Four AI Approaches Revisited

We started the course with four approaches to AI. Let's revisit them with the
tools we've now built.

Symbolic AI (Definition 10.0.1) — intelligence comes from manipulating
symbols according to formal rules. This is what SMAI is about.

Shines when:
- The problem has clear, formal structure (math, logic, programs).
- You need an explanation of why an answer is right.
- You want correctness guarantees (proofs, type systems).
- The rules are known but the data is scarce.

Statistical AI (Definition 10.0.2) — intelligence from learning patterns in
data. Bayesian networks, probabilistic programming, decision theory.

Shines when:
- You have lots of data.
- Rules are hard to write but easy to learn.
- Uncertainty is fundamental.

Subsymbolic AI (Definition 10.0.3) — intelligence emerges from many small
numerical units firing together. Neural networks, deep learning.

Shines when:
- The input is high-dimensional (pixels, audio, text).
- You have massive compute and data.
- You can tolerate some errors.

Embodied AI (Definition 10.0.4) — intelligence requires a body in an
environment. Robotics, situated agents, sensorimotor learning.

Shines when:
- The agent acts in the real world.
- Perception-action loops are central.
- Physical constraints shape cognition.

Synthesis. Modern AI systems are hybrid: a symbolic shell around a
neural core (e.g. AlphaGo combines neural evaluation with Monte Carlo tree
search), or a neural system inside symbolic constraints (e.g. type-checking
an LLM's output). Each paradigm has strengths the others lack.

The course's view: symbolic methods are not obsolete — they're the only
ones that give you guarantees. Statistics and neural networks give you
coverage.

The four AI approaches can be classified along two axes:

• Deep vs Shallow: Does the system understand (have a model of the world) or just react (statistical pattern-matching)?
• Narrow vs Wide: Is the system specialised to one task or general-purpose?

              Shallow          Deep
Narrow   Statistical AI    Symbolic AI
         (NLP, vision,     (theorem provers,
          translation)      planners, math)

Wide     Subsymbolic AI    Embodied AI
         (LLMs,             (robots, agents,
          transformers)     simulation)

This course focuses on Symbolic AI — deep and narrow. The next course in the sequence will likely cover Statistical / Subsymbolic AI — shallow and wide. Embodied AI sits at the deep/wide corner and remains an open research frontier.

The two-by-two view clarifies why different techniques suit different problems: a chatbot (narrow, shallow) is well-served by a transformer; a theorem prover (narrow, deep) needs formal logic; a robot (wide, deep) needs both reasoning and reactivity.