The treatment of negation in logic programs for representing legislation

Logic programs represent knowledge in the form of <italic>implications</italic> A if B<subscrpt>1</subscrpt> and … B<subscrpt>n</subscrpt>, n ≥ 0 where the <italic>conclusion</italic> A is an atomic formula and each <italic>condition</italic> B<subscrpt>i</subscrpt> 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 A<subscrpt>i</subscrpt>” is deemed to hold if the corresponding positive condition A<subscrpt>i</subscrpt> 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.