Compositionality and Underspecification

Although underspecification has become a ubiquitous technique is formal semantics, it is not settled whether or not the principle of compositionality is strictly adhered to by this technique. Given the analysis of dependency grammar above in terms of an underspecified Montague Grammar, a central question beckons, namely how compositional are underspecified structures (if at all)? Naturally, I will argue that functional dependency structures are indeed compositional, specifically in the weak direct sense of the term. Let us return to our definition of compositionality from the first part.

Principle: The meaning of a complex expression is a function of the meaning of its compo- nents and their method of combination.

The way in which we chose to interprete this principle was through the means of a homomorphism between the syntactic algebra and the semantic algebra. Specifically, for every rule of the dependency syntax there is a semantic rule providing the meaning of the syntactic expression produced by the rule. We encountered certain problems, however, when we attempted to account for quantifier scope. This led us to adopt an alternative strategy to the one employed by Montague, namely underspecifying the information presented in the

32_{This distinction is linguistically motivated. See Biberauer (2008a) for four differing characteristics of the}

dependency structures. There are two possible ways in which this technique could lead to a violation of the principle. (1) The meanings of complex terms are not determined by the meanings of their component parts or (2) the method of combination used does not maintain structural similarity between the algebras or more generally does not establish the appropriate relationship between the syntax and semantics.

It should be admitted that this alternative strategy does affect our original conception of compositionality. We are no longer assigning the meaning of components (constituents) in isolation and then using these assignments to generate the meaning of more complex expressions. Underspecification interferes with this process as the assignment of basic meanings is delayed (or stored) for later resolution. The important thing though is surely that the meanings of complex expressions are built up from the meanings of their components, a property which is still preserved during the resolution of underspecified structures. Therefore, the controversy comes down to whether the ”method of combination” is the ”intended method” for compositional analysis.

This objection stems from the fact that underspecification (through either enumerative or constraint-based approaches) involves taking functional structures as the input of semantic interpretation and not surface syntax. Indeed this is a worry since such a strategy could miss the point of a compositional syntax-semantics interface. The problem is that this is too general. If we do not consider the specific surface syntactic structures in our semantic analysis then it seems that we are not giving a semantics for that formalism specific. Consider, if both a phrase-structure tree and a dependency graph can be mapped onto the same functional structure. This structure is then interpreted in the semantics without any relation to the original syntactic configuration. Thus, we no longer have a direct homomorphism between the syntactic algebra and the semantic algebra, in fact the specific syntactic structure does not make much of a difference at all.

Moreover, the step from functional structures to semantic output is also problematic. As Fenstad claimed for his situation schemata, they can be interpreted through various semantic theories based on the proclivities of the semanticist. This means that neither the syntax nor the semantics is of particular importance for an account of the syntax-semantics interface given functionally underspecified structures, which is absurd. Using underspecified structures in this way is too general and does not provide us with an account of the syntax-semantics interface, which compositionality is meant to be. Therefore, it indeed does not provide the compositional analysis at which we are aiming.

The above is a serious concern for semantic underspecification techniques in general. However, this is not to say that these concerns cannot be mitigated by specific implementation which aims to avoid these problems. In this thesis, I have undertaken such a task.

The uniqueness of the current approach is that it renders the surface syntactic structures to functional structure conversion in such a way that the syntactic relations of dependency grammar are preserved in the functional structures.

In the present framework, it is not an arbitrary matter what the surface syntax is since it is from this syntax that the functional structures are generated. This process is a specific one, i.e. it would not be the same for a syntactic algebra based on phrase-structure or categorial

grammar. The functional structures are composed of the root and dependency rules of the syntax algebra. The translation rules provide the guidelines for the semantic output of these structures specifically. But the translation rules too are married to the head semantics ordered by the governance relation of the syntax.

The point at which the underspecification enters into the analysis is no longer arbitrary and it aims to represent purely semantic ambiguities without resorting to altering the syntax. But at each step of both creating the underspecified structures and interpreting them, we work towards to goal of representing the surface syntactic formalism through a compositional semantics.

The analysis does not constitute a strongly direct compositional system since individual components (words) are not interpreted in isolation. However, as was noted in section 2.4.4, the requirement of direct compositionality is quite strong and not well justified in many cases. Our system does allow for synonyms 33 and thus is not a trivial account of the syntax-semantics interface and importantly it is an account of this interface in the intended sense. This latter claim is brought out by the fact that any alteration in the syntactic algebra will have a domino effect on the rest of the processes involved in interpretation, i.e. the nature of the functionalDS and the eventual intensional logic translation.