Knowledge Representation and Reasoning Based on Propositional Logic: Experiment on AI Logical Agents

This article explores how AI uses propositional logic to represent knowledge, builds logical agents through rule engines and fact bases, performs accurate reasoning using model checking methods, and learns to encode real-world scenarios into computable logical systems. As a fundamental logical system, propositional logic lays a theoretical foundation for understanding complex knowledge representation methods, and the experimental project demonstrates its applications and limitations in building agents.

One of the core challenges of artificial intelligence is knowledge representation—encoding real-world information into a form understandable by machines. Logic-based representation has become an important direction due to its formal semantics and rigorous reasoning mechanisms, with propositional logic as the foundation. Propositional logic consists of atomic propositions (e.g., "It is raining"), logical connectives (conjunction ∧, disjunction ∨, implication →, etc.). A knowledge base includes facts (known true propositions) and rules (logical relationships between propositions), and the goal of reasoning is to derive new conclusions from the knowledge base.

The experiment uses model checking as the core reasoning method. Principle: For a knowledge base KB and query α, enumerate all truth assignments of propositional variables and check whether all assignments that satisfy KB also satisfy α (KB⊨α). Although its complexity is O(2^n), it is intuitive and guarantees correctness. Comparison with other methods: Resolution reasoning (CNF conversion + resolution rules, suitable for automation but poor readability), forward chaining (fact-driven), backward chaining (goal-driven). The advantage of model checking lies in its simple concept, suitable for teaching and small-scale verification.

The logical agent system built in the experiment includes: 1. Knowledge base construction (supports storage of atomic/compound propositions, CRUD operations, and consistency checks); 2. Logical formula parsing (infix expression processing, operator precedence, abstract syntax tree conversion); 3. Model checking engine (enumerate assignments, evaluate KB satisfiability, verify implication); 4. Real-scene encoding cases (weather reasoning, security systems, diagnostic reasoning), demonstrating how to transform real-world problems into logical systems.

Limitations of propositional logic agents: 1. Insufficient expressive power (cannot represent object relationships, temporal changes, uncertainty); 2. Low reasoning efficiency (exponential complexity of model checking); 3. Knowledge acquisition bottleneck (building an accurate knowledge base requires a lot of manual work). These limitations drive the development of more powerful systems such as first-order logic and temporal logic.

The experiment has important educational value: 1. Formal thinking training (converting natural language to logical formulas); 2. Understanding of logical reasoning (mechanical process of model checking algorithms); 3. Foundation for AI system construction (knowledge representation + reasoning engine pattern); 4. Combination of theory and practice (combining abstract logic with programming implementation).

Applications of propositional logic ideas in modern AI include: 1. Knowledge graphs (logical implication for query reasoning); 2. Rule engines (rule reasoning such as Drools/Jess); 3. Formal verification (system correctness verification in software engineering); 4. Neuro-symbolic AI (combining neural network learning with symbolic reasoning).

Knowledge representation and reasoning based on propositional logic is a classic topic in AI, whose core idea is to simulate human rational thinking through formal representation and rigorous reasoning. Although modern AI has more powerful methods, the foundation laid by propositional logic still has theoretical and practical value. Implementing a logical agent by hand is a valuable experience to deeply understand AI principles, laying the foundation for learning advanced AI technologies.