First Order Logic

Extends propositional logic by introducing objects, relations, and quantifiers. Allows agents to reason about individuals and their properties instead of treating statements as atomic facts.

Ontological Engineering

Defines the concepts and relationships that form an agent’s view of the world. It answers two questions:

• Can we represent everything in the world?
• Is it necessary to represent everything?

In practice, agents use general ontologies for broad concepts (e.g., PhysicalObject) and fill in specific details later.

Ontology

Study of being, existence, and relationships among entities.

In AI, ontology provides structured categories (concepts, properties, relations).

• Upper ontology: general entities (e.g., Object, Event, Time).
• Domain ontology: specific entities (e.g., Car, Engine, DriveEvent).

Model

A model gives meaning to symbols.

• Relations
  Sets of tuples that describe connections among objects. Ex. $\text{Married} = {(\text{John}, \text{Mary}), (\text{Mary}, \text{John})}$.

Objects

An entity in the world. Either constants or variables.

Domain

Set of all objects.

Term

Expression that refers to an object.

Relation

Connects objects to express properties or relationships.

Function

A special relation. Maps input objects to another single object.

A total function is a function which is defined for all possible inputs.

Predicate

A relation that returns a boolean value.

Equality

A special predicate indicating two objects are identical.

Quantifiers

Allows statements about groups of objects.

• Universal Quantifier ($\forall$): states that a property holds for all objects.
• Existential Quantifier ($\exists$): states that a property holds for at least one object

Connective

Logical operators to combine statements.