Unification Algorithm and Clause Normal Form Conversion

Lecture 21 of CS607 Artificial Intelligence details the mathematical algorithms required to apply resolution to First-Order Predicate Logic. First, students master the 9-step conversion of arbitrary FOPL formulas into Clause Normal Form (CNF): eliminating implications, moving negations inward via De Morgan's laws, standardizing variables apart, Skolemization (eliminating existential quantifiers by substituting Skolem constants or Skolem functions depending on universally quantified variables), dropping universal quantifiers, and distributing disjunction over conjunction. Next, the lecture explores Unification, the algorithmic process of finding variable substitutions theta that make two distinct predicate expressions syntactically identical. Students study the recursive Unification Algorithm, learning to calculate the Most General Unifier (MGU) and avoid the circular variable assignment trap through the Occurs Check. The discussion highlights how heuristic evaluation functions guide search algorithms toward goal states while dramatically reducing computational overhead. Key concepts such as chromosome encoding, fitness proportional selection, and genetic diversity preservation are analyzed in evolutionary computation. The lecture details formal logic inference mechanisms, demonstrating how resolution refutation and unification derive valid theorems from clausal knowledge bases. Production rule architectures are analyzed to understand how forward chaining and backward chaining drive automated expert diagnostic systems. CLIPS rule-based programming constructs provide practical engineering frameworks for managing working memory facts and agenda activations. Fuzzy membership functions and linguistic variables are formulated to model real-world vagueness and human approximate reasoning mathematically. Defuzzification techniques such as center of gravity and mean of maxima are applied to convert fuzzy inference outputs into crisp operational control signals. Supervised learning algorithms are contrasted regarding inductive bias, hypothesis space representations, and generalization capabilities on unseen data. Information theoretic metrics including entropy and information gain are computed to construct optimal decision trees using the ID3 algorithm. The curriculum traces the evolutionary transition from single-layer linear perceptrons to multi-layer feedforward networks trained via backpropagation. Practical considerations for activation function selection, learning rates, and gradient descent convergence provide rigorous quantitative decision support. Scholars examine how automated planning algorithms decompose high-level goals into partially ordered action sequences with verified causal links.