This comprehensive book provides an adequate framework to establish various calculi of
logical inference. Being an? enriched? system of natural deduction, it helps to formulate …

In proof theory the notion of canonical proof is rather basic, and it is usually taken for granted
that a canonical proof of a sentence must be unique up to certain minor syntactical details …

We present a way of formalizing the intensional identity type based on the notion of
computational paths which will be taken to be proofs of propositional equality, and thus …

As a celebration of the Tractatus 100th anniversary it might be worth revisiting its relation to
the later writings. From the former to the latter, David Pears recalls that “everyone is aware of …

The intention here is that of giving a formal underpinning to the idea of 'meaning-is-
use'which, even if based on proofs, it is rather different from proof-theoretic semantics as in …

The treatment of equality as a type in type theory gives rise to an interesting type-theoretic
structure known asidentity type'. The idea is that, given terms $ a, b $ of a type $ A $, one …

On the basis of a labelled deduction system (LND TRS), we demonstrate how to formalize
the concept of computational paths (sequences of rewrites) as equalities between two terms …

One of the most interesting entities of homotopy type theory is the identity type. It gives rise to
an interesting interpretation of the equality, since one can semantically interpret the equality …

A central problem in proof-theory is that of finding criteria for identity of proofs, that is, for
when two distinct formal derivations can be taken as denoting the same logical argument. In …

The main objective of this work is to study mathematical properties of computational paths.
Originally proposed by de Queiroz\& Gabbay (1994) assequences or rewrites' …