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Modular specifications with supernormal defaults

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Abstract

We add a simple module system to specifications with supernormal defaults. It allows to distinguish between “defining” and “calling” occurrences of predicates. This greatly improves the understandability of large default specifications and especially helps to solve the problem of unwanted contrapositions of rules. Our approach is similar to the distinction between head and body of logic programming rules, but it works on the higher level of default theories. So our results can help to integrate both approaches — at least on the semantical side for specification purposes. We also clarify the relation to prioritized defaults and argue that modular specifications are often preferable. Finally, we give a theoretical basis for query evaluation.

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References

  1. G. Antoniou, Modules in computer science and artificial intelligence, Osnabrücker Schriften zur Mathematik I-26, Universität Osnabrück (1991).

  2. A.B. Baker and M.L. Ginsberg, A theorem prover for prioritized circumscription, in:Proc. 11th Int. Joint Conf. on Artificial Intelligence (IJCAI), 1989, pp. 463–467.

  3. F. Baader and B. Hollunder, How to prefer more specific defaults in terminological default logic, Research Report RR-92-58, DFKI, Kaiserslautern (1992).

    Google Scholar 

  4. S. Brass and U.W. Lipeck, Specifying closed world assumptions for logic databases, in: J. Demetrovics and B. Thalheim (eds.),2nd Symp. on Mathematical Fundamentals of Database Syst. (MFDBS' 89), LNCS 364 (Springer, 1989) pp. 68–84.

  5. S. Brass and U.W. Lipeck, Semantics of inheritance in logical object specifications, in: C. Delobel, M. Kifer and Y. Masunaga (eds.),Deductive and Object-Oriented Databases, 2nd Int. Conf. (DOOD' 91), LNCS 566 (Springer, 1991) pp. 411–430.

  6. S. Brass and U.W. Lipeck, Bottom-up query evaluation with partially ordered defaults, in:Proc. 3rd Int. Conf. on Deductive and Object-Oriented Databases (DOOD '93), LNCS 760 (Springer, 1993) pp. 253–266.

  7. S. Brass, Logic programs viewed as modular specifications, Research Report, Institut für Informatik, Universität Hannover (1992).

  8. S. Brass, Deduction with supernormal defaults, in: G. Brewka, K.P. Jantke and P.H. Schmitt (eds.),Nonmonotonic and Inductive Logics, 2nd Int. Workshop (NIL '91), LNAI 659 (Springer, 1993) pp. 153–174.

  9. S. Brass, On the semantics of supernormal defaults, in: R. Bajcsy (ed.),Proc. 13th Int. Joint Conf. on Artificial Intelligence (IJCAI '93) (Morgan Kaufmann, 1993) pp. 578–583.

  10. G. Brewka,Nonmonotonic Reasoning: Logical Foundations of Commonsense (Cambridge University Press, 1991).

  11. J. Dix, Default theories of Poole-type and a method for constructing cumulative versions of default logic, in: B. Neumann (ed.),Proc. 10th European Conf. on Artificial Intelligence (ECAI '92), (Wiley, 1992) pp. 289–293.

  12. J.P. Delgrande and W.K. Jackson, Default logic revisited, in: J. Allen, R. Fikes and E. Sandewall (eds.),Principles of Knowledge Representation and Reasoning, Proc. 2nd Int. Conf. (KR '91) (Morgan Kaufmann, 1991) pp. 118–127.

  13. M.L. Ginsberg, A circumscriptive theorem prover, Artificial Intelligence 39 (1989) 209–230.

    Google Scholar 

  14. G. Gottlob, The power of beliefsor Translating default logic into standard autoepistemic logic, in: R. Bajcsy (ed.),Proc. 13th Int. Joint Conf. on Artificial Intelligence (IJCAI '93) (Morgan Kaufmann, 1993) pp. 570–575.

  15. S. Hanks and D. McDermott, Nonmonotonic logic and temporal projection, Artificial Intelligence 33 (1987) 379–412.

    Google Scholar 

  16. V. Lifschitz, Pointwise circumscription, in: M.L. Ginsberg (ed.),Readings in Nonmonotonic Reasoning (Morgan Kaufmann, 1987) pp. 179–193.

  17. Y. Moinard, Pointwise circumscription is equivalent to predicate completion (sometimes), in: R.A. Kowalski and K.A. Bowen (eds.),Logic Programming, Proc. 5th Int. Conf. and Symp. (MIT Press, 1988) pp. 1097–1105.

  18. W. Marek and M. Truszczyński, Stable models for logic programs and default theories, in:Logic Programming, Proc. North American Conf. (MIT Press, 1989).

  19. W. Marek and M. Truszczyński,Nonmonotonic Logic: Context-Dependent Reasoning (Springer, 1993).

  20. R.A. O'Keefe, Towards an algebra for constructing logic programs, in:Symp. on Logic Programming, 1985, pp. 152–160.

  21. D. Poole, A logical framework for default reasoning, Artificial Intelligence 36 (1988) 27–47.

    Google Scholar 

  22. D. Poole, Compiling a default reasoning system into prolog, New Generation Comput. 9 (1991) 3–38.

    Google Scholar 

  23. H. Przymusinska and T.C. Przymusinski, Weakly perfect model semantics for logic programs, in: R.A. Kowalski and K.A. Bowen (eds.),Logic Programming, Proc. 5th Int. Conf. and Symp. (MIT Press, Cambridge, Mass., 1988) pp. 1106–1122.

    Google Scholar 

  24. T.C. Przymusinski, On the declarative semantics of deductive databases and logic programs, in: J. Minker (ed.),Foundations of Deductive Databases and Logic Programming (Morgan Kaufmann, Los Altos, Calif., 1988) pp. 193–216.

    Google Scholar 

  25. T.C. Przymusinski, An algorithm to compute circumscription, Artificial Intelligence 38 (1989) 49–73.

    Google Scholar 

  26. M. Ryan, Defaults and revision in structured theories, in:Proc. IEEE Symp. on Logic in Computer Science (LICS '91), 1991, pp. 362–373.

  27. C. Sernadas, J. Fiadeiro and A. Sernadas, Modular construction of logic knowledge bases: An algebraic approach, Information Syst. 15 (1990) 37–59.

    Google Scholar 

  28. D.T. Sanella and L.A. Wallen, A calculus for the construction of modular prolog programs, J. Logic Progr. 12 (1992) 147–177.

    Google Scholar 

  29. W.M. Turski and T.S.E. Maibaum,The Specification of Computer Programs (Addison-Wesley, 1987).

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Authors and Affiliations

  1. Institut für Informatik, Universität Hannover, Lange Laube 22, D-30159, Hannover, Germany

    Stefan Brass

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  1. Stefan Brass
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Additional information

This work was partially supported by the CEC under the ESPRIT Working Group 6071 IS-CORE (Information Systems — COrrectness and REusability).

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Brass, S. Modular specifications with supernormal defaults. Ann Math Artif Intell 12, 189–213 (1994). https://doi.org/10.1007/BF01530785

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