OTRAS PLAGAS

Formal syntax is an essential part of the homomorphism and thus the compositionality definition. The syntax of the formal language which we choose is what feeds directly into the relationship with the semantics such that the concept of compositionality can be applied. Thus, besides the requirements placed on the syntax by the formal algebraic concerns of the homomorphism there are other linguistically motivated principles which a good compositional theory of meaning should follow.

These principles can help guide the formation and evaluation of various proposals of compositional semantics for specific formal languages or grammar formalisms. In most cases, the syntax employed in a theory of compositional semantics is relatively naive. Thus, syntactic considerations are often guided by semantic ones. For instance, most theories of compositional semantics assume a context-free grammar for the syntax. Dowty (2006) criticises this tradition and offers insights into a novel methodology for compositional semantics, one which approaches a particular linguistic problem in three independent ways. Firstly, it considers the syntax-semantics interface which the problem entails independently of the syntax which is to be evaluated in purely syntactic terms and the semantics which is to be evaluated likewise. This paradigm shift advocates that results in natural language syntax and semantics share in each others advances and thus not develop with biases based on unconsidered assumptions. Towards these three goals, Dowty proposes three corresponding principles:

Compositional Transparency: This is the degree to which a compositional semantics is obvious, simple, and easy to compute from a given syntactic structure

Syntactic economy: This is conceived of as the degree to which the syntax is efficiently and easily (i.e. only as complex as necessary) formed in order to produce meanings compositionally

Structural Semantic economy: This is the semantic version of the previous principle, i.e. that the meaning operations used to build the meanings of complex expressions from the meanings of less complex constituents in the simplest way as possible.

These principles are to be viewed as useful criteria upon which to judge various theories of compositional meaning. All these criteria heavily favour simplicity over complex structures whenever possible. For example, in terms of the direct compositionality thesis, these principles can guide our decisions about whether certain linguistic constructions warrant directly compositional treatment or if the simplest solutions involve more complex semantic structure. However, these principles although useful still manage to neglect a certain feature which I believe to be essential to any compositional analysis of a formal language and a natural language via such a formal language, namely that the semantics needs to respect the syntactic structure of the grammar formalism or formal language in question. I believe that this is in the spirit of the similarity constraint of Janssen discussed in section 2.4.3. It forces a certain sort of similarity between the syntax and semantics (and the associated algebras) without imposing the problematic strong bijection requirement between elements and operations of the respective algebras. In light of these considerations, I propose the following principle,

Syntactic Integrity: The degree to which the semantic structures align with the syntactic structures to which they provide interpretations.

This is still quite vague. The idea is brought out in practice in section 3.4 but I will adumbrate the point here. For a simple example of this principle in action, consider Categorial Grammar. Let us assume that it contains an operation δ which concatenates two expressions a and

b iff a belongs to sort s ∈ S and b belongs to s0 ∈ S such that s 6= s0 and either s or

s0 is a primitive syntactic sort. The semantics for such a fragment would need to respect the syntactic combination such that the semantics composes two nonidentical elements at least one of which is a primitive semantic type, unless such an analysis comes at the cost of consistency or complexity.

The way in which I think this idea of guiding principles should be viewed is as a tableaux in Optimality Theory (OT). OT provides a framework for deciding between rival analyses of various natural language phenomena. Initially, conceived of as a tool for accessing phonetic structure, it is now widely used across linguistics within syntax, semantics and pragmatics. A standard tableaux is comprised of a violable ranked set of constraints (from a universal set of such constraints) and a candidate set of possible interpretations/phonetic structures/syntactic analyses etc generated by GEN (which is the set of such candidates) for a given input. The constraint set selects the optimal candidate from the set generated by GEN. An illustration

of the procedure is given below for the ranking Compositional Transparency, Syntactic In- tegritySyntactic Economy, Structural Semantic Economy.24 _{Different rankings will result}

in different optimal outcomes. In certain cases, there will be more than one optimal solution. Syntax Semantics Comp.Trans Syn.Int Syn.Eco Sem.Eco

Σ µ1 * * *

µ2 * *

⇒ µ3 **

2.5

Conclusion

In this part, we have shifted the focus from natural language to the formal languages we use to model its nature. The theme has been largely devoted to syntactic considerations. We then used these considerations in a formal description of the principle of compositionality. Modifications and clarifications were presented with relation to the principle. A key feature of its definition, namely constituency, was discussed and formalised. Finally, I offered another principle toward the aim of guiding the compositional semantics of a given formal language or grammar. The principle of syntactic integrity should serve as a guiding principle for the formation of the semantic analysis of the next part and the evaluation of alternatives already on the market.

Part III

A Compositional Semantics for

Dependency Grammar

In this part, we explore the grammar formalism known as Dependency Grammar (DG). First, I will outline the nature of this formalism and compare it to other formalisms such Context Free Grammar (CFG) and Tree Adjoining Grammar (TAG). Next, I will describe some of the advantages of this “constituentless” way of dealing with natural language syntax.

I then define a universal algebra to generate dependency structures and I attempt to provide an analogous semantic algebra both of which constitute a homomorphism between the term algebra of the former and the type-algebra of the latter. In terms of this homomorphism, I offer a rule-to-rule semantic analysis which takes dependency structures to semantic representations which are in turn interpreted in Montague Grammar.