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COMPOSITIONALITY, COMPUTABILITY, AND COMPLEXITY

Part of: Computational number theory Theory of computing

Published online by Cambridge University Press:  29 June 2020

PETER PAGIN
PETER PAGIN*
Affiliation:
DEPARTMENT OF PHILOSOPHY STOCKHOLM UNIVERSITY STOCKHOLM, SWEDENE-mail: [email protected]
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Abstract

This paper starts from the observation that the standard arguments for compositionality are really arguments for the computability of semantics. Since computability does not entail compositionality, the question of what justifies compositionality recurs. The paper then elaborates on the idea of recursive semantics as corresponding to computable semantics. It is then shown by means of time complexity theory and with the use of term rewriting as systems of semantic computation, that syntactically unrestricted, noncompositional recursive semantics leads to computational explosion (factorial complexity). Hence, with combinatorially unrestricted syntax, semantics with tractable time complexity is compositional.

Keywords

semantic compositionalityrecursive semanticscomputable semanticssemantic complexitycognitive difficulty

MSC classification

Primary: 11Y16: Algorithms; complexity
Secondary: 68Q55: Semantics
Type
Research Article
Information
The Review of Symbolic Logic , Volume 14 , Issue 3 , September 2021 , pp. 551 - 591
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Copyright
© Association for Symbolic Logic, 2020

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