This paper presents a novel approach to automated reasoning in System P. System P axiomatizes a set of core properties that describe reasoning with defeasible assertions (defaults) of the form: if α then normally (usually or typically) β. A logic with approximate conditional probabilities is used for modeling default rules. That representation enables reducing the satisfiability problem for default reasoning to the (non)linear programming problem. The complexity of the obtained instances requires the application of optimization approaches. The main heuristic that we use is the Bee Colony Optimization (BCO). As an alternative to BCO, we use Simplex method and Fourier-Motzkin Elimination method to solve linear programming problems. All approaches are tested on a set of default reasoning examples that can be found in literature. The general impression is that Fourier-Motzkin Elimination procedure is not suitable for practical use due to substantially high memory usage and time consuming execution, the Simplex method is able to provide useful results for some of the tested examples, while heuristic approach turns out to be the most appropriate in terms of both success rate and time needed for reaching conclusions. In addition, the BCO method was tested on a set of randomly generated examples of larger dimensions, illustrating its practical usability.

本文提出了一种新的系统P中自动推理的方法。系统P公理化了一组核心属性，这些核心属性使用以下形式的不可行断言（默认值）描述了推理：如果α，则通常（通常或通常）β。具有近似条件概率的逻辑用于对默认规则进行建模。该表示使得能够将针对默认推理的可满足性问题减少到（非线性）编程问题。获得的实例的复杂性要求应用优化方法。我们使用的主要启发式方法是Bee Colony Optimization（BCO）。作为BCO的替代方法，我们使用Simplex方法和Fourier-Motzkin消除方法来解决线性规划问题。所有方法都在一组默认推理示例上进行了测试，这些示例可以在文献中找到。总体印象是由于大量内存使用和耗时的执行，Fourier-Motzkin消除程序不适合实际使用，Simplex方法能够为某些测试示例提供有用的结果，从成功率和得出结论所需的时间来看，启发式方法最合适。此外，BCO方法在一组随机生成的较大尺寸的示例上进行了测试，从而说明了其实用性。