This paper describes a working system which performs natural language inference using polarity-marked parse trees. The system handles all of the instances of monotonicity inference in the FraCaS data set. Except for the initial parse, it is entirely deterministic. It handles multi-premise arguments, and the kind of inference performed is essentially “logical”, but it goes beyond what is representable in first-order logic. In any case, the system works on surface forms rather than on representations of any kind.

This paper shows how to take parse trees in CCG and algorithmically find the polarities of all the constituents. Our work uses the well-known polarization principle corresponding to function application, and we have extended this with principles for type raising and composition. We provide an algorithm, extending the polarity marking algorithm of van Benthem. We discuss how our system works in practice, taking input from the C&C parser.