Automating Free Logic in HOL, with an Experimental Application in Category Theory

  • Christoph BenzmüllerEmail author
  • Dana S. Scott


A shallow semantical embedding of free logic in classical higher-order logic is presented, which enables the off-the-shelf application of higher-order interactive and automated theorem provers for the formalisation and verification of free logic theories. Subsequently, this approach is applied to a selected domain of mathematics: starting from a generalization of the standard axioms for a monoid we present a stepwise development of various, mutually equivalent foundational axiom systems for category theory. As a side-effect of this work some (minor) issues in a prominent category theory textbook have been revealed. The purpose of this article is not to claim any novel results in category theory, but to demonstrate an elegant way to “implement” and utilize interactive and automated reasoning in free logic, and to present illustrative experiments.


Free logic Classical higher-order logic Category theory Interactive and automated theorem proving 



We thank Günter Rote, Lutz Schröder and and Emil Weydert for their comments to [10], which together with [9] forms the basis for this article. We also want to express our gratitude to the reviewers of this article. Their fruitful feedback definitely helped to improve the final version.

Supplementary material

10817_2018_9507_MOESM1_ESM.thy (34 kb)
Supplementary material 1 (thy 33 KB)
10817_2018_9507_MOESM2_ESM.thy (35 kb)
Supplementary material 2 (thy 35 KB)


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Freie Universität BerlinBerlinGermany
  2. 2.University of LuxembourgEsch-sur-AlzetteLuxembourg
  3. 3.University of CaliforniaBerkeleyUSA

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