Abstract

In this paper I look at a number of apparently trivial validinferences (as well as some invalid and missing inferences) associatedwith the possessive construction and with different types ofadjectival modification of nouns. In the case of possessives, allanalyses I know of, whether implemented or not, systematicallysanction invalid inferences. In the case of adjectives, there are somemodel-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 adjectivalconstructions is that to derive the correct inferences we need secondorder quantification. This is an uncontroversial move withinmodel-theoretic formal semantics but a problem for computationalsemantics, since we have no fully automated theorem provers foranything other than first order logic (and only for subsets of firstorder logic do we have provers that are both fully decidable andefficient). I explore what is needed to provide a proof-theoreticaccount of the relevant inference patterns, and suggest some analysesrequiring second order axioms. In order to make this a practicalcomputational possibility I go on to propose two techniques forapproximating such inferences in a first order setting. The suggestedanalyses have been fully implemented, and in an appendix I provide asmall FraCaS-like corpus of relevant examples, all of which arehandled correctly by the implementation.

Highlights

  • In this paper I look at a number of apparently trivial valid inferences associated with the possessive construction and with different types of adjectival modification of nouns

  • A common thread between the possessive and the adjectival constructions is that to derive the correct inferences we need second 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 other than first order logic

  • I will assume a simple and standard setting in which to address this problem, assuming that we have a syntax-driven compositional semantics producing logical forms for a parsed sentence in a familiar way. These logical forms will ideally be sent to an automated theorem prover of some type which can mechanically check the validity of the inferences

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Summary

Stephen Pulman

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. Whatever the undoubted merits of these approaches to defining interpretation conditions for adjectives or other context dependent constructs, the exercise is not very practically relevant for computational purposes, for which we need an explicit logical form that will support the relevant inferences proof theoretically, or which will lend itself to computationally tractable model building and checking techniques In this respect, computational semantics for natural language is a rather different pursuit than purely linguistic semantics. The interaction with related predicates only needs one (second order) axiom (again generated from a schema, we assume), which quantifies over every possible standard of comparison: While this is satisfactory from the point of view of linguistic analysis, we are still no nearer to a solution to the problem of how to automate inferences involving these logical forms: they are still second order.

An initial simple analysis
Det of
Encoding via combinators
Adjective inferences
An alternative approach
No proof found Yes
Yes Yes No proof found No proof found
Full Text
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