Distributed Automated Deduction

of the Dissertation Distributed Automated Deduction by Maria Paola Bonacina Doctor of Philosophy in Computer Science State University of New York at Stony Brook 1992 This thesis comprises four main contributions: an abstract framework for theorem proving, a methodology for parallel theorem proving in a distributed environment, termed deduction by Clause-Diffusion, a study of special topics in distributed deduction with contraction and an implementation, the theorem prover Aquarius, of the Clause-Diffusion methodology. In our abstract framework, Knuth-Bendix type completion procedures are treated as semidecision procedures for theorem proving, rather than procedures to generate confluent systems. A theorem proving derivation is conceived as a process of reducing a proof of the target or goal. Accordingly, all the basic notions, such as contraction inference rules, redundancy of clauses, refutational completeness of the inference mechanism and fairness of the search plan, are defined in a target-oriented fashion. The most important feature of our framework is that it provides the first notion of fairness for theorem proving, which is weaker than the fairness property required to generate confluent systems. A weaker fairness requirement means that fewer inference steps are necessary. Therefore, a weaker fairness requirement is a theoretical pre-condition to the design of more efficient theorem proving strategies. The Clause-Diffusion methodology exploits parallelism at the search level, by