[2]
Awodey, S. (2010). Category Theory (second edition). Oxford, UK: Clarendon Press.

[3]
Belnap, N. D. (1962). Tonk, plonk and plink. Analysis, 22(6), 130–134.

[4]
Bernays, P. (1922). Über hilberts gedanken zur grundlegung der arithmetik. Jahresbericht der Deutschen Mathematiker-Vereinigung, 31, 10–19.

[7]
Dummett, M. (1981). Frege: Philosophy of Language. Cambridge, MA: Harvard University Press.

[8]
Dummett, M. (1991). The Logical Basis of Metaphysics. Cambridge, MA: Harvard University Press.

[10]
Jacobs, B. (1999). Categorical Logic and Type Theory. Amsterdam: Elsevier.

[11]
Koslow, A. (2005). A Structuralist Theory of Logic. New York: Cambridge University Press.

[12]
Ladyman, J. & Presnell, S. (2014). Does homotopy type theory provide a foundation for mathematics. The British Journal for the Philosophy of Science, forthcoming.

[13]
Ladyman, J. & Presnell, S. (2015). Identity in homotopy type theory, part I: The justification of path induction. Philosophia Mathematica, 23(3), 386–406.

[14]
Lawvere, F. W. (1969). Adjointness in foundations. Dialectica, 23(3–4), 281–296.

[15]
Lawvere, F. W. (1970). Equality in hyperdoctrines and comprehension schema as an adjoint functor. Applications of Categorical Algebra, 17, 1–14.

[16]
Martin-Löf, P. (1995). Verificationism then and now. In van der Schaar, M., editor. The Foundational Debate: Complexity and Constructivity in Mathematics and Physics. Vienna Circle Institute Yearbook, Vol. 3. Dordrecht: Springer Netherlands, pp. 3–14.

[17]
Martin-Löf, P. (1996). On the meanings of the logical constants and the justifications of the logical laws. Nordic Journal of Philosophical Logic, 1(1), 11–60.

[18]
Maruyama, Y. (2016). Categorical harmony and paradoxes in proof-theoretic semantics. In Piecha, T. and Schroeder-Heister, P., editors. Advances in Proof-Theoretic Semantics. Trends in Logic, Vol. 43. Heidelberg: Springer, pp. 95–114.

[19]
Mayberry, J. (1994). What is required of a foundation for mathematics?
Philosophia Mathematica, 2(1), 16–35.

[20]
Morehouse, E. (2013). An Adjunction-Theoretic Foundation for Proof Search in Intuitionistic First-Order Categorical Logic Programming, Ph.D. Thesis, Wesleyan University.

[21]
Peregrin, J. (2012). What is inferentialism? In Gurova, L., editor. Inference, Consequence, and Meaning: Perspectives on Inferentialism. Newcastle upon Tyne, UK: Cambridge Scholars Publishing, pp. 3–16.

[22]
Peregrin, J. (2014). Inferentialism: Why Rules Matter. New York: Palgrave Macmillan.

[23]
Pfenning, F. & Davies, R. (2001). A judgemental reconstruction of modal logic. Mathematical Structures in Computer Science, 11(4), 511–540.

[24]
Prawitz, D. (1965). Natural Deduction: a Proof-Theoretical Study. Stockholm: Almqvist & Wiksell.

[25]
Prior, A. N. (1960). The runabout inference-ticket. Analysis, 21(2), 38–39.

[26]
Schroeder-Heister, P. (2007). Generalized definitional reflection and the inversion principle. Logica Universalis, 1(2), 355–376.

[27]
Steinberger, F. (2009). Harmony and Logical Inferentialism. Ph.D. Thesis, University of Cambridge.

[28]
Steinberger, F. (2009). Not so stable. Analysis, 69(4), 655–661.

[29]
Stevenson, J. T. (1961). Roundabout the runabout inference-ticket. Analysis, 21(6), 124–128.

[30]
Tennant, N. (1978). Natural Logic. Edinburgh: Edinburgh University Press.

[31]
Tennant, N. (1987). Anti-realism and Logic: Truth as Eternal. Oxford: Clarendon Press.

[32]
Tennant, N. (2007). Inferentialism, logicism, harmony, and a counterpoint. Essays for Crispin Wright: Logic, Language, and Mathematics, 2, 105–132.

[33]
Tennant, N. (2010). Inferential semantics for first-order logic: Motivating rules of inference from rules of evaluation. In Smiley, T. J., Lear, J., and Oliver, A., editors. The Force of Argument: Essays in Honor of Timothy Smiley. London: Routledge, pp. 223–257.

[34]
The Univalent Foundations Program (2013). Homotopy Type Theory: Univalent Foundations of Mathematics. Institute for Advanced Study. Available at: http://homotopytypetheory.org/book.
[35]
Walsh, P. (2015). Justifying Path Induction: An Inferentialist Analysis of Identity Elimination in Homotopy Type Theory. Master’s Thesis, Carnegie Mellon University.