caa a22 4500 605539030 CHVBK 20210128100905.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s10992-014-9322-x doi (NATIONALLICENCE)springer-10.1007/s10992-014-9322-x Failure of Completeness in Proof-Theoretic Semantics [Elektronische Daten] [Thomas Piecha, Wagner de Campos Sanz, Peter Schroeder-Heister] Several proof-theoretic notions of validity have been proposed in the literature, for which completeness of intuitionistic logic has been conjectured. We define validity for intuitionistic propositional logic in a way which is common to many of these notions, emphasizing that an appropriate notion of validity must be closed under substitution. In this definition we consider atomic systems whose rules are not only production rules, but may include rules that allow one to discharge assumptions. Our central result shows that Harrop's rule is valid under substitution, which refutes the completeness conjecture for intuitionistic logic. Springer Science+Business Media Dordrecht, 2014 Proof-theoretic semantics nationallicence Intuitionistic logic nationallicence Mints's rule nationallicence Harrop's rule nationallicence Completeness nationallicence Piecha Thomas Department of Computer Science, University of Tübingen, Sand 13, 72076, Tübingen, Germany aut de Campos Sanz Wagner Faculdade de Filosofia, Campus II, Universidade Federal de Goiás, 74001-970, Goiânia, GO, Brasil aut Schroeder-Heister Peter Department of Computer Science, University of Tübingen, Sand 13, 72076, Tübingen, Germany aut Journal of Philosophical Logic Springer Netherlands 44/3(2015-06-01), 321-335 0022-3611 44:3<321 2015 44 10992 https://doi.org/10.1007/s10992-014-9322-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10992-014-9322-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Piecha Thomas Department of Computer Science, University of Tübingen, Sand 13, 72076, Tübingen, Germany aut NATIONALLICENCE 700 1- de Campos Sanz Wagner Faculdade de Filosofia, Campus II, Universidade Federal de Goiás, 74001-970, Goiânia, GO, Brasil aut NATIONALLICENCE 700 1- Schroeder-Heister Peter Department of Computer Science, University of Tübingen, Sand 13, 72076, Tübingen, Germany aut NATIONALLICENCE 773 0- Journal of Philosophical Logic Springer Netherlands 44/3(2015-06-01), 321-335 0022-3611 44:3<321 2015 44 10992