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On inductive inference of cyclic structures

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Abstract

We examine the problem of inductive inference in the domain of pointer-based data structures. We show how these data structures can be formalized as rational trees. Our main technical results concern the expressiveness of a language of rational term expressions. These results place limitations on techniques of inductive inference for this description language. The results are also relevant to implementation of negation in logic programming languages.

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References

  1. D. Chan, Constructive negation based on completed database,Proc. 5th Symp. on Logic Programming (1988) pp. 111–125.

  2. K.L. Clark, Negation as failure, in:Logic and Databases, eds. H. Gallaire and J. Minker (Plenum Press, New York, 1978) pp. 293–322.

    Google Scholar 

  3. A. Colmerauer, Prolog and infinite trees, in:Logic Programming, eds. K.L. Clark and S.-A. Tarnlund (Academic Press, New York, 1982) pp. 231–251.

    Google Scholar 

  4. A. Colmerauer, Equations and inequations on finite and infinite trees,Proc. 2nd Int. Conf. on Fifth Generation Computer Systems, Tokyo (1984) pp. 85–99.

  5. H. Comon, Unification et disunification: Theorie et applications, Ph.D. Thesis, Grenoble (1988).

  6. H. Comon, Disunification, in:Computational Logic: Essays in Honor of Alan Robinson, eds. J.-L. Lassez and G. Plotkin (MIT Press, 1991) pp. 322–359.

  7. H. Comon and P. Lescanne, Equational problems and disunification, J. Symb. Comp., to appear.

  8. B. Courcelle, Fundamental properties of infinite trees, Theor. Comp. Sci. 25(1983)95–169.

    Google Scholar 

  9. B. Courcelle, Equivalences and transformation sof regular systems — application to recursive program schemes and grammars, Theor. Comp. Sci. 42(1986)1–122.

    Google Scholar 

  10. E. Eder, Properties of substitutions and unifications, J. Symb. Comp. 1(1985)31–46.

    Google Scholar 

  11. G. Huet, Resolution d'equations dans des langages d'ordre 1, 2,⋯,gw, These d'Etat, Université de Paris VII (1976).

  12. G. Huet, Confluent reductions: Abstract properties and applications to term rewriting systems, J. ACM 27(1980)797–821.

    Google Scholar 

  13. J. Jaffar and J.-L. Lassez, Constraint logic Programming,Proc. Conf. on Principles of Programming Languages (1987) pp. 111–119.

  14. J. Jaffar, J.-L. Lassez and M.J. Maher, Prolog-II as an instance of the logic programming language scheme, in:Formal Descriptions of Programming Concepts III, ed. M. Wirsing (North-Holland, 1987) pp. 275–299.

  15. J. Jaffar and P.J. Stuckey, Semantics of infinite tree logic programming, Theor. Comp. Sci. 46(1986)141–158.

    Google Scholar 

  16. E. Kounalis, An algorithm for learning from examples and counterexamples, Manuscript (1989).

  17. K. Kunen, Negation in logic programming, J. Logic Progr. 4(1987)289–308.

    Google Scholar 

  18. K. Kunen, Answer sets and negation as failure,Proc. 4th Int. Conf. on Logic Programming, Melbourne (1987) pp. 219–228.

  19. G. Kuper, K. McAloon, K. Palem and K. Perry, Efficient parallel algorithms for anti-unification and relative complement,Proc. 3rd Symp. on Logic in Computer Science, Edinburgh (1988) pp. 112–120.

  20. J.-L. Lassez and K.G. Marriott, Explicit representation of terms defined by counter examples, J. Autom. Reasoning 3(1987)301–317.

    Google Scholar 

  21. J.-L. Lassez, M.J. Maher and K.G. Marriott, Unification revisited, in:Foundations of Deductive Databases and Logic Programming, ed. J. Minker (Kaufmann, 1987).

  22. J.-L. Lassez, M.J. Maher and K. Marriott, Elimination of negation in term algebras,Proc. Mathematical Foundations of Computer Science (1991).

  23. J.W. Lloyd,Foundations of Logic Programming (Springer, 1984).

  24. M.J Maher, On parameterized substitutions, IBM Research Report RC16042, T.J. Watson Research Center (1990).

  25. M.J. Maher, Logic semantics for a class of committed-choice programs,Proc. 4th Int. Conf. on Logic Programming, Melbourne (1987) pp. 858–876.

  26. M.J. Maher, Complete axiomatization of the algebras of finite, rational and infinite trees,Proc. 3rd Symp. on Logic in Computer Science, Edinburgh (1988) pp. 348–357. Full version: IBM Research Report, T.J. Watson Researcn Center.

  27. M.J. Maher, Representing sets of rational trees using techniques of non-monotonic reasoning,Proc. 1st Int. Workshop on Logic Programming and Non-Monotonic Reasoning, eds. A. Nerode, W. Marek and V.S. Subrahmanian (MIT Press, 1991) pp. 181–195.

  28. K. Marriott, Finding explicit representations for subsets of the Herbrand universe, Ph.D. Thesis, University of Melbourne (1988).

  29. J. Maluszyński and T. Näslund, Fail substitutions for negation as failure,Proc. NACLP 89, Cleveland (1989) pp. 461–476.

  30. C. Mellish, The description identification problem, Manuscript (1990).

  31. T.M. Mitchell, Version spaces: A candidate elimination approach to rule learning,Proc. IJCAI-77 (1977) pp. 305–310.

  32. T.M. Mitchell, Generalization as search, Artificial Intelligence 18(1982)203–226.

    Google Scholar 

  33. G. Plotkin, A note on inductive generalization,Machine Intelligence 5, eds. B. Meltzer and D. Michie (1970) pp. 153–163.

  34. G. Plotkin, A further note on inductive generalization,Machine Intelligence 6, eds. B. Meltzer and D. Michie (1971) pp. 153–163.

  35. J Reynolds, Transformational systems and the algebraic structure of atomic formulas,Machine Intelligence 5, eds. B. Meltzer and D. Michie (1970) pp. 135–152.

  36. T. Sato and H. Tamaki, Transformational logic programming synthesis,Proc. FGCS'84, Tokyo (1984) pp. 195–201.

  37. J.R. Shoenfield, Mathematical Logic (Addison-Wesley, 1967).

  38. P. Stuckey, Constructive negation for constraint logic programming,Proc. LICS'91, Amsterdam (1991) pp. 328–339.

  39. M. Wallace, Negation by constraints: A sound and efficient implementation of negation in deductive databases,Proc. 1987 Symp. on Logic Programming (1987) pp. 253–263.

  40. R. Young, G. Plotkin and R. Linz, Analysis of an extended concept-learning task,Proc. IJCAI-77 (1977) p. 285.

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Authors and Affiliations

  1. IBM-T.J. Watson Research Center, 10598, Yorktown Heights, NY, USA

    Michael J. Maher

  2. Department of Computer Science, University of Melbourne, 3052, Parkville, Australia

    Peter J. Stuckey

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  1. Michael J. Maher
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  2. Peter J. Stuckey
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Maher, M.J., Stuckey, P.J. On inductive inference of cyclic structures. Ann Math Artif Intell 15, 167–208 (1995). https://doi.org/10.1007/BF01534454

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