Weak equivalence is a relationship between the outputs of two systems that are being compared. If these systems are only weakly equivalent, then we can say that they are computing the same function (or generating the same external behavior), but that they are using different procedures to do so. For example, human chess players and computer chess players are weakly equivalent, in the sense that they both play the game of chess, but use very different procedures to decide which move to make next in a game. (Computer chess players usually use some form of intensive search, which is beyond the memory capacity of human players. Indeed, an interesting question is how humans can play chess so well given that they do not use brute force search methods!)
Weak equivalence is important in cognitive science in two respects. First, it is the kind of comparison that the Turing test offers, which is why it is also sometimes called Turing equivalence. Second, although weak equivalence is necessary for validating theories in cognitive science, it is not sufficient. This is because while it is required of theories or simulations in cognitive science that they compute the same functions as the to-be-explained system, it is also crucial that they compute these functions in the same way. This later requirement is called strong equivalence.
- Pylyshyn, Z.W. (1984). Computation and cognition. Cambridge, MA: MIT Press.
(Revised October 2009)