This paper presents a logic language for expressing search and optimization problems. Specifically, first a language obtained by extending (positive) DATALOG with intuitive and efficient constructs (namely, stratified negation, constraints, and exclusive disjunction) is introduced. Next, a further restricted language only using a restricted form of disjunction to define (nondeterministically) subsets (or partitions) of relations is investigated. This language, called atalog, captures the power of DATALOG¬ in expressing search and optimization problems. A system prototype implementing atalog is presented. The system translates atalog queries into Optimization Programming Language (OPL) programs which are executed by the ILOG OPL Development Studio. Our proposal combines easy formulation of problems, expressed by means of a declarative logic language, with the efficiency of the ILOG System. Several experiments show the effectiveness of this approach.

Action description languages, such as and ℬ (Gelfond and Lifschitz, Electronic Transactions on Artificial Intelligence, 1998, vol. 2, pp. 193—210), are expressive instruments introduced for formalizing planning domains and planning problem instances. The paper starts by proposing a methodology to encode an action language (with conditional effects and static causal laws), a slight variation of ℬ, using Constraint Logic Programming over Finite Domains. The approach is then generalized to raise the use of constraints to the level of the action language itself. A prototype implementation has been developed, and the preliminary results are presented and discussed.