Natural deduction and arbitrary objects

Natural deduction and arbitrary objects

This paper is an abridged and simplified version of my monograph Reasoning with Arbitrary Objects [4]. It may be read by the diligent as a preparation for the longer work or by the indolent as a substitute for it. But the reader, in either case, may find it helpful to consult the paper, A Defence of Arbitrary Objects [3], for general philosophical orientation. This paper deals with certain prob...

Neuro-Evolution and Natural Deduction

Natural deduction is essentially a sequential decision task, similar to many game-playing tasks. Such a task is well suited to benefit from the techniques of neuro-evolution. Symbiotic, Adaptive Neuro-Evolution (SANE)(Moriarty and Miikkulainen 1996) has proven successful at evolving networks for such tasks. This paper will show that SANE can be used to evolve a natural deduction system on a neu...

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