In this work we propose a multi-valued extension of logic programs under the
stable models semantics where each true atom in a model is associated with a
set of justifications. These justifications are expressed in terms of causal
graphs formed by rule labels and edges that represent their application
ordering. For positive programs, we show that the causal justifications
obtained for a given atom have a direct correspon- dence to (relevant)
syntactic proofs of that atom using the program rules involved in the graphs.
The most interesting contribution is that this causal information is obtained
in a purely semantic way, by algebraic op- erations (product, sum and
application) on a lattice of causal values whose ordering relation expresses
when a justification is stronger than another. Finally, for programs with
negation, we define the concept of causal stable model by introducing an
analogous transformation to Gelfond and Lifschitz's program reduct. As a
result, default negation behaves as "absence of proof" and no justification is
derived from negative liter

本文提出一种基于稳定模型语义的逻辑程序的多值扩展，其中每个模型中的真实原子都与一组证明相关联，这些证明是由规则标签形成的因果图表示它们的应用顺序而表达的。通过在因果值的格子上进行代数运算（乘积，和，应用），可以以纯粹语义的方式获得这种因果信息。对于带否定的程序，引入一种类似的转换来定义因果稳定模型。