On minimal models for pure calculi of names
DOI:
https://doi.org/10.12775/LLP.2013.023Keywords
calculus of names, Leśniewski’s Ontology, cardinality of models, Horn theories, axiomatic rejectionAbstract
By pure calculus of names we mean a quantifier-free theory, based on the classical propositional calculus, which defines predicates known from Aristotle’s syllogistic and Leśniewski’s Ontology. For a large fragment of the theory decision procedures, defined by a combination of simple syntactic operations and models in two-membered domains, can be used. We compare the system which employs `ε’ as the only specific term with the system enriched with functors of Syllogistic. In the former, we do not need an empty name in the model, so we are able to construct a 3-valued matrix, while for the latter, for which an empty name is necessary, the respective matrices are 4-valued.References
Hodges, W., “Logical features of Horn Clauses”, pages 449–503 in: Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 1, Logical Foundations, Oxford University Press, Inc., New York, NY, 1993.
Ishimoto, A., “A propositional fragment of Lśniewski’s ontology”, Studia Logica, 36 (1977): 285–299. DOI: 10.1007/BF02120666
Johnson, F., “Three-membered domains for Aristotle’s syllogistic”, Studia Logica, 50 (1991): 181–187. DOI: 10.1007/BF00370181
Kulicki, P., “Remarks on axiomatic rejection in Aristotle’s syllogistic”, Studies in Logic and Theory of Knowledge, 5 (2002): 231–236.
Kulicki, P., “Minimalne empiryczne podstawy teorii bytu a modele dla logiki nazw”, Roczniki Filozoficzne, 58 (2010), 2: 29–39.
Kulicki, P., Aksjomatyczne systemy rachunku nazw (Axiomatic Systems of Calculus of Names), Redakcja Wydawnictw KUL, Lublin, 2011.
Kulicki, P., “An axiomatisation of the pure calculus of names”, Studia Logica, 100 (2012), 5: 921–946. DOI: 10.1007/s11225-012-9441-8
Łukasiewicz, J., Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic, Clarendon Press, Oxford, 1957.
McKinsey, J.C.C., “The decision problem for some classes of sentences without quantifiers”, The Journal of Symbolic Logic, 8 (1943): 61–76. DOI: 10.2307/2268172
Pietruszczak, A., Bezkwantyfikatorowy rachunek nazw. Systemy i ich metateoria (Quantifier-free Name Calculus. Systems and their Metatheory), Wydawnictwo Adam Marszałek, Toruń, 1991.
Pietruszczak, A. “Standardowe rachunki nazw z funktorem Leśniewskiego” (Pure calculi of names with Leśniewski’s functors) Acta Universitatis Nicolai Copernici, Logika, I (1991): 5–29.
Pietruszczak, A., “Cardinalities of models for pure calculi of names”, Reports on Mathematical Logic, 28 (1994): 87–102.
Słupecki, J., Z badań nad sylogistyką Arystotelesa, Wrocław, 1948.
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