In this paper, we introduce the convex fragment of Łukasiewicz logic and discuss its possible applications in different learning schemes. The provided theoretical results are highly general because they can be exploited in any learning framework involving logical constraints. The method is of particular interest since the fragment guarantees to deal with convex constraints, which are shown to be equivalent to a set of linear constraints. Within this framework, we are able to formulate learning with kernel machines as well as collective classification as a quadratic programming problem.

中文翻译：

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用于学习和推理的凸逻辑片段

在本文中，我们介绍了 Łukasiewicz 逻辑的凸片段，并讨论了它在不同学习方案中的可能应用。所提供的理论结果非常通用，因为它们可以在任何涉及逻辑约束的学习框架中加以利用。该方法特别令人感兴趣，因为片段保证处理凸约束，这些约束被证明等效于一组线性约束。在这个框架内，我们能够将使用内核机器的学习以及作为二次规划问题的集体分类公式化。