On the compositional extension problem

Journal of Philosophical Logic 33 (6):549-582 (2004)
A semantics may be compositional and yet partial, in the sense that not all well-formed expressions are assigned meanings by it. Examples come from both natural and formal languages. When can such a semantics be extended to a total one, preserving compositionality? This sort of extension problem was formulated by Hodges, and solved there in a particular case, in which the total extension respects a precise version of the fregean dictum that the meaning of an expression is the contribution it makes to the meanings of complex phrases of which it is a part. Hodges' result presupposes the so-called Husserl property, which says roughly that synonymous expressions must have the same category. Here I solve a different version of the compositional extension problem, corresponding to another type of linguistic situation in which we only have a partial semantics, and without assuming the Husserl property. I also briefly compare Hodges' framework for grammars in terms of partial algebras with more familiar ones, going back to Montague, which use many-sorted algebras instead
Keywords Philosophy
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DOI 10.1023/B:LOGI.0000046069.01088.0b
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References found in this work BETA
Richard Montague (1975). Formal Philosophy. Canadian Journal of Philosophy 4 (3):573-578.
Wlodek Zadrozny (1994). From Compositional to Systematic Semantics. Linguistics and Philosophy 17 (4):329 - 342.
Tim Fernando (1997). Ambiguity Under Changing Contexts. Linguistics and Philosophy 20 (6):575-606.
George Grätzer (1982). Universal Algebra. Studia Logica 41 (4):430-431.

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