Objects, Speciicity, Logic, and Chance

Recent deductive approaches to reasoning about action and chance allow to model objects and methods in a deductive framework. In these approaches, 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 speciicity, which states that more speciic methods are preferred to less speciic ones. Speciicity is computed with the help of negation as failure. We specify equational logic programs and show that their completed versions behave as intended. Furthermore, we prove that SLDENF-resolution is complete if the equational theory is nitary, the completed programs are consistent, and no derivation ounders or is innnite; and we give syntactic conditions which guarantee non-oundering and niteness. Over the last years three new deductive approaches to deal with situations, actions , and change were proposed, each of them solving the technical frame problem 1 without the need to state frame axioms explicitly. First, the linear connection method restricts proofs such that each literal is connected at most once 2]. Thus, connecting a literal during the inference process simulates consumption of the corresponding fact. Conversely, if the conditions of an implication are fulllled then the conclusion can be used and, thus, the literals occurring in the conclusion are produced. This treatment of literals resembles the concept of resources. Second, in a similar way linear logic 5] can be used, which is a Gentzen{style proof system without weakening and contraction rules. In the multiplicative fragment of the linear logic, literals and formulas cannot be copied or erased which also provides the idea of resources 11]. Third, in the equational logic programming approach 8] facts about a situation are represented as multisets of facts on the term level. An action with (the multiset of) conditions C and (the multiset of) eeects E is applicable in a situation S if C is contained in S ; and if is applied in S then C is deleted from S and E is added. Thus, planning in the equational logic approach is closely related to planning in Strips 4] except that multisets are used instead of sets and that planning is performed in a purely deductive system. As argued in 7] multisets represent resources more adequately than sets and, moreover, it is more eecient to compute with multisets instead of sets. These …