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Causal Graph Justifications of Logic Programs*


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 correspondence 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 operations (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 literals, something that turns out convenient for elaboration tolerance, as we explain with a running example.

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This research was partially supported by Spanish MEC project TIN2009-14562-C05-04, Xunta projects GPC2013/070 and INCITE 2011, Inditex-University of Corunna 2013 grants and the Austrian Science Fund (FWF) project P24090.

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Theory and Practice of Logic Programming
  • ISSN: 1471-0684
  • EISSN: 1475-3081
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CABALAR et al.
Causal Graph Justifications of Logic Programs

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