Abstract
The time has come for us to find out how conclusions can be drawn from our world descriptions, i.e. how to execute Prolog programs. The conclusions are verified or refuted by a deduction. The clauses of the program are the premises of the deduction. A deduction consists of a sequence of deduction steps. To create a new step in the sequence we apply an inference rule either on premises or on formulas we have obtained from previous deduction steps. An inference rule states how a formula will follow from certain premises, i.e. an inference rule takes a set of premises and produces a conclusion: $$ \frac{{P_1 \, \cdots \,P_n }} {S} $$ S is a conclusion inferred from the premises P1,…, P n .
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