A natural deduction system for first degree entailment

Download PDF

Allard Tamminga, Koji Tanaka

Published: 20 Mar 1999, Last Modified: 24 Feb 2026Notre Dame Journal of Formal LogicEveryoneCC BY 4.0
Abstract: This paper is concerned with a natural deduction system for First Degree Entailment (FDE). First, we exhibit a brief history of FDE and of combined systems whose underlying idea is used in developing the natural deduction system. Then, after presenting the language and a semantics of FDE, we develop a natural deduction system for FDE. We then prove soundness and completeness of the system with respect to the semantics. The system neatly represents the four-valued semantics for FDE.