Declarative problem solving attempts to tackle problems using a high-level representation of the expert knowledge on the problem at hand. In a logical setting such a declarative representation would employ an alphabet of constants, functions and predicate symbols that naturally represent objects, functions and relationships between these objects in the domain of discourse. In a truly declarative representation of the problem, the logic theory contains knowledge known to be true about the problem domain rather than information on how to solve tasks, i.e. it does not contain deยฎnitions of concepts describing problem solving methods. In such a setting, problem solving in many cases consists simply in ยฎlling in missing information. This could for example be ยฎnding the extension of a predicate or some logical relation between existing predicates.
In such cases, therefore, problem solving with a declarative representation consists of extending the existing description (e.g., logical theory) of the problem to a new one such that the problem goal is satisยฎed in this extended description. This process is otherwise known by the name of abduction. In this logical setting, abduction as a problem solving method assumes that the general data structure for the solution to a problem (or solution carrier) is at the predicate level and hence a solution is described in the same terms and level as the problem itself.
In artiยฎcial intelligence a prototypical problem where abduction is used is that of diagnosis. Here abduction is employed to produce an explanation for the observed, often faulty, behavior of the system in terms of primitive causes according to some theory describing how primitive faults in a system propagate and lead to observable faults. Similarly, in the problem of knowledge assimilation a new piece of information is assimilated via abduction by ยฎnding a coherent reason for this information according to the current state of the knowledge. In planning, the task of reaching