Abstract
graphical sentential logic, the system of alpha graphs, is much more than an historical curiosity. Although a large alpha graph is difficult to manipulate hand, the alpha graphs are admirably suited to automation. In particular, a simple decision procedure for the alpha graphs is tailor-made for the programming language LISP. This decision procedure is described in section I below and is implemented by a LISP program CSProve in section II. Section III gives examples of CSProve as it ran on a desktop computer and indicates how the program is easily adapted to parallel processing. The decision procedure differs from tableau methods and the widely used Robinson resolution method in at least two interesting ways: unlike resolution it does not require that a formula be put into a normal form before the method can be applied, and unlike both tableau methods and resolution it does not require any branching tree constructions. If the method were formulated as a proof procedure in the usual notation it would have only four onepremise inference rules of the form:
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