The Truth Table Formulation of Propositional Logic

Teorema: International Journal of Philosophy (forthcoming)
  Copy   BIBTEX

Abstract

Developing a suggestion of Wittgenstein, I provide an account of truth tables as formulas of a formal language. I define the syntax and semantics of TPL (the language of Tabular Propositional Logic), and develop its proof theory. Single formulas of TPL, and finite groups of formulas with the same top row and TF matrix (depiction of possible valuations), are able to serve as their own proofs with respect to metalogical properties of interest. The situation is different, however, for groups of formulas whose top rows differ. For them I provide (i) a tree-style system of ‘row tree proofs’, which is shown to be sound and complete, and (ii) an alternative, re-writing strategy.

Categories

Keywords

Reprint years

Links

PhilArchive

External links

  • This entry has no external links. Add one.
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

Introduction to Logic: Propositional Logic.Howard Pospesel - 1974 - Englewood Cliffs, NJ, USA: Prentice-Hall.
forall x: Calgary. An Introduction to Formal Logic (4th edition).P. D. Magnus, Tim Button, Robert Trueman, Richard Zach & Aaron Thomas-Bolduc - 2023 - Calgary: Open Logic Project.
What Is an Inconsistent Truth Table?Zach Weber, Guillermo Badia & Patrick Girard - 2016 - Australasian Journal of Philosophy 94 (3):533-548.
Dictionary of Logical Terms and Symbols.Carol Horn Greenstein - 1978 - New York, NY, USA: Van Nostrand Reinhold Company.
Ontologically Minimal Logical Semantics.Uwe Meixner - 1995 - Notre Dame Journal of Formal Logic 36 (2):279-298.
Propositional logic.Kevin C. Klement - 2004 - Internet Encyclopedia of Philosophy.
Logic.Paul Tomassi - 1999 - London and New York: Routledge.
Truth Diagrams Versus Extant Notations for Propositional Logic.Peter C.-H. Cheng - 2020 - Journal of Logic, Language and Information 29 (2):121-161.
forall x: Dortmund (2nd edition).Simon Wimmer, P. D. Magnus, Tim Button, Aaron Thomas-Bolduc, Richard Zach, J. Robert Loftis & Robert Trueman - 2021 - Dortmund:
A Propositional Theory of Truth.Yannis Stephanou - 2018 - Notre Dame Journal of Formal Logic 59 (4):503-545.
Aristotelian Logic Axioms in Propositional Logic: The Pouch Method.Enrique Alvarez-Fontecilla & Tomas Lungenstrass - 2018 - History and Philosophy of Logic 40 (1):12-21.
Quantified Propositional Gödel Logics.Matthias Baaz, Agata Ciabattoni & Richard Zach - 2000 - In Andrei Voronkov & Michel Parigot (eds.), Logic for Programming and Automated Reasoning. 7th International Conference, LPAR 2000. Berlin: Springer. pp. 240-256.
Arguments: Deductive Logic Exercises. [REVIEW]G. N. T. - 1971 - Review of Metaphysics 25 (2):364-364.
A Note on Algebraic Semantics for $mathsf{S5}$ with Propositional Quantifiers.Wesley H. Holliday - 2019 - Notre Dame Journal of Formal Logic 60 (2):311-332.
A Note on Algebraic Semantics for S5 with Propositional Quantifiers.Wesley H. Holliday - 2019 - Notre Dame Journal of Formal Logic 60 (2):311-332.

Analytics

Added to PP
2023-05-07

Downloads
529 (#35,598)

6 months
353 (#5,636)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Tristan Grøtvedt Haze
University of Melbourne

Citations of this work

No citations found.

Add more citations

References found in this work

Tractatus logico-philosophicus.Ludwig Wittgenstein, G. C. M. Colombo & Bertrand Russell - 1975 - London: Routledge and Kegan Paul. Edited by C. K. Ogden.
Notebooks, 1914-1916.Ludwig Wittgenstein - 1979 - Chicago: University of Chicago Press. Edited by G. H. von Wright & G. E. M. Anscombe.
Logic: The Laws of Truth.Nicholas J. J. Smith - 2012 - Princeton, N.J.: Princeton University Press.
Wittgenstein's notes on logic.Michael D. Potter - 2009 - New York: Oxford University Press.

View all 6 references / Add more references