The Collapse of Higher-order Inference Rules
Year: 2026
Type: article
Abstract: Developments of proof-theoretic semantics that locate meaning uniformly either with introduction rules or with elimination rules give rise to higher-order inference rules. These higher-order rules typically resist straightforward formulation in natural deduction and appear to license a more general class of valid inference patterns than the corresponding rules in Gentzen’s original calculus. Examples from Koslow’s and Schroeder-Heister’s approaches to proof-theoretic semantics illustrate the pattern. We show that this apparent generality is an illusion. In every case in which they arise, the higher-order rule is seen to be a twofold universalization of Gentzen’s lower-level rule and is proven to be interderivable with it. The result highlights the primacy of the universal construction—rather than the details of any particular presentation—as determining meaning. An application to identity shows that higher-order rules can even make explicit universal constructions that remain hidden at the level of familiar inferential patterns.
Source: The Review of Symbolic Logic
Author: CURTIS FRANKS
Institution: University of Notre Dame
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W7165965099
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