Abstract
In this paper we discuss reasoning about reasoning in a multiple agent scenario. We consider agents that are perfect reasoners, loyal, and that can take advantage of both the knowledge and ignorance of other agents. The knowledge representation formalism we use is (full) first order predicate calculus, where different agents are represented by different theories, and reasoning about reasoning is realized via a meta-level representation of knowledge and reasoning. The framework we provide is pretty general: we illustrate it by showing a machine checked solution to the three wisemen puzzle. The agents' knowledge is organized into units: the agent's own knowledge about the world and its knowledge about other agents are units containing object-level knowledge; a unit containing meta-level knowledge embodies the reasoning about reasoning and realizes the link among units. In the paper we illustrate the meta-level architecture we propose for problem solving in a multi-agent scenario; we discuss our approach in relation to the modal one and we compare it with other meta-level architectures based on logic. Finally, we look at a class of applications that can be effectively modeled by exploiting the meta-level approach to reasoning about knowledge and reasoning.
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References
R.W. Weyhrauch, “An example of FOL using meta-theory: Formalizing reasoning systems and introducing derived inference rules,” Proc. of CADE 82, edited by D.W. Loveland, LCNS 138, Springer Verlag: 1982, pp. 151–158.
R.W. Weyhrauch, “Prolegomena to a theory of mechanized formal reasoning”, Artificial Intelligence, vol. 13(1), pp. 133–170, 1980.
L. Aiello, D. Nardi, and M. Schaerf, “Yet another solution to the three wisemen puzzle,” Proc. of ISMIS 88, 1988, edited by Z. Ras and L. Saitta, pp. 398–407.
L. Aiello, D. Nardi, and M. Schaerf, “Reasoning about knowledge and ignorance,” Proc. of FGCS 88, 1988, pp. 618–627.
L. Fariñas del Cerro, “MOLOG: a system for modal logics,” New Generation Computing, 1986.
K. Konolige, “Belief and incompleteness,” in Formal Theories of the Commonsenve World, edited by J. Hobbs and R.C. Moore, Ablex Pub. Corp.: 1985, pp. 358–403.
K. Konolige, A Deduction Model of Belief, Morgan Kaufmann Pub: 1986.
L. Aiello, C. Cecchi, and D. Sartini, “Representation and use of metaknowledge,” in Proceedings of the IEEE, vol. 74:10, 1986, pp. 1304–1321.
L. Aiello, and G. Levi, “The uses of metaknowledge in AI systems,” in Proc. of ECAI 84, edited by T. O'Shea, North-Holland: 1984, pp. 705–717.
K.A. Bowen, and R.A. Kowalski, “Amalgamating language and metalanguage,” in Logic Programming, edited by Tarnlund, Academic Press: New York, pp. 153–173, 1982.
M.R. Genesereth, “An overview of meta-level architectures,” Proc. of AAAI 83, 1983, pp. 119–124.
J. Hintikka, Knowledge and Belief, Cornell University Press: Ithaca, New York, 1962.
S.A. Kripke, “Semantical considerations on modal logic”, Acta Philosphica Fennica vol. 16, pp. 83–94, 1963.
J. Batali, “Computational introspection”, MIT, Cambridge, MA, AI Memo 701, 1983.
P. Maes, and D. Nardi, (Eds.), Meta-level Architectures and Reflection, North Holland: 1988.
B.C. Smith, “Varieties of self-reference,” Proc. of the 1986 Conference on Theoretical Aspects on Reasoning about Knowledge, edited by J. Halpern, Morgan Kaufman: 1986, pp. 19–43.
F. Giunchiglia, and R.W. Weyhrauch, “A multi-context monotonic axiomatization of inessential non-monotonicity,” in Meta-level Architectures and Reflections, edited by P. Maes and D. Nardi, North-Holland: pp. 271–285, 1988.
M. Lenzerini, and D. Nardi, “Belief revision as metareasoning,” Proc. of ECAI 88, 1988, pp. 577–579.
G. Attardi, and M. Simi, “Reasoning across view-points,” Proc. of ECAI 84, edited by T. O'Shea, North-Holland, 1984, pp. 315–325.
D. Nardi, “Evaluation and reflection in FOL,” in Meta-level Architectures and Reflections, edited by P. Maes and D. Nardi, North-Holland: pp. 195–207, 1988.
M.R. Genesereth, and N. Nilsson, Fundamentals of Artificial Intelligence, Morgan-Kaufmann: 1987.
D. Perlis, “Languages with self-references I”, Artificial Intelligence, vol. 25, pp. 301–322, 1985.
D. Perlis, “Meta in logic,” in Meta-level Architectures and Reflections, edited by P. Maes and D. Nardi, North-Holland: pp. 37–49, 1988.
D. Perlis, “Languages with self-references II”, Artificial Intelligence, vol. 34, pp. 179–212, 1988.
J. des Rivieres, and H.J. Levesque, “The consistency of syntactical treatments of knowledge,” Proc. of the 1986 Conference on Theoretical Aspects on Reasoning about Knowledge, edited by J. Halpern, Morgan Kaufman: 1986, pp. 115–130.
L. Aiello, D. Nardi, and M. Schaerf, “Reasoning about reasoning in a meta-level architecture,” Technical Report Dipartimento di Informatica e Sistemistica, Univ. di Roma “La Sapienza”, 1989.
C. Geissler, and K. Konolige, “A resolution method for quantified modal logics of knowledge and belief,” Proc. of the 1986 Conference on Theoretical Aspects on Reasoning about Knowledge, edited by J. Halpern, Morgan Kaufman: 1986, pp. 309–324.
K. Konolige, “Circumscriptive ignorance,” Proc. of AAAI 82, 1982, pp. 202–204.
P. Coscia, P. Franceschi, G. Levi, G. Sardu, and L. Torre, “Object level reflection of inference rules by partial evaluation”, in Meta-level Architectures and Reflections, edited by P. Maes and D. Nardi, North-Holland: pp. 313–327, 1988.
M. Simi, and E. Motta, “OMEGA: an integrated reflective framework,” in Meta-level Architectures and Reflections, edited by P. Maes and D. Nardi, North-Holland: pp. 209–226, 1988.
J.S. Kim, and R.A. Kowalski, “An application of amalgamated logic to multi-agent belief,” Proc. of Meta-90, 1990.
D.E. Appelt, and K. Konolige, “A nonmonotonic logic for reasoning about speech acts and belief revision,” Proc. of 2nd International Workshop on Non-Monotonic Reasoning LNAI 346, 1988, pp. 164–175.
M. Cialdea, A. Micarelli, D. Nardi, J.C. Spohrer, and L. Aiello, “A rational reconstruction of the diagnostic process in intelligent tutoring systems,” Technical Report Dipartimento di Informatica e sistemistica, Univ. di Roma “La Sapienza”, 1989.
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Aiello, L.C., Nardi, D. & Schaerf, M. Reasoning about reasoning in a meta-level architecture. Appl Intell 1, 55–67 (1991). https://doi.org/10.1007/BF00117746
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DOI: https://doi.org/10.1007/BF00117746