Other Frameworks

I have already compared the analysis in this paper to pure Montague Grammar and to the pure underspecification semantics of Halvorsen and Fenstad. In this section, I will match the system described above to other theories which possess the common goal of providing a semantics for dependency grammar.

The Semantics of Word Grammar

Hudson (1984, 1991, 1998) offers an dependency based grammar formalism which takes the dependencies between pairs of words to be central. Word Grammar (WG) is considered to be a branch of cognitive linguistics. WG considers only words as syntactic units and dependencies between these words as constituting sentence structure. In general, word grammar is given a strong lexical semantics in terms of Frame Semantics (Fillmore 1982). This semantic formalism interprets individual words through a network of related words and concepts. Words relate to frames of knowledge related to concepts surrounding the use of that word.

However, the semantics of WG in terms of Frame Semantics does not pretend to be compositional. Whatever its advantages, they fall outside of the scope of this work.

Categorial Dependency Grammar

Categorial Dependency Grammar (Dekhtyar and Dikovsky 2008, Dikovsky 2004) does aim to provide a compositional account of dependency grammar syntax. Although it is similar in some ways to the analysis above, e.g. it includes underspecified semantic representation and a rule-to-rule translation from syntax to semantics, it fails to do so in a way that respects the nature of dependency syntax. By enforcing categorial rules on dependency grammar, we move toward a constituency based account of grammar. In these theories, dependencies are expressed in terms of classical categorial grammar with the addition of polarized valencies.

From this point, the semantics might become more standard, whether we use Descriptive Semantics as in Dikovsky (2012) or older formalisms to interpret the syntax since categorial grammar-like composition is assumed. Not only does this account fail to respect the integrity of the syntax but it also involves additional levels of semantic representation in terms of Descriptive Semantic Representations (DSRs) to which the account in this paper is not strictly committed.

Extensible Dependency Grammar

Debusmann and Kuhlmann (2008) propose a radical approach to the exploration of dependency grammars. XDG, as it is called, consists of “multigraphs” which are tuples of dependency graphs which share the same sets of nodes and a relational syntax-semantic interface. This is a multidimensional model-theoretic framework in which the XDG grammar narrows down the set of candidate grammars that eventual act as the models of the grammar itself. Dependency structures themselves are defined algebraically. The dependency algebra is generated through order-annotations which are interpreted as composition operations on the structures. As for the semantics, these multidimensional structures are interpreted through a relational interface which constrains the relation between the syntax and semantics through dominance constraints (which falls within the underspecification genre of semantic techniques), unlike accounts which derive the semantics from the syntax, as I have done.

The spirit of this account seems to be geared toward parsing efficiency and computational implementation. In so far as it achieves these goals, it also veers away from the principles discussed in this research. Both the syntactic and semantic structures are quite complex, involving multiple levels of analysis. Dependency multigraphs are so complex at times that they no longer possess the simple flat structure initially favoured by dependency syntacticians. Of course, this is not a knock down argument against this theory, it merely illustrates the divergent underlying motivations for this particular account of the syntax-semantics interface of dependency grammars.

3.5

Conclusion

This thesis has drawn together evidence and arguments from philosophy, linguistics and logic to lend insight into the topic of compositionality, its nature and implementation. The first part was devoted to describing the debate which has captured the contemporary field of natural language philosophy and linguistics. I discuss some of the foundations for the view that natural language is compositional and dismiss them in turn.

The next part opens up the compositionality debate in the arena of formal language theory. I argue that there are reasons based on complexity and the legitimacy of infinity considerations which make for a more compelling evidence in favour of compositional semantics for formal languages. I also define more precisely what the definition of compositionality entails for formal languages used to model natural language.

In the final section of the thesis, I offer a modified Montague Grammar for one such formal language, namely dependency grammar. This formalism is especially interesting since it lacks constituency, a property which forms part of most definitions of compositionality. The methodology I used is mixed. I utilise the flat structure of dependency syntactic analysis to represent the syntax-semantics interface in terms of functional dependency structures which are the generated by the syntactic algebra. I then interpret these structures through a series of rules, constraint equations and underspecification techniques into intensional logic. The result is a compositional system which can account for both the syntax and semantics of various natural language phenomena from scope ambiguity and floating quantifiers to negation and negative concord. This framework has many advantages over other accounts of the semantics of dependency grammar, which are detailed in section 3.4.7.

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