Interpreting Natural Language often requires dealing with linguistic information of different quality. The syntactic information can be minimal, like in "Monday washing Tuesday ironing Wednesday resting"; the degree of acceptability can vary as in "(a) Which book has Paul read? (b) Which book has read Paul? (c) Which book Paul has read?". When faced with a deviant construction it is necessary, in order to build an interpretation, to rely on partial information and to take into account information coming from different linguistic dimensions, like syntax, prosody, and pragmatics. Combined with the appropriate linguistic theory, the field of Constraint Satisfaction provides a natural way of representing and dealing at the same level with the multi-dimensional aspect of the linguistic information, but still lacks formal tools for dealing with (the semantics of) partial information. The aim of my research is to investigate the formal properties of a constraint-based computational model with respect to representing and interpreting partial information.

During this talk I will discuss a part of work in progress around the notion of density, which I presented at the Constraint Solving and Language Processing workshop (CSLP 2004). We will see how density, for example, can be used to quantify degree of acceptability, which will provide a way of assessing the accuracy of partial information.

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