{"type":"ScholarlyArticle","title":"On Quantifying Literals in Boolean Logic and its Applications to Explainable AI (Extended Abstract)","authors":[{"name":"Adnan Darwiche","slug":"adnan-darwiche","given":"Adnan","family":"Darwiche","affiliation":"Computer Science Department , UCLA"},{"name":"Pierre Marquis","slug":"pierre-marquis","given":"Pierre","family":"Marquis","affiliation":"Univ. Artois , CNRS , CRIL; Institut Universitaire de France"}],"abstract":"Quantified Boolean logic results from adding operators to Boolean logic for existentially and universally quantifying variables. This extends the reach of Boolean logic by enabling a variety of applications that have been explored over the decades. The existential quantification of literals (variable states) and its applications have also been studied in the literature. We complement this by studying universal literal quantification and its applications, particularly to explainable AI. We also provide a novel semantics for quantification and discuss the interplay between variable/literal and existential/universal quantification. We further identify classes of Boolean formulas and circuits that allow efficient quantification. Literal quantification is more fine-grained than variable quantification, which leads to a refinement of quantified Boolean logic with literal quantification as its primitive.","doi":"10.24963/ijcai.2022/797","url":"https://ijcai.org/proceedings/2022/797","pdf":"https://ijcai.org/proceedings/2022/0797.pdf","markdown":"https://ijcai.org/proceedings/2022/797.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/797","volume":{"slug":"2022","title":"Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2022","url":"https://ijcai.org/proceedings/2022/","year":2022,"location":"Vienna","dates":"23-29 July 2022","editors":"Luc De Raedt","isbn":"978-1-956792-00-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2022"},"section":"Journal Track","track":"Journal Track","number":797,"pages":{"first":5718,"last":5721},"keywords":["Knowledge Representation and Reasoning: Knowledge Compilation and Tractable Languages","Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving","AI Ethics, Trust, Fairness: Explainability and Interpretability"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38987246","length_sec":95,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38985389","length_sec":685,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Audemard et al., 2020] Gilles Audemard, Frédéric Koriche, and Pierre Marquis. On tractable XAI queries based on compiled representations. In Proc. of KR'20, pages 838- 849, 2020.","title":"On tractable XAI queries based on compiled representations","authors":"Audemard","year":"2020","venue":"Proc. of KR'20","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Boole, 1854] G. Boole. An investigation of the laws of thought. Walton and Maberley, London, 1854.","title":"An investigation of the laws of thought","authors":"G Boole","year":"1854","venue":"Walton and Maberley","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Chan and Darwiche, 2003] Hei Chan and Adnan Darwiche. Reasoning about Bayesian network classifiers. In Proc. of UAI'03, pages 107-115, 2003.","title":"Reasoning about Bayesian network classifiers","authors":"Chan, Darwiche ; ] Hei Chan, Adnan Darwiche","year":"2003","venue":"Proc. of UAI'03","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Choi et al., 2020] Arthur Choi, Andy Shih, Anchal Goy- anka, and Adnan Darwiche. On symbolically encoding the behavior of random forests. In Proc. of FoMLAS'20, 3rd Workshop on Formal Methods for ML-Enabled Au- tonomous Systems, 2020.","title":"On symbolically encoding the behavior of random forests","authors":"Arthur Choi, Andy Shih, Anchal Goyanka, Adnan Darwiche","year":"2020","venue":"Proc. of FoMLAS'20, 3rd Workshop on Formal Methods for ML-Enabled Autonomous Systems","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Darwiche and Hirth, 2020] Adnan Darwiche and Auguste Hirth. On the reasons behind decisions. In Proc. of ECAI'20, pages 712-720, 2020.","title":"On the reasons behind decisions","authors":"Hirth Darwiche, Adnan Darwiche, Auguste Hirth","year":"2020","venue":"Proc. of ECAI'20","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Darwiche and Marquis, 2021] Adnan Darwiche and Pierre Marquis. On