On the compositional extension problem

Journal of Philosophical Logic 33 (6):549-582 (2004)

Authors
Dag Westerståhl
Stockholm University
Abstract
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

Formal Philosophy. [REVIEW]Richard Montague - 1975 - Canadian Journal of Philosophy 4 (3):573-578.
Formal Features of Compositionality.Wilfrid Hodges - 2001 - Journal of Logic, Language and Information 10 (1):7-28.
From Compositional to Systematic Semantics.Wlodek Zadrozny - 1994 - Linguistics and Philosophy 17 (4):329 - 342.
Some Combinatorics of Imperfect Information.Peter Cameron & Wilfrid Hodges - 2001 - Journal of Symbolic Logic 66 (2):673-684.
Aspects of Compositionality.Gabriel Sandu & Jaakko Hintikka - 2001 - Journal of Logic, Language and Information 10 (1):49-61.

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Citations of this work BETA

Compositionality I: Definitions and Variants.Peter Pagin - 2010 - Philosophy Compass 5 (3):250-264.
Pure Quotation and General Compositionality.Peter Pagin & Dag Westerståhl - 2010 - Linguistics and Philosophy 33 (5):381-415.

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