Average implication between sequences: some basic results

The investigations begun by W. Bandler and S.I. Hruska (1992) are continued and generalized. A property of implication operators is defined which gives a concrete construction of optimal and pessimal pairings for arbitrary given sequences, thereby determining upper and lower bounds for the average degree of implication between them. Three of the most commonly used operators are shown to possess this property. High and low values obtainable by all operators for suitable special sequences are described, and are seen to be actual least upper and greatest lower bounds, respectively, for each of the same three operators