A CLP-Based, Diagnosticity-Driven System for Concept Combinations

1 Introduction

Noun-noun combinations play a central role in language and cognition. People produce two main types of interpretation to noun-noun composite concepts: relational interpretations that hinge on a relation being found to connect the two con-

finger cup: "a cup to clean fingers in") and property interpretations that hinge on transferring a property from one concept to the other (e.g., finger cup: "a thin cup") (see [Levi, 1978]). In this process, the diagnostic predicates of the concepts combined have been found to play a key role. Furthermore, several computational models use the diagnosticity constraint as an important selection criterion (e.g., [Costello and Keane, 2000]). However, the diagnosticity mechanisms have so far only been formalized for property predicates, partly because it has not been clear how one can operationally define diagnosticity for relational predicates. Property predicates typically represent perceptual or physical aspects of objects. Relational predicates usually put the concept in connection with other concepts or refer to functions.

In this study, we use a new method for characterizing the diagnosticity of property and relational predicates, which is based on van Rijsbergen's [1979] tf-idf information retrieval schema. We applied this method to compute the diagnosticity values of the predicates of a set of concepts. The data are input to a reasoning system that attempts to provide meaningful interpretation(s) for a given noun-noun combination based on

Daniela Ferrari University of Siena Department of Philosophy and Social Sciences via Roma, Siena 53100, Italy daniela.ferrari@ucd.ie

Mark T. Keane

University College Dublin Department of Computer Science Dublin 4, Ireland mark.keane@ucd.ie

its interpretation type, the diagnosticity values of the predicates of its constituent concepts and a small set of rules.

2 Formalizing Diagnosticity

The idea underlying the formalization of diagnosticity is that a feature predicate F is important for a concept C within a set of concepts, if it occurs often in descriptions of concept C, and rarely in descriptions of the rest of the concepts in the set [Ferarri and Keane, 2005]. Given a set of descriptions of concepts, we can thus compute diagnosticity values for each feature relative to a concept DC;F by adapting the information retrieval tf-idf formula [van Rijsbergen, 1979] as:

where f fC;F is the frequency of the feature in a certain concept, and log2NCS=nF is a non-linear measure derived from the ratio between the number of concepts NCS in the set and the number of concepts nF described by the feature at issue.

Once the diagnosticity values for concept predicates are derived, we can class every concept as property or relational depending on whether its total diagnosticity is given mainly by relations or properties. When we make a combination from two single concepts each of them bears diagnosticity of property features (DPF) and diagnosticity of relational features (DRF). These values can in turn be summed as to characterize the combination with a total property diagnosticity (TPD) and a total relational diagnosticity (TRD).

A list of predicates was formed by asking subjects to describe a set of concepts and any associated knowledge. Formula 1 was used to compute diagnosticity values for their diagnostic predicates. Predicates with one standard deviation or more above the mean score were defined as highly diagnostic (HD). A combination was classified as relational, when TRD > TPD or property, when TPD > TRD.

3 Diagnosticity-Driven Interpretation Generation

To test the potential of diagnosticity as a driving force in concept combination, we developed a reasoning system (in Prolog) using constraint programming techniques. The techniques were developed after analysis of the data of a previous Algorithm 1 Diagnosticity-Driven Combination Rules for Relational Noun-Noun Composite Concepts

get all MN and HN's property and relational diagnostic features (DPFMN, DRFMN, DPFHN, DRFHN) if 1 or more DPFMN � HD then if all DRFMN < HD then HN that [DPFMN], s.t. DPFMN � HD HN [DRFMN] (MN), s.t. DRFMN = DRFmaxMN MN [DRFHN] (HN), s.t. DRFHN = DRFmaxHN else HN [DRFMN] (MN), s.t. DRFMN � HD MN [DRFHN] (HN), s.t. DRFHN = DRFmaxHN HN that [DPFMN], s.t. DPFMN � HD end if else if all DRFMN < HD then HN [DRFMN] (MN), s.t. DRFMN = DRFmaxMN MN [DRFHN] (HN), s.t. DRFHN = DRFmaxHN else HN [DRFMN] (MN), s.t. DRFMN = DRF � HD MN [DRFHN] (HN), s.t. DRFHN = DRFmaxHN end if end if

empirical study, where 30 people were asked to provide interpretations to 60 novel noun-noun combinations with predicates of varied diagnosticity scores and distributions.

3.1 Architecture and Implementation

The system has an interface that asks the user to enter the modifier noun (MN) and the head noun (HN) of a composite concept. This input is parsed and checked against its knowledge base. The knowledge base is in clausal form and consists of a declarative definition of concepts with their predicates and their corresponding diagnostic values as computed above. If both nouns are known to the system, it proceeds to apply the reasoning procedures. The core procedure for the interpretation of relational combinations is sketched in Algorithm 1 and that of the property ones in Algorithm 2. Action constraints are represented as binary functions and enforce valid transitions between states.

3.2 Evaluation

Evaluation of the interpretations produced was conducted with 30 noun-noun concepts, half of which were property and half relational, with constituent concepts (N = 50) of varying diagnosticity scores. All reasoning sub-mechanisms were tested. The results were compared with existing people's data. Sixty two interpretations were produced. 81% (N = 50) of the interpretations were deemed to be sensible by two judges. Half of the meanings generated were among those people had produced. For the property combinations in particular, it was found that the interpretations generated were those people produced more often.

4 Discussion

Currently, the application of the new method for computing diagnosticity to "diagnostically mark" concept predicates of Algorithm 2 Diagnosticity-Driven Combination Rules for Property Noun-Noun Composite Concepts

get all MN and HN's property and relational diagnostic features (DPFMN, DRFMN, DPFHN, DRFHN) if 1 or more DPFMN � HD then if all DRFMN < HD then HN that [DPFMN], s.t. DPFMN � HD else HN that [DPFMN], s.t. DPFMN � HD HN [DRFMN] (MN), s.t. DRFMN � HD end if else if all DRFMN < HD then HN that [DPFMN], s.t. DPFMN = DPFmaxMN HN [DRFMN] (MN), s.t. DRFMN = DRFmaxMN else HN [DRFMN] (MN), s.t. DRFMN � HD HN that [DPFMN], s.t. DPFMN = DPFmaxMN end if end if

concept glosses of large, standardized knowledge bases (e.g., WordNet) is being examined. The benefits of exploiting such a rich information for concept combination has been demonstrated in [Tagalakis and Keane, 2004]. Diagnosticity marking can be an important enhancement to the knowledge representation of ontology systems in general.

As regards the reasoning model, the percentage of correct interpretations it produces based on diagnostic values is very encouraging; especially when one considers that the system is self-contained and does not take into account other key aspects of concept understanding (e.g., plausibility, informativeness, previous knowledge). Future work will provide additional model validation and programming methodology details.