The use of integrity constraints to perform Semantic Query Optimization (SQO) in deductive databases can be formalized in a way similar to the use of integrity constraints in Abductive Logic Programming (ALP) and the use of Constraint Handling Rules in Constraint Logic Programming (CLP). Based on this observation and on the similar role played by, respectively, extensional, abducible and constraint predicates in SQO, ALP and CLP, we present a unified framework from which (variants of) SQO, ALP and CLP can be obtained as special instances. The framework relies on a proof procedure which combines backward reasoning with logic programming clauses and forward reasoning with integrity constraints.