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An Axiomatisation of a Pure Calculus of Names

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Abstract

A calculus of names is a logical theory describing relations between names. By a pure calculus of names we mean a quantifier-free formulation of such a theory, based on classical propositional calculus. An axiomatisation of a pure calculus of names is presented and its completeness is discussed. It is shown that the axiomatisation is complete in three different ways: with respect to a set theoretical model, with respect to Leśniewski’s Ontology and in a sense defined with the use of axiomatic rejection. The independence of axioms is proved. A decision procedure based on syntactic transformations and models defined in the domain of only two members is defined.

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Kulicki, P. An Axiomatisation of a Pure Calculus of Names. Stud Logica 100, 921–946 (2012). https://doi.org/10.1007/s11225-012-9441-8

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