Comments on some completeness theorems of Urquhart and Mendez and Salto

Authors
Harris, K Fitelson, B
Citation
K. Harris et B. Fitelson, Comments on some completeness theorems of Urquhart and Mendez and Salto, J PHILOS LO, 30(1), 2001, pp. 51-55
Citations number
9
Categorie Soggetti
Philosiphy
Journal title
JOURNAL OF PHILOSOPHICAL LOGIC
ISSN journal
00223611 → ACNP
Volume
30
Issue
1
Year of publication
2001
Pages
51 - 55
Database
ISI
SICI code
0022-3611(200102)30:1<51:COSCTO>2.0.ZU;2-9
Abstract
Urquhart and Mendez and Salto claim to establish completeness theorems for the system C and two of its negation extensions. In this note, we do that f ollowing three things: (1) provide a counterexample to all of these alleged completeness theorems, (2) attempt to diagnose the mistakes in the reporte d completeness proofs, and (3) provide complete axiomatizations of the desi red systems.