. van der Hoek. Epistemic Logic for AI and Computer Science, Cambridge Tracts in Theoretical Computer Science 41, Cambridge University Press, 1995.
R.C. Moore. Semantical Considerations on Nonmonotonic Logic. Artificial Intelligence, 25, 75–94, 1985.
Y. Shoham. Reasoning about Change. MIT Press, Cambridge, 1988.
Y.-H. Tan and J. Treur. A Bi-Modular Approach to Non-Monotonic Reasoning. In: Proc. WOCFAI’91, M. DeGlas and D. Gabbay, (eds.), Paris, 461–475, 1991.
J. Treat. Modelling nonclassical reasoning patterns by interacting reasoning modules. Report IR-236, Free University Amsterdam, 1990.
J. Treur. Interaction types and chemistry of generic task models. In: B. Gaines and M. Linter (eds), Proc. EKAW’91, GMD Studien 211, Bonn, 1992.
J. Treur. Towards dynamic and temporal semantics of meta-level architectures. Report IR-321, Free University Amsterdam, 1992. Also: Proc. META’94, 1994.
R.W. Weyhrauch. Prolegomena to a Theory of Mechanized Formal Reasoning. Artificial Intelligence J., 13, 133–170, 1980.
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van der Hoek, W., Meyer, JJ., Treur, J. (2001). Formal Semantics of Temporal Epistemic Reflection. In: Meyer, JJ.C., Treur, J. (eds) Dynamics and Management of Reasoning Processes. Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol 6. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1743-4_4
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