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Two's Company: “The Humbug of Many Logical Values”

  • Conference paper
Logica Universalis

Abstract

The Polish logician Roman Suszko has extensively pleaded in the 1970s for a restatement of the notion of many-valuedness. According to him, as he would often repeat, “there are but two logical values, true and false.” As a matter of fact, a result by Wójcicki-Lindenbaum shows that any tarskian logic has a many-valued semantics, and results by Suszko-da Costa-Scott show that any many-valued semantics can be reduced to a two-valued one. So, why should one even consider using logics with more than two values? Because, we argue, one has to decide how to deal with bivalence and settle down the trade-off between logical 2-valuedness and truth-functionality, from a pragmatical standpoint.

This paper will illustrate the ups and downs of a two-valued reduction of logic. Suszko's reductive result is quite non-constructive. We will exhibit here a way of effectively constructing the two-valued semantics of any logic that has a truth-functional finite-valued semantics and a sufficiently expressive language. From there, as we will indicate, one can easily go on to provide those logics with adequate canonical systems of sequents or tableaux. The algorithmic methods developed here can be generalized so as to apply to many non-finitely valued logics as well —or at least to those that admit of computable quasi tabular two-valued semantics, the so-called dyadic semantics.

The work of the first and the fourth authors was partially supported by FEDER (European Union) and FCT (Portugal), namely via the Projects POCTI / MAT / 37239 / 2001 FibLog and POCTI / MAT / 55796 / 2004 QuantLog of the Center for Logic and Computation (CLC / IST, Portugal), and the grant SFRH / BD / 8825 / 2002. The second author was partially supported by CNPq (Brazil) and by a senior scientist research grant from the CLC / IST.

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Author information

Authors and Affiliations

  1. CLC / IST, Av. Rovisco Pais, 1049-001, Lisbon, Portugal

    Carlos Caleiro & João Marcos

  2. CLE and IFCH / Unicamp, CP 6133 — Barão Geraldo, 13083-970, Campinas, SP, Brazil

    Walter Carnielli & Marcelo Coniglio

  3. IFCH / Unicamp, CP 6133 — Barão Geraldo, 13083-970, Campinas, SP, Brazil

    João Marcos

Authors
  1. Carlos Caleiro
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  2. Walter Carnielli
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  3. Marcelo Coniglio
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  4. João Marcos
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Editor information

Editors and Affiliations

  1. Institute of Logic, University of Neuchâtel, Espace Louis Agassiz 1, 2000, Neuchâtel, Switzerland

    Jean-Yves Beziau

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© 2005 Birkhäuser Verlag Basel/Switzerland

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Caleiro, C., Carnielli, W., Coniglio, M., Marcos, J. (2005). Two's Company: “The Humbug of Many Logical Values”. In: Beziau, JY. (eds) Logica Universalis. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7304-0_10

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