Semantic Foundations of Reductive Reasoning.

IF 2 2区哲学 0 PHILOSOPHY

TOPOI-AN INTERNATIONAL REVIEW OF PHILOSOPHY Pub Date : 2026-01-01 Epub Date: 2025-05-20 DOI:10.1007/s11245-025-10211-6

Alexander V Gheorghiu, David J Pym

引用次数: 0

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.

查看原文本刊更多论文

还原推理的语义基础。

逻辑的发展很大程度上是通过演绎范式：结论是从既定的前提推断出来的。然而，在人类和机器推理的背景下，逻辑的使用通常是通过对偶还原的视角：从假定的结论中产生充分前提的集合。我们称之为范式，还原逻辑。这种逻辑表达包含了各种各样的推理活动，从证明一个正式系统中的公式到寻求在周六中午之前见到一个朋友。本文是对还原逻辑的语义分析。特别是，我们为约简算子的表示和推理提供了数学基础。启发式地，约简运算符可以被认为是“向后”推理规则。在本文中，我们讨论了它们的数学表示，它们如何在还原推理的背景下使用，以及至关重要的是，是什么使它们有效。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

TOPOI-AN INTERNATIONAL REVIEW OF PHILOSOPHY PHILOSOPHY-

CiteScore

3.10

自引率

7.10%

发文量

期刊介绍： Topoi''s main assumption is that philosophy is a lively, provocative, delightful activity, which constantly challenges our received views, relentlessly questions our inherited habits, painstakingly elaborates on how things could be different, in other stories, in counterfactual situations, in alternative possible worlds. Whatever its ideology, whether with the intent of uncovering a truer structure of reality or of soothing our anxiety, of exposing myths or of following them through, the outcome of philosophical activity is always the destabilizing, unsettling generation of doubts, of objections, of criticisms. It follows that this activity is intrinsically a ''dialogue'', that philosophy is first and foremost philosophical discussion, that it requires bringing out conflicting points of view, paying careful, sympathetic attention to their structure, and using this dialectic to articulate one''s approach, to make it richer, more thoughtful, more open to variation and play. And it follows that the spirit which one brings to this activity must be one of tolerance, of always suspecting one''s own blindness and consequently looking with unbiased eye in every corner, without fearing to pass a (fallible) judgment on what is there but also without failing to show interest and respect. Topoi''s structure is a direct expression of this view. To maximize discussion, we devote most or all of this issue to a single topic. And, since discussion is only interesting when it is conducted seriously and responsibly, we usually request the collaboration of a guest-editor, an expert who will identify contributors and interact with them in a constructive way. Because we do not feel tied to any definite philosophical theme (or set of them), we choose the topic with absolute freedom, looking for what is blossoming and thriving, occasionally betting on what might - partly through our attention - ''begin'' to blossom and thrive. And because we do not want our structur e to become our own straightjacket, we are open to contributions not fitting the ''topos'', and do not rule out in principle the possibility of topic-less issues.