Logical Structures for Representation of Knowledge and Uncertainty

To answer questions concerning previously supplied informat- ion the book uses a truth table or 'chain set' logic which combines probabilities with truth values (possibilities). Answers to questions can be 1 (yes); 0 (no); m (a fraction in the case of uncertain information); 0m, m1 or 0m1 (in the case of 'ignorance' or insufficient information). An IF THEN statement is interpreted as specifying a conditional probab- ility value. No predicate calculus is needed in this probab- ility logic which is built on top of a yes-no logic. Quanti- fication sentences are represented as IF THEN sentences with variables. Strange results of first order logic are more reasonable in the chain set logic. E.g., (p->q)->(p->NOTq), (p->q) AND (p->NOTq), (p->q)-> NOT(p->q), p->NOT p, are contradictory statements only in the chain set logic.