Abstract. This paper proposes a natural extension of conditional functional dependencies (cfds [14]) and conditional inclusion dependencies (cinds [8]), denoted by cfdp s and cindp s, respectively, by specifying patterns of data values with =, <, ≤, > and ≥ predicates. As data quality rules, cfdp s and cindp s are able to capture errors that commonly arise in practice but cannot be detected by cfds and cinds. We establish two sets of results for central technical problems associated with cfdp s and cindp s. (a) One concerns the satisfiability and implication problems for cfdp s and cindp s, taken separately or together. These are important for, e.g., deciding whether data quality rules are dirty themselves, and for removing redundant rules. We show that despite the increased expressive power, the static analyses of cfdp s and cindp s retain the same complexity as their cfds and cinds counterparts. (b) The other concerns validation of cfdp s and cindp s. We show that given a ...