Dayton AI Class 4

In which we design agents that can form representations of the world, use a process of inference to derive new representations about the world, and use these new representations to deduce what to do.

This unit covers logical representation and planning. "Pushing against complexity":

  • Complexity of the agent: start with simple reflex-based agents, move towards goal- and utility-based agents
  • Complexity of the environment: start with simple environments, then look at partial observability, and stochastic actions, and multiple agents
  • Complexity of the representation: the agent's model of the world becomes increasingly complex
Tools of logic used to better model the world.
Type of Logic Ontological Commitment Epistemological Commitment
First Order Logic Relations, Objects, Functions True, False, Unknown
Propositional Logic Facts True, False, Unknown
Probability Theory Facts [0,1]
States can be described as atomic, factored, or structured.

Propositional Logic.

We can use inference mechanisms to determine the validity and satisfiability of propositions, but there are significant limitations of this framework.
  • No capability to handle uncertainty
  • Can only talk about events, not objects
  • No shortcuts to talk about a lot of different things happening

First-order Logic. Two of the limitations of propositional logic are addressed by first-order logic (not uncertainty). The syntax of first-order logic is made up of sentences and terms which can be combined using the operators from propositional logic. In first-order logic the relations are about objects, but not relations. In higher-order logic there are relations about relations.

When the world is not fully observable and deterministic we have to adapt the plan (feedback control). Why do we have

  • stochastic: we don't know exactly what will happen as a result of our actions
  • multi-agent: trying to predict what others are going to do
  • partial observability: we can't know everything (we don't know exactly what state we're in)
Instead of planning in the space of world-states, we plan in the space of belief-states.

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