dc.contributor.author | Łyczak, Marcin | |
dc.contributor.author | Pietruszczak, Andrzej | |
dc.date.accessioned | 2019-05-24T07:15:57Z | |
dc.date.available | 2019-05-24T07:15:57Z | |
dc.date.issued | 2018 | |
dc.identifier.issn | 0138-0680 | |
dc.identifier.uri | http://hdl.handle.net/11089/28481 | |
dc.description.abstract | 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. | en_GB |
dc.language.iso | en | en_GB |
dc.publisher | Wydawnictwo Uniwersytetu Łódzkiego | en_GB |
dc.relation.ispartofseries | Bulletin of the Section of Logic; 4 | |
dc.rights | This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. | en_GB |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0 | en_GB |
dc.subject | elementary ontology | en_GB |
dc.subject | quantifier-free fragment of ontology | en_GB |
dc.subject | ontology-like theories | en_GB |
dc.subject | copula ‘is’ | en_GB |
dc.subject | calculus of names | en_GB |
dc.subject | Leśniewski's ontology | en_GB |
dc.subject | subtheories of Leśniewski’s ontology | en_GB |
dc.title | On the Definability of Leśniewski’s Copula ‘is’ in Some Ontology-Like Theories | en_GB |
dc.type | Article | en_GB |
dc.page.number | 233-263 | |
dc.contributor.authorAffiliation | Cardinal Stefan Wyszyński University, Institute of Philosophy, Department of Logic | |
dc.contributor.authorAffiliation | Nicolaus Copernicus University in Toru´n, Department of Logic | |
dc.identifier.eissn | 2449-836X | |
dc.references | [1] A. Ishimoto, A propositional fragment of Leśniewski’s ontology, Studia Logica 36 (1977), pp. 285–299. | en_GB |
dc.references | [2] B. Iwanuś, On Leśniewski’s elementary ontology, Studia Logica 31 (1973), pp. 73–119. Reprint: pages 165–215 in [9]. | en_GB |
dc.references | [3] A. Pietruszczak, Bezkwantyfikatorowy rachunek nazw. Systemy i ich metateoria (Quantifier-free Calculus of Names. Systems and their Metatheory), Wydawnictwo Adam Marszałek, Toruń 1991. | en_GB |
dc.references | [4] A. Pietruszczak, Standardowe rachunki nazw z funktorem Leśniewskiego (Standard calculus of name with Leśniewski’s copula), Acta Universitatis Nicolai Copernici, Logika I (1991), pp. 5–29. | en_GB |
dc.references | [5] A. Pietruszczak, O teoriach pierwszego rzędu związanych z elementarnym fragmentem ontologii Leśniewskiego (About first-order theories connected with elementary fragment of Leśniewski’s ontology), pages 127–168 in J. Perzanowski and A. Pietruszczak (eds.), Logika & Filozofia Logiczna 1996–1998, Wydawnictwo Naukowe UMK, Toruń 2000. | en_GB |
dc.references | [6] H. Rasiowa and R. Sikorski, The Mathematics of Metamathematics, PWN, Warszawa 1970. | en_GB |
dc.references | [7] J. Słupecki, S. Leśniewski’s calculus of name, Studia Logica 3 (1955), pp. 7–72. Reprint: pages 59–122 in [9]. | en_GB |
dc.references | [8] B. Sobociński, O kolejnych uproszczeniach aksomatyki »ontologji« Prof. St. Leśniewskiego (On the successive simplifications of the axiom of professor Leśniewski’s »ontology«), pages 145–160 in Fragmenty Filozoficzne. Księga pamiątkowa ku uczczeniu 15-lecia pracy nauczycielskiej w Uniwersytecie Warszawskim Prof. Tadeusza Kotarbińskiego, Warszawa, 1934. English translation by Z. Jordan in S. McCall (ed.), Polish Logic 1920–1939, Clarendon Press, Oxford, 1967. | en_GB |
dc.references | [9] J. Srzednicki et al. (eds.), Leśniewski’s Systems. Ontology and Mereology, Martinus Nijhoff Publishers and Ossolineum, The Hage, Boston and Wrocław, 1984. | en_GB |
dc.references | [10] M. Takano, A semantical investigation into Leśniewski’s axiom of his ontology, Studia Logica 44, 1 (1985), pp. 71–77. | en_GB |
dc.contributor.authorEmail | m.lyczak@uksw.edu.pl | |
dc.contributor.authorEmail | Andrzej.Pietruszczak@umk.pl | |
dc.identifier.doi | 10.18778/0138-0680.47.4.02 | |
dc.relation.volume | 47 | en_GB |