Conditional Existence of Variables in Generalised Constraint Networks

Classical constraint systems require that the set of variables which exist in a problem be known ab initio. However, there are some applications in which the existence of certain variables is dependent on conditions whose truth or falsity can only be determined dynamically. In this paper, we show how this conditional existence of variables can be handled in a mathematically well-founded fashion by viewing a constraint network as a set of sentences in free logic. Based on these ideas, we have developed, implemented and applied, a constraint language in which any sentence in full first-order free logic, about a many-sorted universe of discourse which subsumes %!, is a well-formed constraint. Classical constraint systems [8] require that the set of variables which exist in a problem be known ab initio. However, there are some applications [4; 91 in which not just the value of certain variables, but also their very existence, depends on conditions whose truth can only be determined dynamically. In this paper, we show how this conditional existence of variables can be handled in a mathematically well-founded fashion by viewing a constraint network as a set of sentences in first-order free logic (FOFL) [7]. A s well as having a better-developed theoretical underpinning, this approach is more general than that presented in [9]. We briefly review a language, based on these ideas, which we have developed, implemented and applied to a range of CAD applications. In the literature, several different definitions are given for classical constraint networks, with varying degrees of formality. However, they may all be regarded as variations of the following theme: *This work was supported in part by NSF grant number