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Second order inferencje in natural language semantics

Pulman S.

Journal of Language Modelling

2018

Vol. 6, No. 1

1--40

In this paper I look at a number of apparently trivial valid inferences (as well as some invalid and missing inferences) associated with the possessive construction and with different types of adjectival modification of nouns. In the case of possessives, all analyses I know of, whether implemented or not, systematically sanction invalid inferences. In the case of adjectives, there are some model-theoretic linguistic analyses that are adequate at a theoretical level, but no satisfactory practical computational implementations that I am aware of which capture the correct inference patterns. A common thread between the possessive and the adjectival construction is that to derive the correct inferences we need secondo order quantification. This is an uncontroversial move within modeltheoretic formal semantics but a problem for computational semantics, since we have no fully automated theorem provers for anything Rother than first order logic (and only for subsets of first order logic do we have provers that are both fully decidable and efficient). I explore what is needed to provide a proof-theoretic account of the relevant inference patterns, and suggest some analyses requiring second order axioms. In order to make this a practical computational possibility I go on to propose two techniques for approximating such inferences in a first order setting. The suggested analyses have been fully implemented, and in an appendix I provide a small FraCaS-like corpus of relevant examples, all of which are handled correctly by the implementation.