On the Adequateness of the Connection Method

Roughly speaking, adequatness is the property of a theorem proving method to solve simpler problems faster than more difficult ones. Automated inferencing methods are often not adequate as they require thousands of steps to solve problems which humans solve effortlessly, spontaneously, and with remarkable efficiency. L. Shastri and V. Ajjanagadde -- who call this gap the artificial intelligence paradox -- suggest that their connectionist inference system is a first step toward bridging this gap. In this paper we show that their inference method is equivalent to reasoning by reductions in the well-known connection method. In particular, we extend a reduction technique called evaluation of isolated connections such that this technique -- together with other reduction techniques -- solves all problems which can be solved by Shastri and Ajjanagadde's system under the same parallel time and space requirements. Consequently, we obtain a semantics for Shastri and Ajjanagadde's logic. But, most importantly, if Shastri and Ajjanagadde's logic really captures the kind of reasoning which humans can perform efficiently, then this paper shows that a massively parallel implementation of the connection method is adequate.