M. Kapetanović, A. Krapež Semantic tableaux method and its application to automated theorem provers in logical systems Beograd, 15.06.2010.

Algorithm Procedure should be complete but as fast as possible and as small as possible

Choices Order in which tableau rules are applied Choice of the linear order of negatomic sentences (clause ordering) Allocation of clauses among processors

1. Order in which tableau rules are applied Introduce only neccessary constants Postpone introduction of new constants Postpone splitting of branches Use breadth first tree traversal globally but depth first locally

2. Choice of the linear order of negatomic sentences Linear order of sentences is isomorphic to integers, otherwise arbitrary and fixed

3. Distribution of clauses among processors PC – user interface Processor 0 – tableau transformation, clause ordering, clause allocation Other processors: ring of processors, some are connected to processor 0, resolution (paramodulation), new clause allocation, structured bases of clauses

3. Distribution of clauses among processors Clauses are allocated by minimal sentence Function (relation) not of maximal arity is allocated to one processor Functions (relations) of maximal arity are allocated among all processors in the ring

Organization of the base of clauses Ternary tree left – negated sentences right – sentences next – clauses with larger minimal negatomic sentence