Selective Linear Definite clause resolution (SLD resolution) is a fundamental inference technique used in logic programming, especially in languages like Prolog. It forms the backbone of how these systems answer queries using a knowledge base structured as a set of logical rules, or definite clauses.
To break it down, a *definite clause* is a logical statement that has exactly one positive literal (the conclusion) and any number of negative literals (the conditions or premises). SLD resolution is called “linear” because at each step, it works on a single goal (or subgoal) at a time, creating a linear chain of reasoning. The “selective” part comes from the process of choosing which subgoal to focus on next, which can impact efficiency and the order in which solutions are found.
Here’s how SLD resolution works in practice: Given a query, the inference engine looks for rules in the knowledge base whose conclusions match the current subgoal. When it finds such a rule, it replaces the subgoal with the rule’s conditions, effectively breaking the problem into smaller pieces. This process repeats recursively, working its way through the chain of logic until either all subgoals are satisfied (meaning a solution has been found) or there are no more applicable rules (meaning the query cannot be proven from the knowledge base).
This method is especially powerful because it enables logic programming systems to automatically deduce answers from complex rule sets, without requiring the programmer to specify how the inference should proceed. The key advantage of SLD resolution is its efficiency for definite clauses, as it avoids unnecessary exploration of unrelated possibilities.
In practical terms, SLD resolution is what allows Prolog programs to answer questions like “Who are all the ancestors of Alice?” by chaining together facts and rules about parent relationships. The process is systematic and can be visualized as a search tree, with each branch representing a possible series of inferences. Traversing this tree efficiently is crucial, and the selection strategy (which subgoal to resolve next) can significantly affect both performance and completeness.
While SLD resolution is highly effective for definite clauses, it does not handle more complex logical constructs like negation or disjunctions as naturally. Extensions and variations, such as SLDNF (Selective Linear Definite clause resolution with Negation as Failure), have been developed to address some of these limitations.
Understanding SLD resolution is essential for anyone delving into logic programming, knowledge representation, or automated reasoning. It illustrates how symbolic AI systems can perform logical deductions in a way that is both principled and efficient, serving as a bridge between theoretical computer science and practical applications in artificial intelligence.
