What Are the Inference Steps Really Stepping on? Brief History of Two-Dimensional Inference (konference)
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| Year of publication | 2013 |
| Type | Appeared in Conference without Proceedings |
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| Description | Our main aim is to examine various shapes that inference steps took in the not so distant past. In particular, we focus on similarities that can be found in the works of Frege (1879), Tichý (1988) and de Queiroz, de Oliveira and Gabbay (2011). Their general approach to logical inference constitutes quite distinct school of thought which may be roughly dubbed as two-dimensional conception of inference (deduction). Frege himself, however, never explicitly used the term two-dimensional inference, unlike Tichý and de Queiroz, de Oliveira and Gabbay, who view him as their main source of inspiration. Although Tichý and de Queiroz, de Oliveira and Gabbay slightly differ in their motivations for the introduction of the so called two-dimensional inference and despite the fact that they rely on different proof theories Tichý prefers as a basis for his deduction system Gentzen's sequent calculus, while de Queiroz, de Oliveira and Gabbay favour natural deduction), deep conceptual similarities can be found between their notions of two-dimensional inference, which can be indeed traced back to the father of modern logic, Frege. In other words, all of them seem to share common goal: do better "book-keeping" of proof steps, so that no unacknowledged assumptions get in the inferential sequence. And by better book-keeping methods for inference we mean more rigorous, elaborate and extended way of recording inference steps, i.e., explicit tracking of all the assumptions, which have been previously made, withdrawn or are still in force. As Frege put it himself in the preface of his Begriffsschrift, we need to keep the chain of inferences free of gaps. |
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