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  1. Immanent Reasoning or Equality in Action: A Plaidoyer for the Play Level.Nicolas Clerbout, Ansten Klev, Zoe McConaughey & Shahid Rahman - 2018 - Cham, Switzerland: Springer Verlag.
    This monograph proposes a new way of implementing interaction in logic. It also provides an elementary introduction to Constructive Type Theory. The authors equally emphasize basic ideas and finer technical details. In addition, many worked out exercises and examples will help readers to better understand the concepts under discussion. One of the chief ideas animating this study is that the dialogical understanding of definitional equality and its execution provide both a simple and a direct way of implementing the CTT approach (...)
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  • EM + Ext_ + AC~i~n~t is equivalent to AC~e~x~t.Jesper Carlström - 2004 - Mathematical Logic Quarterly 50 (3):236.
    It is well known that the extensional axiom of choice implies the law of excluded middle. We here prove that the converse holds as well if we have the intensional axiom of choice ACint, which is provable in Martin-Löf's type theory, and a weak extensionality principle, which is provable in Martin-Löf's extensional type theory. In particular, EM is equivalent to ACext in extensional type theory.
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  • EM + Ext− + ACint is equivalent to ACext.Jesper Carlström - 2004 - Mathematical Logic Quarterly 50 (3):236-240.
    It is well known that the extensional axiom of choice implies the law of excluded middle . We here prove that the converse holds as well if we have the intensional axiom of choice ACint, which is provable in Martin-Löf's type theory, and a weak extensionality principle , which is provable in Martin-Löf's extensional type theory. In particular, EM is equivalent to ACext in extensional type theory.
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  • Classical predicative logic-enriched type theories.Robin Adams & Zhaohui Luo - 2010 - Annals of Pure and Applied Logic 161 (11):1315-1345.
    A logic-enriched type theory is a type theory extended with a primitive mechanism for forming and proving propositions. We construct two LTTs, named and , which we claim correspond closely to the classical predicative systems of second order arithmetic and . We justify this claim by translating each second order system into the corresponding LTT, and proving that these translations are conservative. This is part of an ongoing research project to investigate how LTTs may be used to formalise different approaches (...)
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