Harmonising natural deduction

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

Classical Natural Deduction

In the tradition which considers formal logic as an organon of thought a central role has been played by the “method of analysis”, which amounts to what today, in computer science circles, is called a “bottom-up” or “goaloriented” procedure. Though the method was largely used in the mathematical practice of the ancient Greeks, its fullest description can be found in Pappus (3rd century A.D.), w...

Parsing as Natural Deduction

The logic behind parsers for categorial grammars can be formalized in several different ways. Lambek Calculus (LC) constitutes an example for a natural deduction 1 style parsing method. In natural language processing, the task of a parser usually consists in finding derivations for all different readings of a sentence. The original Lambek Calculus, when it is used as a parser / theorem prover, ...