Assumption - Based Reasoning with Algebraic Clauses ∗

Ten years ago, de Kleer introduced assumption-based truth maintenance systems (ATMS) as a powerful tool for different applications in the domain of uncertain reasoning (de Kleer, 1986). A traditional ATMS is based on propositional logic, but it is limited to Horn clauses and to simple queries. An ATMS requires that there is a subset of propositions declared as assumptions. Assumptions are needed to express uncertainty. The fundamental ATMS problem is to identify combinations of assumptions (labels) such that a given query holds. The weak point of the traditional ATMS concept is the restriction to Horn clauses. In many cases, also non-Horn clauses are needed to express the knowledge. The advantage of ATMS lies in its efficient computations.