The notions of word identification and syntactic processing in language comprehension are relatively constrained. The notion of discourse-level processing is much less clearly defined. Syntax is generally regarded as a sentence-level phenomenon. Thus, syntactic analysis groups together words within sentences ready for interpretation. Interpretation is a much more complex phenomenon and is not restricted to processes operating on single sentences.
Some basic aspects of meaning are determined by within-sentence syntactic structure. Each clause in a sentence usually presents one eventuality (event, action, state or process). The finite verb in the clause specifies what kind of eventuality and the other parts of the clause present the participants in the eventuality, so that the clause as a whole conveys local 'who did what to whom' information. One view, popular among formal semanticists, is that this kind of information follows from syntactic structure, with each rule of syntactic combination paired with a rule of syntactic interpretation (the so-called rule-to-rule hypothesis of Bach, 1976). So, a very simple sentence might be formed by having a subject noun phrase (itself comprising a proper name) followed by an intransitive verb (e.g. 'John walks'). The interpretation is that the person denoted by the proper name performs the action described by the verb. Note that the syntactic and semantic rules, though paired, are very different in content: one is about structure, the other about meaning conveyed by structure.
The rule-to-rule hypothesis implies compositionality of semantics. However, it deals only with the literal meaning of sentences, and not with other aspects of their meaning, those that depend on context, for example, or non-literal aspects of meaning. Some cross-sentence aspects of interpretation have been analysed in the same kind of formal semantics framework as within-clause interpretation, in theories such as discourse representation theory (Kamp, 1981; Kamp & Reyle, 1993). In particular, this approach has been applied to the interpretation of anaphoric expressions (e.g. pronouns and ellipses, which take their meaning from a previous part of the text).
Formal, compositional, semantics characterizes both word meanings and combinatorial operations in a highly abstract way. Because of its roots in philosophical logic it recognizes the distinction between sense (roughly speaking, meaning as provided by definitions) and denotation (the thing or things in the world that a word stands for). Hence, it indirectly recognizes what has been called in cognitive science the grounding problem (Harnad, 1990). The grounding problem is the problem of explaining how language links with the world and hence how understanding language is understanding information about the world.
This problem is particularly acute for certain types of approach to both language and language understanding, those that treat language as merely a formal symbolic system and model language understanding as the manipulation of symbols. In formal semantics, the denotation of a common noun, such as 'table', might be modelled as a set of tables, or rather as a function from possible words to sets of tables.
Thus, 'table' means (in the sense of denotes) all those things that are tables ...