Logical Agents

Agents that reason about the world using formal logic. Maintains an internal representation of the world. Infers new facts from known facts. Acts based on reasoning rather than fixed behavior.

Logic Fundamentals

Logic provides a formal language for representing and reasoning about facts.

Logical Sentence

A statement that can be either true or false. Used to represent facts, rules, and relationships about the world. Typically expressed in a formal language such as propositional logic or first-order logic. The language is called the knowledge representation language.

Tautology

A sentence which is true in all models.

Satisfiable

A sentence is satisfiable if it’s true in at least one model.

Syntax

Specifies how valid sentences are formed.

Semantics

Defines how to interpret sentences in different models.

If sentence $s$ is true in model $m$, $m$ is a model of $s$ or $m$ satisfies $s$.

The set of all models that satisfy $s$ is $M(s)$.

Logical Equivalence

Two sentences $\alpha$ and $\beta$ are logically equivalent if they are true in exactly the same models.

$$\alpha ≡ \beta \iff M(\alpha) = M(\beta)$$

Logical Entailment

A sentence $\alpha$ entails $\beta$ iff $M(\alpha) \subset M(\beta)$.

Grounding

Connecting logical sentences in KB to real-world facts. If the KB correctly represents the world, then any conclusion drawn by a sound inference process must also be true in the real world.

Knowledge Base

A collection of logical sentences. Used to infer new knowledge.

The agent interacts with the KB through two operations:

• TELL(KB, sentence): Add new information.
• ASK(KB, query): Retrieve or infer information.

Can be huge, complex, and dynamic.

Knowledge

Information that helps achieve goals efficiently.

Two knowledge types:

• Procedural
  “How to” information. Actions or methods.
• Declarative
  “What is” information. Facts and relationships.

Ontology Commitment

Refers to what the logic assumes about the world.

Higher-order logic is more ontological but more complex to reason with.

Epistemological Commitment

Describes what kinds of knowledge states a logic system can express about facts.