The Complexity of Causality and Responsibility for Query Answers and non-Answers
by Alexandra Meliou, Wolfgang Gatterbauer, Katherine F. Moore, Dan Suciu
Abstract:
An answer to a query has a well-defined lineage expression (alternatively called how-provenance) that explains how the answer was derived. Recent work has also shown how to compute the lineage of a non-answer to a query. However, the cause of an answer or non-answer is a more subtle notion and consists, in general, of only a fragment of the lineage. In this paper, we adapt Halpern, Pearl, and Chockler's recent definitions of causality and responsibility to define the causes of answers and non-answers to queries, and their degree of responsibility. Responsibility captures the notion of degree of causality and serves to rank potentially many causes by their relative contributions to the effect. Then, we study the complexity of computing causes and responsibilities for conjunctive queries. It is known that computing causes is NP-complete in general. Our first main result shows that all causes to conjunctive queries can be computed by a relational query which may involve negation. Thus, causality can be computed in PTIME, and very efficiently so. Next, we study computing responsibility. Here, we prove that the complexity depends on the conjunctive query and demonstrate a dichotomy between PTIME and NP-complete cases. For the PTIME cases, we give a non-trivial algorithm, consisting of a reduction to the max-flow computation problem. Finally, we prove that, even when it is in PTIME, responsibility is complete for LOGSPACE, implying that, unlike causality, it cannot be computed by a relational query
Citation:
Alexandra Meliou, Wolfgang Gatterbauer, Katherine F. Moore, and Dan Suciu, The Complexity of Causality and Responsibility for Query Answers and non-Answers, PVLDB, vol. 4, no. 1, 2010, pp. 34–45.
Bibtex:
@article{DBLP:journals/pvldb/MeliouGMS11,
    Abstract = {An answer to a query has a well-defined lineage expression
    (alternatively called how-provenance) that explains how the answer was
    derived. Recent work has also shown how to compute the lineage of a
    non-answer to a query. However, the cause of an answer or non-answer is a
    more subtle notion and consists, in general, of only a fragment of the
    lineage. In this paper, we adapt Halpern, Pearl, and Chockler's recent
    definitions of causality and responsibility to define the causes of
    answers and non-answers to queries, and their degree of responsibility.
    Responsibility captures the notion of degree of causality and serves to
    rank potentially many causes by their relative contributions to the
    effect. Then, we study the complexity of computing causes and
    responsibilities for conjunctive queries. It is known that computing
    causes is NP-complete in general. Our first main result shows that all
    causes to conjunctive queries can be computed by a relational query which
    may involve negation. Thus, causality can be computed in PTIME, and very
    efficiently so. Next, we study computing responsibility. Here, we prove
    that the complexity depends on the conjunctive query and demonstrate a
    dichotomy between PTIME and NP-complete cases. For the PTIME cases, we
    give a non-trivial algorithm, consisting of a reduction to the max-flow
    computation problem. Finally, we prove that, even when it is in PTIME,
    responsibility is complete for LOGSPACE, implying that, unlike causality,
    it cannot be computed by a relational query},
    Author = {Alexandra Meliou and Wolfgang Gatterbauer and Katherine F. Moore and Dan Suciu},
    Journal = {PVLDB},
    Number = {1},
    Pages = {34-45},
    Title = {\href{http://www.vldb.org/pvldb/vol4/p34-meliou.pdf}{The Complexity of Causality and Responsibility for Query Answers and non-Answers}},
    Venue = {PVLDB},
    Volume = {4},
    Year = {2010}
}