On Minimal Models for Pure Calculi of Names

  title={On Minimal Models for Pure Calculi of Names},
  author={Piotr Kulicki},
  journal={Logic and Logical Philosophy},
  • Piotr Kulicki
  • Published 2013
  • Mathematics
  • Logic and Logical Philosophy
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 `e’ as the only specific term with the system enriched with functors of Syllogistic. In the former, we do… Expand
3 Citations
Pure Modal Logic of Names and Tableau Systems
By a pure modal logic of names (PMLN) we mean a quantifier-free formulation of such a logic which includes not only traditional categorical, but also modal categorical sentences with modalities de reExpand
Aristotle's Syllogistic as a Deductive System
The essential elements of the Aristotelian system of syllogistic and Łukasiewicz’s reconstruction of it based on the tools of modern formal logic are discussed, with special attention to the notion of completeness of a deductive system. Expand


An Axiomatisation of a Pure Calculus of Names
It is shown that the axiomatisation of a pure calculus of names is complete in three different ways: with respect to a set theoretical model, withrespect to Leśniewski's Ontology and in a sense defined with the use of axiomatic rejection. Expand
Remarks on Axiomatic Rejection in Aristotle’s Syllogistic
In the paper we examine the method of axiomatic r ejection used to describe the set of nonvalid formulae of Aristotle’s syllogistic. First we show that the condition which the system of syllog isticExpand
The Decision Problem for Some Classes of Sentences Without Quantifiers
  • J. McKinsey
  • Mathematics, Computer Science
  • J. Symb. Log.
  • 1943
A rather broad sufficient condition for the existence of a decision method for sentences without quantifiers is formulated, and it is shown that this condition holds of lattices. Expand
Three-membered domains for aristotle's syllogistic
  • F. Johnson
  • Mathematics, Computer Science
  • Stud Logica
  • 1991
The paper shows that for any invalid polysyllogism there is a procedure for constructing a model with a domain with exactly three members and an interpretation that assigns non-empty, non-universalExpand
Bezkwantyfikatorowy rachunek nazw. Systemy i ich metateoria (Quantifier-free Name Calculus. Systems and their Metatheory)
  • Wydawnictwo Adam Marszałek, Toruń,
  • 1991
A propositional fragment of Lśniewski’s ontology
  • Studia Logica,
  • 1977
Standardowe rachunki nazw z funktorem Leśniewskiego” (Pure calculi of names with Leśniewski’s functors
  • Acta Universitatis Nicolai Copernici,
  • 1991
Aksjomatyczne systemy rachunku nazw (Axiomatic Systems of Calculus of Names)
  • Redakcja Wydawnictw KUL,
  • 2011
Minimalne empiryczne podstawy teorii bytu a modele dla logiki nazw
  • Roczniki Filozoficzne,
  • 2010
Cardinalities of Models for Pure Calculi of Names