Semantic foundations of reductive reasoning
Semantic foundations of reductive reasoning
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.
Logical systems, Tactics, Reductive logic, Tactical proof, Theorem proving, Proof-search, Proof-theoretic semantics
Gheorghiu, Alexander V.
4569dbd7-8426-4631-80a1-424e922436da
Pym, David J.
dcd2c0b6-80dd-4486-9649-8f0ee547d110
20 May 2025
Gheorghiu, Alexander V.
4569dbd7-8426-4631-80a1-424e922436da
Pym, David J.
dcd2c0b6-80dd-4486-9649-8f0ee547d110
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.
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Accepted/In Press date: 17 April 2025
e-pub ahead of print date: 20 May 2025
Published date: 20 May 2025
Keywords:
Logical systems, Tactics, Reductive logic, Tactical proof, Theorem proving, Proof-search, Proof-theoretic semantics
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Local EPrints ID: 502233
URI: http://eprints.soton.ac.uk/id/eprint/502233
ISSN: 0167-7411
PURE UUID: b147ad79-32bb-4c80-8ede-773dd0cd5f80
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Date deposited: 18 Jun 2025 16:46
Last modified: 04 Sep 2025 02:43
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Author:
Alexander V. Gheorghiu
Author:
David J. Pym
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