Completeness Theorems for Semantic Resolution in Consequence-Finding

The object of consequence-finding is to deduce l o g i c a l consequences from a set of axioms. The theory of J.R. S lag le ' s semantic reso lu t ion p r i n c i p l e , an inference ru l e fo r f i r s t o r d e r pred icate ca l cu lus , is extended to consequence-f inding. Given an i n t e r p r e t a t i o n I , i t is proved that any prime ( n o n t r i v i a l ) consequence, which is fa l se in I, can be der ived from a set of axioms by apply ing I (semant ic) r e s o l u t i o n .