Automated Deduction: a Technological Point of View

There are recent successes of automated deduction techniques in various application domains, such as mathematics, classical and nonmonotonic logics, diagnosis, planning and within software engineering. We will briefly review some of them and observe that these successes have been made only after a careful analysis of the application domain as well as the deduction system under consideration. The purpose of this article is to argue that automated deduction systems can be usefully applied in practice, but it is necessary to have available a variety of deduction methods, to understand their properties and their computational power in order to tailor them for the application under consideration. In the early days of automated deduction, research concentrated on the development of general purpose deduction systems. “Applications” were toy examples, which did not scale up to realistically sized problems. Nowadays, the theorem prover community discovers applications again. The key to success quite often is the specific knowledge of the application domain which is used to optimise the deduction systems, i.e. the knowledge is used to guide the search for a proof or a model. Indeed, there are some recent impressive results which show that such deductive systems are even able to handle realistic problems. Domains to be mentioned here include mathematics (see Sections 1 and 4.1), planning [18] (see Section 3.1), model checking (see Section 3.2), diagnosis (see Section 3.3), software reuse [22] and verification (see Section 3.4), or view deletion in databases [2]. Another realistically sized problem solved by the Protein prover [5] was the analysis of banking fees rule sets, which was successfully tackled with constraints [44] (see Section 3.5).