The law is known as an abstract domain, with the interplay betweencomplex concepts at the heart of its logic. On the other hand, the lawis also concerned with the most minute of particulars, with each detailcontributing to the overall case. This duality led Yoshino, who headed ahuge legal expert systems effort, to a problem in knowledgerepresentation: How can we speak abstractly about relations betweenrelations and at the same time speak concretely of the particularrelations that are the objects of other relations?

This is a bit abstract, so let me clarify it with an example fromhis project, which was to formalize reasoning for the United NationsConvention for the International Sale of Goods. Article 16(1) of theconvention stipulates that “a revocation of an offer becomeseffective if and only if the revocation reaches the offeree before hehas dispatched an acceptance of the offer.” Notice thatdispatching is a relation between a person, a revocation, and a time; arevocation, in turn, is a relation between an offer and a person; and anoffer is a relation between two persons and a particular deal. So wehave a hierarchy of relations, with relations higher up in the hierarchyneeding to refer concretely to relations that are lower in thehierarchy. Thus, although the revocation is by a person of an offer, theoffer is a particular one between a particular offerer and offeree for aparticular bargain.

First-order logic is inadequate to represent a hierarchy ofrelations when concrete references to instances of relations are needed.Following some work of Davidson, Yoshino introduces a simple and elegantsolution. Each time a relation is instantiated, a uniqueidentifier--a name--is generated and becomes thek+1th argument of the otherwise k-ary predicate. The result, which Yoshino calls acompound predicate formula, meets the need. The paper also introducescases and gives a formal syntax and semantics for compound predicateformulas.

The paper should interest both those whose primary areaof research is knowledge representation and those whose primary goal isapplying logic. Although the technique was developed in and for thelegal context, it is generally applicable.