Abstract
We present cellular automata on appropriate digraphs and show that any covered normal logic program is a cellular automaton. Seeing programs as cellular automata shifts attention from classes of Herbrand models to orbits of Herbrand interpretations. Orbits capture both the declarative, model-theoretic meaning of programs as well as their inferential behavior. Logically and intentionally different programs can produce orbits that simulate each other. Simple examples of such behavior are compellingly exhibited with space-time diagrams of the programs as cellular automata. Construing a program as a cellular automaton leads to a general method for simulating any covered program with a Horn clause program. This means that orbits of Horn programs are completely representative of orbits of covered normal programs.
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References
Apt, K. R. “Logic Programming” in Handbook of Theoretical Computer Science, J. van Leeuwen, ed., Elsevier, 1990, pp. 494–574.
Blair, H.A., Jagan Chidella, Fred Dushin, Audrey Ferry & Polar Humenn. “A Continuum of Discrete Systems” Annals of Mathematics and Artificial Intelligence, to appear.
Blair, H.A., Marek, W. and Schlipf, J. “The Expressiveness of Locally Stratified Programs”, Annals of Mathematics and Artificial Intelligence, 15(1995)209–229.
Fitting, M. “Metric methods, three examples and a theorem” Journal of Logic Programming volume 21, 1994, pp 113–127.
Gardner, Martin. “The Fantastic Combinations of John Conway's New Solitaire Game ‘Life',” Scientific American 223(4) (April, 1970), pp. 120–123.
Halmos, P.R. A Hilbert Space Problem Book Springer-Verlag, Graduate Texts in Mathematics no. 19, 1982.
Kelly, J.L. General Topology, Van Nostrand, 1955, Reprinted by Springer-Verlag, Graduate Texts in Mathematics, no. 27.
Mitchell, Melanie (1996). Computation in Cellular Automata: A Selected Review. Santa Fe Institute Working Paper 96-09-074.
Nerode, A. and R. Shore, Logic for Applications, Springer-Verlag, 1993.
Przymusinski, T. “On the Declarative Semantics of Deductive Databases and Logic Programs,” in Foundations of Deductive Databases and Logic Programming, Jack Minker, ed. Morgan-Kaufmann, Los Altos, CA. 1988
Rogers, H. Theory of Recursive Functions and Effective Computability. McGraw-Hill, New York, 1967.
Shepherdson J. C. “Unsolvable Problems for SLDNF-Resolution”, Journal of Logic Programming, 10(1), 1991, pp. 19–22
Subrahmanian, V.S. On the Semantics of Quantitative Logic Programs, Proc. 4th IEEE Symp. on Logic Programming, pps 173–182, Computer Society Press. Sept. 1987.
Toffoli, Tommaso & Norman Margolis. Cellular Automata Machines: a new environment for modeling. MIT Press, 1987.
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© 1997 Springer-Verlag Berlin Heidelberg
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Blair, H.A., Dushin, F., Humenn, P. (1997). Simulations between programs as cellular automata. In: Dix, J., Furbach, U., Nerode, A. (eds) Logic Programming And Nonmonotonic Reasoning. LPNMR 1997. Lecture Notes in Computer Science, vol 1265. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63255-7_9
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DOI: https://doi.org/10.1007/3-540-63255-7_9
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