@article{8545080,
  abstract     = {{Mathematicians prove theorems in a semi-formal setting, providing what we'll call informal proofs. There are various philosophical reasons not to reduce informal provability to formal provability within some appropriate axiomatic theory (Leitgeb, 2009; Marfori, 2010; Tanswell, 2015), but the main worry is that we seem committed to all instances of the so-called reflection schema: B(phi) -> phi (where B stands for the informal provability predicate). Yet, adding all its instances to any theory for which Lob's theorem for B holds leads to inconsistency.

Currently existing approaches (Shapiro, 1985; Horsten, 1996, 1998) to formalizing the properties of informal provability avoid contradiction at a rather high price. They either drop one of the Hilbert-Bernays conditions for the provability predicate, or use a provability operator that cannot consistently be treated as a predicate.

Inspired by (Kripke, 1975), we investigate the strategy which changes the underlying logic and treats informal provability as a partial notion. We use non-deterministic matrices to develop a three-valued logic of informal provability, which avoids some of the above mentioned problems.}},
  author       = {{Pawlowski, Pawel and Urbaniak, Rafal}},
  issn         = {{1755-0203}},
  journal      = {{REVIEW OF SYMBOLIC LOGIC}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{207--223}},
  title        = {{Many-valued logic of informal provability : a non-deterministic strategy}},
  url          = {{http://doi.org/10.1017/S1755020317000363}},
  volume       = {{11}},
  year         = {{2018}},
}

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