COMPUTING CHANGE AND SPECIFICITY WITH EQUATIONAL LOGIC PROGRAMS

Recent deductive approaches to reasoning about action and chance allow us to model objects and methods in a deductive framework. In these ap proaches, inheritance of methods comes for free, whereas overriding of methods is unsupported. In this paper, we present an equational logic framework for objects, methods, inheritance and overriding of methods . Overriding is achieved via the concept of specificity, which states that more specific methods are preferred to less specific ones. Specif icity is computed with the help of negation as failure. We specify equ ational logic programs and show that their completed versions behave a s intended. Furthermore, we prove that SLDENF-resolution is complete i f the equational theory is finitary, the completed programs are consis tent and no derivation flounders or is infinite. Moreover, we give syn tactic conditions which guarantee that no derivation flounders or is i nfinite. Finally, we discuss how the approach can be extended to reaso ning about the past in the context of incompletely specified objects o r situations. It will turn out that constructive negation is needed to solve these problems.