In this section we study arithmetical provability semantics, which, from the be­ginning, was the intended Godel semantics for S4 and for the Logic of Proofs.

Because the latter is the only justification logic discussed in this chapter, we will be using terminology associated with the Logic of Proofs. In particular, justification terms will generally be called proof terms or proof polynomials.

9.1

More on the topic In this section we study arithmetical provability semantics, which, from the be­ginning, was the intended Godel semantics for S4 and for the Logic of Proofs.:

1. Artemov S., Fitting M.. Justification Logic: Reasoning with Reasons. Cambridge: Cambridge University Press,2019. — 271 p., 2019