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On the Definability of Leśniewski’s Copula ‘is’ in Some Ontology-Like Theories

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Łyczak M., Pietruszczak A.

Bulletin of the Section of Logic

2018

tom 47

nr 4

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.

Ograniczanie wyników

1 Bulletin of the Section of Logic

1 Pietruszczak A.

1 Łyczak M.

1 2018

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On the Definability of Leśniewski’s Copula ‘is’ in Some Ontology-Like Theories