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Variations on da Costa C Systems and dual-intuitionistic logics I. Analyses of C ω and CC ω

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Abstract

Da Costa's C systems are surveyed and motivated, and significant failings of the systems are indicated. Variations are then made on these systems in an attempt to surmount their defects and limitations. The main system to emerge from this effort, system CC ω, is investigated in some detail, and “dual-intuitionistic” semantical analyses are developed for it and surrounding systems. These semantics are then adapted for the original C systems, first in a rather unilluminating relational fashion, subsequently in a more illuminating way through the introduction of impossible situations where and and or change roles. Finally other attempts to break out of impasses for the original and expanded C systems, by going inside them, are looked at, and further research directions suggested.

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Authors and Affiliations

  1. 2621, RMB683, Bungendore, Australia

    Richard Sylvan

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  1. Richard Sylvan
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I have been much helped through comments and corrections, criticism and proofs, generously offered by Newton da Costa, Chris Mortensen, John Slaney and Igor Urbas. A part of my role is no more than that, not of under-labourer, but of organiser of their results.

The paper, still incomplete at the edges, has been a good while in the making. It was first drafted in around 1980 for a Festschrift for Newton da Costa; hence the introductory remarks, which it has since seemed should stand. More recent literature on the C systems will be taken in account in a sequel.

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Sylvan, R. Variations on da Costa C Systems and dual-intuitionistic logics I. Analyses of C ω and CC ω . Stud Logica 49, 47–65 (1990). https://doi.org/10.1007/BF00401553

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