A computational model of Lakatos-style reasoning
A computational model of Lakatos-style reasoning
复制标题
拉卡托斯式推理的计算模型
DOI：
10.1007/3-540-48834-0
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
A. Pease
中科院分区：
文献类型：
--
作者：
A. Pease
Lakatos概述了数学发现和理由的理论，该理论提出了通过数学家之间的相互作用逐渐发展的概念，猜想和证据的方式。 。计算代表Lakatos的理论，（ii）这样做是有用的。理论形成系统，可以形成概念并制作概念，从而为所提供的感兴趣的对象所构成的概念。彼此。计算机计划。理论还通过评估他的理论来测试有关它的假设，并根据几个理论家提出的标准评估我们的扩展计算理论精炼概念，证明和概念定义需要一种灵活性，这在处理不明问题的领域（例如理论形成）中固有有用。自动将开放猜想修改为可以证明的猜想，这是对自动定理提供的有价值的贡献。
Lakatos outlined a theory of mathematical discovery and justification, which suggests ways in which concepts, conjectures and proofs gradually evolve via interaction between mathematicians. Different mathematicians may have different interpretations of a conjecture, examples or counterexamples of it, and beliefs regarding its value or theoremhood. Through discussion, concepts are refined and conjectures and proofs modified. We hypothesise that (i) it is possible to computationally represent Lakatos’s theory, and (ii) it is useful to do so. In order to test our hypotheses we have developed a computational model of his theory. Our model is a multiagent dialogue system. Each agent has a copy of a pre-existing theory formation system, which can form concepts and make conjectures which empirically hold for the objects of interest supplied. Distributing the objects of interest between agents means that they form different theories, which they communicate to each other. Agents then find counterexamples and use methods identified by Lakatos to suggest modifications to conjectures, concept definitions and proofs. Our main aim is to provide a computational reading of Lakatos’s theory, by interpreting it as a series of algorithms and implementing these algorithms as a computer program. This is the first systematic automated realisation of Lakatos’s theory. We contribute to the computational philosophy of science by interpreting, clarifying and extending his theory. We also contribute by evaluating his theory, using our model to test hypotheses about it, and evaluating our extended computational theory on the basis of criteria proposed by several theorists. A further contribution is to automated theory formation and automated theorem proving. The process of refining conjectures, proofs and concept definitions requires a flexibility which is inherently useful in fields which handle ill-specified problems, such as theory formation. Similarly, the ability to automatically modify an open conjecture into one which can be proved, is a valuable contribution to automated theorem proving.