With the principles and techniques that were covered in the previous chapters, we can now recapitulate what we have done, and look at further topics and directions.

RECAPITULATION

Throughout this book, two principles have played a key role:

Chapter 2 presented the concept of models and the Truth- Conditionality Criterion as a basis for the compositional analysis of entailment. Compositionality helped us to treat structural ambiguity as a syntactic phenomenon that leads to semantic ambiguity, i.e. systematic uncertainty in certain judgments about entailment. Chapter 3 developed one of the essential ingredients of formal semantics: the use of functions for linguistic denotations. We saw the role that functions of different types play in the compositional treatment of entailment, and how functions are represented in formal semantic analysis. In Chapter 4, we used functions for handling natural language quantification, concentrating on quantified noun phrases. We saw that many complex entailments in language involving monotonicity, coordination and classical syllogisms are immediately accounted for when generalized quantifiers are used as noun phrase denotations. Chapter 5 revealed a connection between three apparently unrelated phenomena: long-distance dependencies, scope ambiguity and verbs with quantified objects. These three phenomena were treated by adding a new compositional principle, hypothetical reasoning, to a grammar architecture that manipulates pairs of forms and meanings packed in linguistic signs. Chapter 6 extended our framework in another direction: the analysis of intensional expressions – words and phrases that refer to psychological states and imaginary situations. We saw that, using our initial system from Chapter 3, we can analyze complex intensional phenomena by adding a basic domain of possible worlds. Relying on the extended framework emanating from Chapters 5 and 6, we captured the intuitive relation between scope ambiguity and de dicto/de re ambiguities with intensional expressions.

WHERE TO GO FROM HERE?

Readers of different backgrounds and interests may choose to follow a number of different directions to further explore formal semantics and related areas. The recommendations below suggest a few possible avenues.