Gentzenizing Schroeder-Heister's natural extension of natural deduction.

Gentzenizing Schroeder-Heister's Natural Extension of Natural Deduction

In this paper we provide a Gentzen-type formulation of Schroeder-Heister's system of 1]. This system is important from both philosophical and practical points of view: Its philisophical importance is due to the characterization which it provides for the intuitionistic connectives, while the practical one is due to the fact that its notion of higher-order rules and its method of treating the eli...

A Natural Extension of Natural Deduction

One of the main ideas of calculi of natural deduction, as introduced by Jaskowski and Gentzen, is that assumptions may be discharged in the course of a derivation. As regards sentential logic, this conception will be extended in so far as not only formulas but also rules may serve as assumptions which can be discharged. The resulting calculi and derivations with rules of any finite level are in...

Bidirectional Natural Deduction

The goal of this paper is to present a theorem prover able to perform both forward and backward reasoning supported by a well deened formal system. This system for bidirectional reasoning has been proved equivalent to Gentzen's classical system of propositional natural deduction. This paper, primarily aimed at developing a deeper theoretical understanding of bidirectional reasoning, provides ba...

Focused Natural Deduction

Natural deduction for intuitionistic linear logic is known to be full of non-deterministic choices. In order to control these choices, we combine ideas from intercalation and focusing to arrive at the calculus of focused natural deduction. The calculus is shown to be sound and complete with respect to first-order intuitionistic linear natural deduction and the backward linear focusing calculus.

Aristotle'S natural deduction reconsidered