Studia Logica 100 (5):921-946 (2012)

Authors
Piotr Kulicki
John Paul II Catholic University of Lublin
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
Keywords Calculus of names  Leśniewski’s Ontology  Horn theories  Axiomatic rejection
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DOI 10.1007/s11225-012-9441-8
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References found in this work BETA

Logics for the Relational Syllogistic.Ian Pratt-Hartmann & Lawrence S. Moss - 2009 - Review of Symbolic Logic 2 (4):647-683.
Formal Logic. Prior - 1955 - Oxford University Press.
Remarks on Axiomatic Rejection in Aristotle’s Syllogistic.Piotr Kulicki - 2002 - Studies in Logic and Theory of Knowledge 5:231-236.
S. Leśniewski's Calculus of Names.Jerzy Słupecki - 1984 - In Jan T. J. Srzednicki, V. F. Rickey & J. Czelakowski (eds.), Studia Logica. Distributors for the United States and Canada, Kluwer Boston. pp. 59--122.
Dual Counterparts of Consequence Operations.Ryszard Wójcicki - 1973 - Bulletin of the Section of Logic 2 (1):54-57.

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Citations of this work BETA

On Minimal Models for Pure Calculi of Names.Piotr Kulicki - 2013 - Logic and Logical Philosophy 22 (4):429–443.

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