The treatment of negation in logic programs for representing legislation

ABSTRACT

Logic programs represent knowledge in the form of implications A if B1 and … Bn, n ≥ 0 where the conclusion A is an atomic formula and each condition Bi is either an atomic formula or the negation of an atomic formula. Any variables are assumed to be universally quantified, with a scope which is the entire sentence. A negated condition “not Ai” is deemed to hold if the corresponding positive condition Ai can be shown to fail to hold. This interpretation of negative conditions is called negation by failure (NBF) [Cl 78]. It has the characteristic that only the positive “if-half” of a definition needs to be given explicity. The negative “only-if” half is given implicitly by NBF. The obvious problem with NBF is that it supplies the only-if halves of implications, whether or not they are intended. I shall discuss a possible solution to this problem in the context of discussing the more general problem of representing negative conclusions. I shall focus on examples taken from our formalisation of the 1981 British Nationality Act (BNA) [SSKKHC 86]. I shall argue that many negative sentences can be regarded as integrity constraints and consequently can be eliminated by transformations such as those developed by Asirelli et al [ASM 85] and Kowalski and Sadri [KS 88]. Among such sentences are ones expressing prohibitions. The interpretation of prohibitions as integrity constraints suggests a possible approach to the treatment of deontic modalities.

REFERENCES

• ASM 85: Patrizia Asirelli , Michele De Santis , Maurizio Martelli, Integrity constraints in logic databases, Journal of Logic Programming, v.2 n.3, p.221-232, Oct. 1985 [doi>10.1016/0743-1066(85)90020-2]
• CI 78: Clark, K. L. {1978}: "Negation as failure", in "Logic and Databases", Gallaire, H. and Minker, J. {Eds}, Plenum Press, pp. 293- 322.
• CGM 88: U. S. Chakravarthy , J. Grant , J. Minker, Foundations of semantic query optimization for deductive databases, Foundations of deductive databases and logic programming, Morgan Kaufmann Publishers Inc., San Francisco, CA, 1988
• EK 89: Eshghi, K. and Kowalski, R. A. {1989}: "Abduction Compared with Negation by Failure", Proceedings of the Sixth International Logic Programming Conference. MIT Press.
• KS 88: Kowalski, R.A. and Sadri, F., {1988}: "Knowledge Representation without Integrity Constraints", Department of Computing, Imperial College, University of London.
• LST 86: J. W. Lloyd , E. A. Sonenberg , R. W. Topor, Integrity constraint checking in stratified databases, Journal of Logic Programming, v.4 n.4, p.331-343, December 1, 1987 [doi>10.1016/0743-1066(87)90009-4]
• R89: T. Routen, Hierarchically organised formalisations, Proceedings of the 2nd international conference on Artificial intelligence and law, p.242-250, May 1989, Vancouver, British Columbia, Canada [doi>10.1145/74014.74045]
• SK 88: F. Sadri , R. Kowalski, A theorem-proving approach to database integrity, Foundations of deductive databases and logic programming, Morgan Kaufmann Publishers Inc., San Francisco, CA, 1988
• SSKKHC 86: M. J. Sergot , F. Sadri , R. A. Kowalski , F. Kriwaczek , P. Hammond , H. T. Cory, The British Nationality Act as a logic program, Communications of the ACM, v.29 n.5, p.370-386, May 1986 [doi>10.1145/5689.5920]

INDEX TERMS

Primary Classification:
  H. Information Systems
  H.2 DATABASE MANAGEMENT
      H.2.0 General
          Subjects: Security, integrity, and protection**

Additional Classification:
  I. Computing Methodologies
  I.2 ARTIFICIAL INTELLIGENCE
      I.2.3 Deduction and Theorem Proving
          Subjects: Logic programming
      I.2.4 Knowledge Representation Formalisms and Methods
          Subjects: Representations (procedural and rule-based)

General Terms:
Design, Legal Aspects