Australasian Journal of Logic 14 (1):181-225 (2017)

Tore Fjetland Øgaard
University of Bergen
This paper shows how to conservatively extend theories formulated in non-classical logics such as the Logic of Paradox, the Strong Kleene Logic and relevant logics with Skolem functions. Translations to and from the language extended by Skolem functions into the original one are presented and shown to preserve derivability. It is also shown that one may not always substitute s=f(t) and A(t, s) even though A determines the extension of a function and f is a Skolem function for A.
Keywords conservative extension  identity  Leibniz’s law  non-classical logics  restricted universal quantification  Skolem functions  unique existential quantifiers
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DOI 10.26686/ajl.v14i1.4031
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References found in this work BETA

An Introduction to Non-Classical Logic.Graham Priest - 2001 - Bulletin of Symbolic Logic 12 (2):294-295.
Paths to Triviality.Tore Øgaard - 2016 - Journal of Philosophical Logic 45 (3):237-276.
Entailment and Relevance.Nuel D. Belnap - 1960 - Journal of Symbolic Logic 25 (2):144-146.

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Citations of this work BETA

From Hilbert Proofs to Consecutions and Back.Tore Fjetland Øgaard - 2021 - Australasian Journal of Logic 18 (2):51-72.
Paths to Triviality.Tore Øgaard - 2016 - Journal of Philosophical Logic 45 (3):237-276.
Substitution in Relevant Logics.Tore Fjetland Øgaard - 2019 - Review of Symbolic Logic (3):1-26.

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