Knowledge Representation & Reasoning

The symbolic dream

If intelligence is manipulating knowledge, then: write facts in a formal language, add inference rules, and correct conclusions follow mechanically. This program — knowledge representation & reasoning (KR&R) — dominated AI's first decades and still runs inside databases, verification tools, and knowledge graphs today.

Logic in two sizes

Propositional logic — whole statements as atoms (P = "it rains", Q = "streets wet") joined by AND/OR/NOT/IMPLIES. Inference chains implications: from P and P→Q, conclude Q (modus ponens).

First-order logic adds objects, relations and quantifiers, expressing real generalizations:

$\forall x\; \big(\text{Bird}(x) \land \neg\text{Penguin}(x) \rightarrow \text{CanFly}(x)\big)$

Logical reasoning is sound (true premises → true conclusions, guaranteed) — a property no neural network offers. The costs: inference can be computationally explosive, and the world resists tidy axioms. Classic pain points: exceptions (birds fly… except penguins, ostriches, oiled birds, cartoon birds — "non-monotonic" reasoning where new facts retract old conclusions) and uncertainty (logic says true/false; reality says "probably" — the gap probability theory fills, which is why Bayesian networks married the two traditions).

Knowledge engineering at scale

• Expert systems (the 1980s boom): IF-THEN rule bases + an inference engine. MYCIN diagnosed blood infections better than junior doctors — and exposed the knowledge acquisition bottleneck: experts can't articulate their intuition as rules, and rule #9,001 breaks rule #217.
• Knowledge graphs — the tradition's thriving descendant: billions of (subject, relation, object) triples, e.g. (Einstein, bornIn, Ulm). Google's box answering "how tall is the Eiffel Tower" queries one; they power product catalogs, drug-interaction checks and increasingly ground LLM answers in verified facts.
• Automated planning — search meets logic: given actions with preconditions and effects (STRIPS formalism), derive a step sequence achieving a goal. Runs logistics, spacecraft (NASA's Deep Space 1 flew with an onboard planner), and factory scheduling.

The common-sense wall, and the pendulum

Decades of effort (the Cyc project hand-coded millions of common-sense facts for 40 years) never captured what every child knows: dropped glasses break, people in queues are waiting, water makes things wet. The paradox: the knowledge easiest for humans is hardest to formalize. LLMs absorbed a surprising amount of it implicitly from text — yet they reason unsoundly, hallucinating with confidence. Hence today's active frontier, neuro-symbolic AI: LLMs for flexible understanding, symbolic engines for guarantees — an LLM that writes a database query or a formal proof, then lets a sound engine execute it. The two traditions turned out to be complements, not rivals.

Key takeaways

• Logic gives sound inference; the world's exceptions and uncertainty resist pure logic.
• Expert systems hit the knowledge bottleneck; knowledge graphs and planners are the tradition's living legacy.
• Common sense defeated hand-coding; neuro-symbolic hybrids are the modern reconciliation.