Abstract
In this chapter, a second component is added to the grammars, that of meanings. A new notion of grammar appears on the scene, that of a bigrammar. Bigrammars interpret the modes by two functions, one for the formation of the expressions, another for the formation of the meanings. Various notions of independence of these two planes are being discussed. Autonomy of syntax means that expression formation proceeds independently of the meaning, and compositionality means that meaning formation proceeds independently of the expressions. The partiality of the composition functions allows to divide the explanatory burden between semantics and syntax in often arbitrary ways. Further, strong generative capacity is linked to the language as relation, while weak capacity only deals with the string language. It is shown that there exist weakly context free languages that are not strongly context free.
The principle of compositionality is introduced in this chapter: it concerns the relationship of strings with their meanings. To be able to formulate it properly, we shall have to introduce interpreted languages and grammars for them.
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Notes
- 1.
Well, there are two: \(f(x,y) := x^{\smallfrown}\!y\) and \(g(x,y) := y^{\smallfrown}\!x\). But this can be handled by constructing a more complex example.
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Kracht, M. (2011). Compositionality. In: Interpreted Languages and Compositionality. Studies in Linguistics and Philosophy, vol 89. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2108-1_3
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