Variable declarations in natural deduction

Variable declarations in natural deduction

We propose the use of variable declarations in natural deduction. A variable declaration is a line in a derivation that introduces a new variable into the derivation. Semantically, it can be regarded as declaring that the variable denotes an element of the universe of discourse. Undeclared variables, in contrast, do not denote anything, and may not occur free in any formula in the derivation. A...

Experiments in Linear Natural Deduction

We investigate several fragments of multiplicative linear logic, in a natural deduction setting and with the aim of a better understanding of the par connective. We study, first, a pre-tensorial calculus, which is strengthened then in the standard tensorial fragment. The addition of a further pre-tensorial connective yields (a natural deduction version of) Full Intuitionistic Linear Logic. A fu...

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