Abstract
A well-known circumscription policy in situation calculus theories of actions is to minimize the Abnormality predicate by varying the Holds predicate. Unfortunately this admitted counter-intuitive models. A different policy of varying the Result function eliminated these models. Explanations of how it did this are not entirely satisfactory, but seem to appeal to informal notions of state minimization. We re-examine this policy and show that there are simple justifications for it that are based on classical automata theory. It incidentally turns out that the description “state minimization” for the varying Result policy is more accurate than the original nomenclature had intended.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
M. Arbib. Theories of Abstract Automata, Prentice-Hall, 1969.
A. Baker. Nonmonotonic Reasoning in the Framework of the Situation Calculus. Artificial Intelligence, 49, 1991, 5–23.
T. Booth, Sequential Machines and Automata Theory, John Wiley, 1968.
N. Foo and P. Peppas. System Properties of Action Theories. Proceedings NRAC’01 Workshop, IJCAI’01, Seattle, August 2001.
S. Hanks and D. McDermott. Nonmonotonic Logic and Temporal Projection. Artificial Intelligence, 33, 1987, 379–412.
V. Lifschitz. Circumscription. In The Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3: Nonmonotonic Reasoning and Uncertain Reasoning, ed. D.M. Gabbay, C.J. Hogger and J.A. Robinson Oxford University Press, 297–352, 1994.
J. McCarthy, “Applications of Circumscription to Formalizing Common-Sense Knowledge”, Artificial Intelligence, 28, pp. 86–116, 1986.
J. McCarthy P.J. Hayes, “Some Philosophical Problems from the Standpoint of Artificial Intelligence”, in Machine Intelligence 4, ed. B. Meltzer and D. Michie, pp. 463–502, Edinburgh University Press, Edinburgh, 1969.
M. Shanahan, Solving the Frame Problem: a mathematical investigation of the commonsense law of inertia, MIT Press, 1997.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Foo, N., Nayak, A., Pagnucco, M., Zhang, D. (2001). State Minimization Re-visited. In: Stumptner, M., Corbett, D., Brooks, M. (eds) AI 2001: Advances in Artificial Intelligence. AI 2001. Lecture Notes in Computer Science(), vol 2256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45656-2_14
Download citation
DOI: https://doi.org/10.1007/3-540-45656-2_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42960-9
Online ISBN: 978-3-540-45656-8
eBook Packages: Springer Book Archive