How to Represent Opaque Sentences in First Order Logic

T h i s paper presents a m e t h o d for a p p l y i n g s t a n d a r d i n fe renc ing mechan isms to a b roader class of sentences t h a n t h a t wh i ch was possi b le before. T h e logic of proposition surrogates al lows rep resen ta t ion of and reason ing w i t h a class of sentences ( the so ca l led opaque sentences) t h a t pose specia l d i f f icu l t ies fo r s tan d a r d logics. W i t h i n th is class are sentences w i t h one or more occurrences of such words as know, believe, aware, search, hunt, etc. I t i s shown t h a t s t a n d a r d f o r m a l ( p r o g r a m m i n g ) languages, e.g. f i rs t o rder log ic , can be ex tended w i t h p r o p o s i t i o n surrogates to deal w i t h facts t h a t have t r a d i t i o n a l l y been expressed in m o d a l o r var ious o ther p roposed logics. I t has been argued t h a t such facts can n o t adequa te ly be expressed in s t a n d a r d logics; t he f ind ings and resul ts recorded here, however, are to t he con t ra ry . P r o p o s i t i o n surrogates can be added , in a conservat ive m a n n e r , to s t a n d a r d a u t o m a t i c reason ing systems. P r o p o s i t i o n surrogates and the i r h i s to r i ca l deve lopment are presented. An inference engine based on the logic of p r o p o s i t i o n surrogates is t hen o u t l i n e d and app l i ed to some p rob lems i n th is area.