A lattice for the language of Aristotle’s syllogistic and a lattice for the language of Vasiľév’s syllogistic
DOI:
https://doi.org/10.12775/LLP.2006.002Słowa kluczowe
Aristotle’s syllogistic, Vasiľév’s syllogistic, vectorial lattice on ?-semilattice, vectorial lattice on closure \cap-semilattice, quartum non daturAbstrakt
In this paper an algebraic system of the new type is proposed (namely, a vectorial lattice). This algebraic system is a lattice for the language of Aristotle’s syllogistic and as well as a lattice for the language of Vasiľév’s syllogistic. A lattice for the language of Aristotle’s syllogistic is called a vectorial lattice on \cap-semilattice and a lattice for the language of Vasiľév’s syllogistic is called a vectorial lattice on closure \cap-semilattice. These constructions are introduced for the first time.Bibliografia
Aristotle, Posterior Analytics, trans. with a Commentary by J. Barnes, 2nd ed., Clarendon Press, Oxford, 1975.
Arruda A., “On the imaginary logic of N.A. Vasiľév”, in: A. I. Arruda, N.C.A. da Costa, R. Chuaqui (eds.), Non-Classical Logic, Model Theory and Computability, North-Holland Publishing Company, Amsterdam, 1997, pages 3–24.
Bocheński, Innocenty M., Ancient Formal Logic, North-Holland P. C., Amsterdam, 1951.
Bocheński, Innocenty M., Formale Logik, Karl Alber, Freiburg-München, 1956.
Bocheński, Innocenty M., A History of Formal Logic, trans. and ed. by I. Thomas, University of Notre Dame Press, Notre Dame (Indiana), 1961.
George L. Kline, “N.A. Vasiľév and the Development of Many-valued Logic”, in: A.T. Tymieniecka (ed.), Contributions to Logic and Methodology in Honour of J.M. Bocheński, North Holland, Amsterdam, 1965, pages 315–326.
Łukasiewicz, J., Aristotle’s Syllogistic From the Standpoint of Modern Formal Logic, 2nd edition, Clarendon Press, Oxford, 1957.
Maier H., Die Syllogistik des Aristoteles, 3 Bde., Verlag der H. Lauppschen Buchhandlung, Tübingen, 1896–1900.
Mill J.S., A System of Logic, Ratiocinative and Inductive. Being a Connected View of the Principles of Evidence and the Methods of Scientific Investigation, 2 vols., Parker, London, 1843.
Pietruszczak, A., Metamereologia (Metamereology), Nicolaus Copernicus University Press, Toruń, 2000.
Pietruszczak, A., “Stała Leśniewskiego w teoriach sylogistycznych: Semantyczne badania pewnych kwantyfikatorowych rachunków nazw”, Acta Universitatis Nicolai Copernici, Logika III (1992), 45–76.
Coniglione F., R. Poli, and J. Woleński, (eds.), Polish Scientific Philosophy: The Lvov-Warsaw School, Poznań Studies in the Philosophy of the Sciences and the Humanities 28, Rodopi, Amsterdam-Atlanta, GA, 1993.
Rayside, D., and G.T. Campbell, “An Aristotelian Understanding of Object-Oriented Programming”, in: D. Lea, (ed.), Proceedings of ACM/SIGPLAN Conference on Object-Oriented Systems, Languages and Applications (OOP-SLA), Minneapolis (Minnesota), October 2000, pages 337–353.
Rose, L. E., Aristotle’s Syllogistic, Charles C. Thomas Publisher, 1968.
Ross, W.D., (ed.), The Works of Aristotle, Volume 1: Logic, Oxford University Press, 1928.
Schumann A., Logika. Osnovy kriticheskogo myshlenia, [Logic. Foundations of critical thinking]. EHU, Minsk, 2004.
Schumann A., Sovremennaja logika: teoria i praktika, [Modern Logic: Theory and Practice], Econompress, Minsk, 2004.
Schumann A., Filosofskaja logika [Philosophical Logic], Econompress, Minsk, 2001.
Trzęsicki K., “Łukasiewicz on Philosophy and Determinism”, in: [12], pages 251–297.
Vasiľév N. A., [On particular propositions, the triangle of oppositions, and the law of excluded fourth], Ucenie zapiski Kazan’skogo Universiteta, 1910.
Vasiľév N. A., [Imaginary non-Aristotelian Logic], Z Ministerstva Narodnogo Prosvescenia 1912.
Woleński J., Logic and Philosophy in the Lvov-Warsaw School, Kluwer, Dordrecht–Boston–London, 1989.
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