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- Title
ON THE DEFINABILITY OF LEŚNIEWSKI'S COPULA 'IS' IN SOME ONTOLOGY-LIKE THEORIES.
- Authors
Łyczak, Marcin; Pietruszczak, Andrzej
- Abstract
We formulate a certain subtheory of Ishimoto's [1] quantifier-free fragment of Le'sniewski's ontology, and show that Ishimoto's theory can be reconstructed in it. Using an epimorphism theorem we prove that our theory is complete with respect to a suitable set-theoretic interpretation. Furthermore, we introduce the name constant 1 (which corresponds to the universal name 'object') and we prove its adequacy with respect to the set-theoretic interpretation (again using an epimorphism theorem). Ishimoto's theory enriched by the constant 1 is also reconstructed in our formalism with into which 1 has been introduced. Finally we examine for both our theories their quantifier extensions and their connections with Le'sniewski's classical quantified ontology.
- Subjects
DEFINABILITY theory (Mathematical logic); COPULA functions; SET theory; MATHEMATICAL proofs; GROUP extensions (Mathematics)
- Publication
Bulletin of the Section of Logic, 2018, Vol 47, Issue 4, p233
- ISSN
0138-0680
- Publication type
Article
- DOI
10.18778/0138-0680.47.4.02