, Volume 31, Issue 1, pp 77-85

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Proof-Theoretic Semantics, Self-Contradiction, and the Format of Deductive Reasoning

  • Peter Schroeder-HeisterAffiliated withWilhelm-Schickard-Institut für Informatik, Universität Tübingen Email author 


From the point of view of proof-theoretic semantics, it is argued that the sequent calculus with introduction rules on the assertion and on the assumption side represents deductive reasoning more appropriately than natural deduction. In taking consequence to be conceptually prior to truth, it can cope with non-well-founded phenomena such as contradictory reasoning. The fact that, in its typed variant, the sequent calculus has an explicit and separable substitution schema in form of the cut rule, is seen as a crucial advantage over natural deduction, where substitution is built into the general framework.


Proof-theoretic semantics Paradoxes Sequent calculus Natural deduction Cut rule