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- Title
Constructive semantics, admissibility of rules and the validity of Peirce's law.
- Authors
De Campos Sanz, Wagner; Piecha, Thomas; Schroeder-Heister, Peter
- Abstract
In his approach to proof-theoretic semantics, Sandqvist claims to provide a justification of classical logic without using the principle of bivalence. Following ideas by Prawitz, his semantics relies on the idea that logical systems extend atomic systems, so-called ‘bases', with respect to which the validity of logically complex formulas is defined. We relate this approach to admissibility-based semantics and show that the latter significantly differs from the former. We also relate it to semantics based on the notion of construction, in which case the results obtained are essentially the same as Sandqvist's. We argue that the form of rules admitted in atomic bases determines which logical rules are validated, as is the fact of whether bases are conceived as information states, which can be monotonely extended, or as non-extensible inductive definitions. This shows that the format of atomic bases is a highly relevant issue in proof-theoretic semantics.
- Subjects
CONSTRUCTIVE proofs; MATHEMATICAL models; SEMANTICS; ADMISSIBLE evidence; MONOTONE operators; INDUCTION (Logic); INTUITIONISTIC mathematics
- Publication
Logic Journal of the IGPL, 2014, Vol 22, Issue 2, p297
- ISSN
1367-0751
- Publication type
Article
- DOI
10.1093/jigpal/jzt029