Knowledge Representation, Propositional Logic, and Expert Systems in AI

Beyond searching through future states, an intelligent agent needs a structured way to store facts about the world and deduce new truths from existing facts. In Chapter 1.4—completing Module 1 of our AI Fundamentals series on aimlrevisited.com—we explore Semantic Networks, Knowledge Graphs, Propositional and First-Order Logic, Forward vs. Backward Chaining, and Expert Systems in Python.

1. Core Knowledge Representation Structures

2. Propositional Logic, First-Order Logic, and Inference

• Propositional Logic: Combines boolean facts using AND, OR, NOT, and IF-THEN implication. Its core deduction rule is Modus Ponens: given P -> Q and P, deduce Q.
• First-Order Logic (FOL): Adds objects, predicates, and universal (for all) or existential (there exists) quantifiers to express general rules across entire classes of entities.
• Forward Chaining (Data-Driven): Starts from known sensor facts and fires satisfied IF-THEN rules to infer new conclusions—ideal for real-time monitoring and alerting.
• Backward Chaining (Goal-Driven): Starts from a target hypothesis and works backward to check whether supporting premises hold—ideal for diagnostic troubleshooting.

3. Hands-On Python Tutorial: Forward-Chaining Expert System

def forward_chain(initial_facts, rules):
    known = set(initial_facts)
    trace = []
    fired = True
    while fired:
        fired = False
        for name, premises, conclusion in rules:
            if premises.issubset(known) and conclusion not in known:
                known.add(conclusion)
                trace.append(f"[{name}] {sorted(premises)} -> '{conclusion}'")
                fired = True
    return known, trace

cloud_kb = [
    ("R1: Bottleneck", {"db_cpu_high", "slow_queries"}, "database_bottleneck"),
    ("R2: Pool Full", {"database_bottleneck", "high_traffic"}, "connection_pool_full"),
    ("R3: Auto-Scale", {"connection_pool_full"}, "scale_read_replicas_and_alert"),
]

facts, trace = forward_chain({"db_cpu_high", "slow_queries", "high_traffic"}, cloud_kb)
for step in trace:
    print(step)

4. Key Takeaways & FAQ

• Why did Expert Systems give way to Machine Learning? Hand-coding thousands of deterministic rules hit the Knowledge Acquisition Bottleneck when dealing with noisy, probabilistic real-world data.
• How are Knowledge Graphs used with LLMs today? GraphRAG combines Knowledge Graphs with LLMs to ground answers in verified facts.
• Next up in Module 2 (Chapter 2.1): Linear Algebra for AI: Scalars, Vectors, Matrices, and Tensors.