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We define several canonical problems related to contrastive explanations, each answering a question of the form “Why P but not Q?”. The problems compute causes for both P and Q, explicitly comparing their differences. We investigate the basic properties of our definitions in the setting of propositional logic. We show, inter alia, that our framework captures a cardinality-minimal version of existing contrastive explanations in the literature. Furthermore, we provide an extensive analysis of the computational complexities of the problems. We also implement the problems for CNF-formulas using answer set programming and present several examples demonstrating how they work in practice.

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Why This and Not That? A Logic-Based Framework for Contrastive Explanations

  • 会议论文

  • 发表日期：

    2026年

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  • Tobias Geibinger,
  • Reijo Jaakkola,
  • Antti Kuusisto,
  • Xinghan Liu,
  • Miikka Vilander

摘要

We define several canonical problems related to contrastive explanations, each answering a question of the form “Why P but not Q?”. The problems compute causes for both P and Q, explicitly comparing their differences. We investigate the basic properties of our definitions in the setting of propositional logic. We show, inter alia, that our framework captures a cardinality-minimal version of existing contrastive explanations in the literature. Furthermore, we provide an extensive analysis of the computational complexities of the problems. We also implement the problems for CNF-formulas using answer set programming and present several examples demonstrating how they work in practice.