Towards a More General Concept of Inference
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The main objective of this paper is to sketch unifying conceptual and formal framework for inference that is able to explain various proof techniques without implicitly changing the underlying notion of inference rules. We base this framework upon the so-called two-dimensional, i.e., deduction to deduction, account of inference introduced by Tichý in his seminal work The Foundation’s of Frege’s Logic (1988). Consequently, it will be argued that sequent calculus provides suitable basis for such general concept of inference and therefore should not be seen just as technical tool, but philosophically well-founded system that can rival natural deduction in terms of its “naturalness”.
Mathematics Subject Classification (2010)Primary 03F03 03A05 Secondary 03B99 01A60 01-01 03-01 03-03
KeywordsProof theory inference two-dimensional inference 2D inference inference rule natural deduction sequent calculus Tichý Frege
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