Gheorghiu, Alexander V;
Pym, David J;
(2025)
Semantic Foundations of Reductive Reasoning.
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10.1007/s11245-025-10211-6.
(In press).
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Abstract
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.
| Type: | Article |
|---|---|
| Title: | Semantic Foundations of Reductive Reasoning |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s11245-025-10211-6 |
| Publisher version: | https://doi.org/10.1007/s11245-025-10211-6 |
| Language: | English |
| Additional information: | Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| Keywords: | Arts & Humanities, Philosophy, Logical systems, Reductive logic, Proof-search, Theorem proving, Tactics, Tactical proof, Proof-theoretic semantics, LOGIC |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10213117 |
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