Logic Programming Decomposition

Origin. FGCP's adoption of Prolog and development of KL1 (Kernel Language 1) as the system programming language; influenced by Kowalski's logic programming thesis.

Mechanism. Represents a problem as a set of logical relations (Horn clauses) and computes solutions by resolution — proving the goal by finding variable bindings that satisfy all constraints. The decomposition is declarative: state what must be true, not how to compute it. The inference engine handles search. Complex problems decompose into conjunctions of subgoals, each provable independently.

Procedure. State the problem as a query. Define the domain as facts and rules. Let the resolver work backward from the goal, unifying variables and generating subgoals. If the search space is too large, add constraints to prune branches. If the logic is inefficient, restructure clauses to fail fast — put the most selective conditions first.

Applies to. Configuration, scheduling, symbolic reasoning, and any problem expressible as constraint satisfaction over symbolic structures.

Limitations. Declarative does not mean efficient. The resolution order matters enormously, and naive clause ordering produces combinatorial explosion. Also: negation-as-failure is not logical negation; assuming something is false because it cannot be proved true conflates epistemics with ontology. Works for closed-world domains; fails silently in open-world domains.