Geodesic
On the Definability of Leśniewski’s Copula ‘is’ in Some Ontology-Like Theories
Bulletin of the Section of Logic, Tome 47 (2018) no. 4

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We formulate a certain subtheory of Ishimoto’s [1] quantifier-free fragment of Leśniewski’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 Leśniewski’s classical quantified ontology.
Keywords: elementary ontology, quantifier-free fragment of ontology, ontology-like theories, copula ‘is’, calculus of names, Leśniewski's ontology, subtheories of Leśniewski’s ontology 
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     title = {On the {Definability} of {Le\'sniewski{\textquoteright}s} {Copula} {\textquoteleft}is{\textquoteright} in {Some} {Ontology-Like} {Theories}},
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Łyczak, Marcin; Pietruszczak, Andrzej. On the Definability of Leśniewski’s Copula ‘is’ in Some Ontology-Like Theories. Bulletin of the Section of Logic, Tome 47 (2018) no. 4. http://geodesic.mathdoc.fr/item/BSL_2018_47_4_a2/