Semantic Foundations of Reductive Reasoning
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915260970041344 |
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| author | Gheorghiu, Alexander V. Pym, David J. |
| author_facet | Gheorghiu, Alexander V. Pym, David J. |
| contents | The development of logic has largely been through the 'deductive' paradigm: conclusions are inferred from established premisses. However, the use of logic in the context of both human and machine reasoning is typically through the dual 'reductive' perspective: collections of sufficient premisses are generated from putative conclusions. We call this paradigm, 'reductive logic'. This expression of logic encompass as diverse reasoning activities as proving a formula in a formal system to seeking to meet a friend before noon on Saturday. This paper is a semantical analysis of reductive logic. In particular, we provide mathematical foundations for representing and reasoning about 'reduction operators'. Heuristically, reduction operators may be thought of as `backwards' inference rules. In this paper, we address their mathematical representation, how they are used in the context of reductive reasoning, and, crucially, what makes them 'valid'. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14758 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Semantic Foundations of Reductive Reasoning Gheorghiu, Alexander V. Pym, David J. Logic in Computer Science Logic The development of logic has largely been through the 'deductive' paradigm: conclusions are inferred from established premisses. However, the use of logic in the context of both human and machine reasoning is typically through the dual 'reductive' perspective: collections of sufficient premisses are generated from putative conclusions. We call this paradigm, 'reductive logic'. This expression of logic encompass as diverse reasoning activities as proving a formula in a formal system to seeking to meet a friend before noon on Saturday. This paper is a semantical analysis of reductive logic. In particular, we provide mathematical foundations for representing and reasoning about 'reduction operators'. Heuristically, reduction operators may be thought of as `backwards' inference rules. In this paper, we address their mathematical representation, how they are used in the context of reductive reasoning, and, crucially, what makes them 'valid'. |
| title | Semantic Foundations of Reductive Reasoning |
| topic | Logic in Computer Science Logic |
| url | https://arxiv.org/abs/2412.14758 |