While propositional logic assumes the world contains facts,

first-order logic (like natural language) assumes the world contains

- Objects: people, house, numbers, colors, baseball games, wars,...

- Relations: red, round, prime, brother of, bigger than, part of, comes between, ...

- Functions: father of, best friend, one more than, plus, ...

"Evil King John England in 1200."

- Object: John, England, 1200; Relation; ruled; Properties: evil, king

Ontological Commitment:

- What exists in the world - TRUTH

- PL : facts hold or do not hold.

- FOL : objects with relations between them that hold or do not hold

Epistemological Commitment:

- What an agent believes about facts - BELIEEF

Constant Symbols:

- Stand for objects

- e.g., KingJohn, 2, UCI, ...

Predicate Symbols

- Stand for relations

- E.g., Brother (Richard, John), greater_than(3,2)....

Function Symbols

- Stand for functions

- E.g., Sqrt(3), LeftLegOf(John),....

Constant KingJohn,2, UCI,...

Predicates Brother,>,....

Function Sqrt, LeftLegOf,....

Variables x,y,a,b,....

Connectives ã„±,⇒,៱,v,⇔

Equality =

Quantifiers ∀,∃

Some relations are properties: they state some fact about a single object: Round (ball), Prime(7).

n-ary relations state facts about two or more objects: Married(John,Mary), LargeThan(3,2).

Some relations are functions: their value is another object: Puls(2,3), Father(Dan).

first-order logic (like natural language) assumes the world contains

- Objects: people, house, numbers, colors, baseball games, wars,...

- Relations: red, round, prime, brother of, bigger than, part of, comes between, ...

- Functions: father of, best friend, one more than, plus, ...

"Evil King John England in 1200."

- Object: John, England, 1200; Relation; ruled; Properties: evil, king

**Logic in General**Ontological Commitment:

- What exists in the world - TRUTH

- PL : facts hold or do not hold.

- FOL : objects with relations between them that hold or do not hold

Epistemological Commitment:

- What an agent believes about facts - BELIEEF

**Syntax of First Order Logic: Basic elements**Constant Symbols:

- Stand for objects

- e.g., KingJohn, 2, UCI, ...

Predicate Symbols

- Stand for relations

- E.g., Brother (Richard, John), greater_than(3,2)....

Function Symbols

- Stand for functions

- E.g., Sqrt(3), LeftLegOf(John),....

Constant KingJohn,2, UCI,...

Predicates Brother,>,....

Function Sqrt, LeftLegOf,....

Variables x,y,a,b,....

Connectives ã„±,⇒,៱,v,⇔

Equality =

Quantifiers ∀,∃

**Relations**Some relations are properties: they state some fact about a single object: Round (ball), Prime(7).

n-ary relations state facts about two or more objects: Married(John,Mary), LargeThan(3,2).

Some relations are functions: their value is another object: Puls(2,3), Father(Dan).

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