quantifying literals in boolean logic and its applications to explainable AI. J. Artif. Intell. Res., 72:285-328, 2021.","title":"On quantifying literals in boolean logic and its applications to explainable AI","authors":"Marquis ; Darwiche, Adnan Darwiche, Pierre Marquis","year":"2021","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Ignatiev et al., 2019a] Alexey Ignatiev, Nina Narodytska, and João Marques-Silva. Abduction-based explanations for machine learning models. In Proc. of AAAI'19, pages 1511-1519, 2019.","title":"Abduction-based explanations for machine learning models","authors":"Ignatiev","year":"2019","venue":"Proc. of AAAI'19","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Ignatiev et al., 2019b] Alexey Ignatiev, Nina Narodytska, and João Marques-Silva. On relating explanations and ad- versarial examples. In Proc. of NeurIPS'19, pages 15857- 15867, 2019.","title":"On relating explanations and adversarial examples","authors":"Ignatiev","year":"2019","venue":"Proc. of NeurIPS'19","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Lang et al., 2003] Jérôme Lang, Paolo Liberatore, and Pierre Marquis. Propositional independence: Formula- variable independence and forgetting. J. Artif. Intell. Res., 18:391-443, 2003.","title":"Propositional independence: Formulavariable independence and forgetting","authors":"Jérôme Lang, Paolo Liberatore, Pierre Marquis","year":"2003","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Lin and Reiter, 1994] F. Lin and R. Reiter. Forget it! In Proc. of AAAI Fall Symposium on Relevance, pages 154- 159, 1994.","title":"Forget it!","authors":"F Lin, R Reiter","year":"1994","venue":"Proc. of AAAI Fall Symposium on Relevance","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Narodytska et al., 2018] Nina Narodytska, Shiva Prasad Kasiviswanathan, Leonid Ryzhyk, Mooly Sagiv, and Toby Walsh. Verifying properties of binarized deep neural net- works. In Proc. of AAAI'18, pages 6615-6624, 2018.","title":"Verifying properties of binarized deep neural networks","authors":"Nina Narodytska, Shiva Prasad Kasiviswanathan, Leonid Ryzhyk, Mooly Sagiv, Toby Walsh","year":"2018","venue":"Proc. of AAAI'18","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Papadimitriou, 1994] Christos H. Papadimitriou. Computa- tional complexity. Addison-Wesley, 1994.","title":"Computational complexity","authors":"Christos H Papadimitriou","year":"1994","venue":null,"doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Shi et al., 2020] Weijia Shi, Andy Shih, Adnan Darwiche, and Arthur Choi. On tractable representations of binary neural networks. In Proc. of KR'20, pages 882-892, 2020.","title":"On tractable representations of binary neural networks","authors":"Weijia Shi, Andy Shih, Adnan Darwiche, Arthur Choi","year":"2020","venue":"Proc. of KR'20","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Shih et al., 2018] Andy Shih, Arthur Choi, and Adnan Dar- wiche. A symbolic approach to explaining Bayesian net- work classifiers. In Proc. of IJCAI'18, pages 5103-5111, 2018.","title":"A symbolic approach to explaining Bayesian network classifiers","authors":"Andy Shih, Arthur Choi, Adnan Darwiche","year":"2018","venue":"Proc. of IJCAI'18","doi":null,"url":null,"internal_url":"/proceedings/2018/708"},{"position":15,"raw":"[Shih et al., 2019] Andy Shih, Arthur Choi, and Adnan Dar- wiche. Compiling Bayesian network classifiers into deci- sion graphs. In Proc. of AAAI'19, pages 7966-7974, 2019.","title":"Compiling Bayesian network classifiers into decision graphs","authors":"Andy Shih, Arthur Choi, Adnan Darwiche","year":"2019","venue":"Proc. of AAAI'19","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Stockmeyer, 1977] Larry J. Stockmeyer. The polynomial- time hierarchy. Theoretical Computer Science, 3:1-22, 1977.","title":"The polynomialtime hierarchy","authors":"Larry J Stockmeyer","year":"1977","venue":"Theoretical Computer Science","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Weber, 1986] Andreas Weber. Updating propositional for- mulas. In Proc. of EDS'86, 1st Int. Conf. on Expert Database Systems, pages 487-500, 1986.","title":"Updating propositional formulas","authors":"Andreas Weber","year":"1986","venue":"Proc. of EDS'86, 1st Int. Conf. on Expert Database Systems","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}