On Axiom Systems of Słupecki for the Functionally Complete Three-Valued Logic

Axiomathes 27 (4):403-415 (2017)
  Copy   BIBTEX

Abstract

The article concerns two axiom systems of Słupecki for the functionally complete three-valued propositional logic: W1–W6 and A1–A9. The article proves that both of them are inadequate—W1–W6 is semantically incomplete, on the other hand, A1–A9 governs a functionally incomplete calculus, and thus, it cannot be a semantically complete axiom system for the functionally complete three-valued logic.

Categories

Keywords

Reprint years

DOI

10.1007/s10516-016-9319-x

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,423

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Simple characterization of functionally complete one‐element sets of propositional connectives.Petar Maksimović & Predrag Janičić - 2006 - Mathematical Logic Quarterly 52 (5):498-504.
Every functionally complete $m$-valued logic has a Post-complete axiomatization.Nuel D. Belnap & Storrs McCall - 1970 - Notre Dame Journal of Formal Logic 11 (1):106-106.
Complete and atomic algebras of the infinite valued łukasiewicz logic.Roberto Cignoli - 1991 - Studia Logica 50 (3-4):375 - 384.
On n-valued functionally complete truth functions.R. L. Graham - 1967 - Journal of Symbolic Logic 32 (2):190-195.
Review: R. L. Graham, On n-Valued Functionally Complete Truth Functions. [REVIEW]Norman M. Martin - 1971 - Journal of Symbolic Logic 36 (4):691-691.
The problem of Quantificational Completeness and the Characterization of All Perfect Quantifiers in 3-Valued Logics.Walter A. Carnielli - 1987 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (1):19-29.
Algorithmic logic. Multiple-valued extensions.Helena Rasiowa - 1979 - Studia Logica 38 (4):317 - 335.
Process algebra with four-valued logic.Jan A. Bergstra & Alban Ponse - 2000 - Journal of Applied Non-Classical Logics 10 (1):27-53.
Determined game logic is complete.Jan van Eijck - unknown
Formalization of intensional functions and epistemic knowledge representation systems.Grzegorz Malinowski - 1999 - Logica Trianguli 3:111-118.
A criterion of fullness of many-valued systems of propositional logic.Jerzy Słupecki - 1972 - Studia Logica 30 (1):153-157.
The shortest possible length of the longest implicational axiom.Dolph Ulrich - 1996 - Journal of Philosophical Logic 25 (1):101 - 108.
Elementary properties of power series fields over finite fields.Franz-Viktor Kuhlmann - 2001 - Journal of Symbolic Logic 66 (2):771-791.
Weakening of Intuitionistic Negation for Many-valued Paraconsistent da Costa System.Zoran Majkić - 2008 - Notre Dame Journal of Formal Logic 49 (4):401-424.
Correspondence analysis for strong three-valued logic.Allard Tamminga - 2014 - Logical Investigations 20:255-268.

Analytics

Added to PP
2016-11-07

Downloads
43 (#362,182)

6 months
11 (#225,837)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Add more citations

References found in this work

Time, Tense, and Causation.Michael Tooley - 1997 - Oxford, GB: Oxford University Press.
The Connectives.Lloyd Humberstone - 2011 - MIT Press. Edited by Lloyd Humberstone.
Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - New York: Cambridge University Press. Edited by Jan Von Plato.
Theory of Logical Calculi: Basic Theory of Consequence Operations.Ryszard Wójcicki - 1988 - Dordrecht, Boston and London: Kluwer Academic Publishers.
Many-valued logic.Nicholas Rescher - 1969 - New York,: McGraw-Hill.

View all 32 references / Add more references