Rule-based systems process data according to sets of constraints established by the user. The results of these systems is a collection of rule findings that can be used to construct the final product or to assist the user in rendering an informed decision.
The above description may seem all-too-general, as that describes the what most programs do. This is indeed correct: rule-based programming is sufficiently powerful enough to describe any computable system. In fact, the rule-based approach is now being viewed by the mainstream as the preferred method for workflow analysis, process, resource scheduling, service-based systems, etc. Nearly every software system has a set of rules, explicit or implied, to which it adheres. The rule-based programming style model these rule constructs directly and facilitate their manipulation as the system grows and changes.
The traditional approach to building logic systems is to construct a set of clauses where the head of the clause matches a condition and the rest of the clause verifies the match through a set of goals for that match. These clauses are known as rules and a set of rules is a predicate, and this predicate can be used, in turn, as a goal in a new rule. Deductive logic matches problem specifications very closely and is a very effective way to convert a set of requirements into a production system. Some examples of types of problems that are easily modelled in deductive logic are expert systems, planning systems and scheduling systems.
Deductive systems are used when the rules are clear, when the user requires certain outcomes, and are very good at "explaining" what the rule findings are and how they were arrived at.
The opposite approach to a deductive system is an inductive one. Whereas in an deductive system, the user has very exacting control over the process and outcome, in an inductive system, the rules are obtained by deriving the relations between input data and their outcomes, with very little guidance, if any, from the builder of the system. Traditional inductive systems required very clean data and had little tolerance for deviation -- a slight perturbation in the data set could cause the system to fall into an undefined state. Modern inductive systems have taken a different approach: reaping the benefits of recent advances in probability and statistics, these systems (such as Bayesian systems and neural networks) are highly redundant and adaptive. These new systems consistently perform well: they have excellent success narrowing to a classification from apparently unrelated attributes, and they have a high rate of stability, being very fault-tolerant, even in the presence of very noisy data. It is also trivial to convert a statically trained inductive system to one that learns continuously from new inputs and outcomes.
Inductive systems are used when users cannot explain how they arrive at decisions (attributing the outcomes to a "feel" for the situation), and where gradual trends result in eventual changes to outcomes. These systems excel at making the correct decision with a very high degree of confidence, but are poor at explaining what prompted the decision.
Logical Types, LLC uses both deductive and inductive logic to build systems as the needs of the customer demand: