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
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