# First-order logic#Find similar titles

First-order logic (1차 논리, FOL) is a formal system used in mathematics, philosophy, linguistics, and computer science. (http://en.wikipedia.org/wiki/First-order_logic)

원소에만 한정 기호를 가할 수 있고, 술어에는 한정 기호를 가할 수 없는 술어 논리(Predicate logic)이다.

# Basics #

FOL models the model in terms of

• Objects
• Properties
• Relations
• Functions

Basic elements

• Constant symbols, which represent individual in the world
• Mary
• 3
• Green
• Function symbols, which map individuals to individuals
• father-of(Mary) = John
• color-of(Sky) = Blue
• Predicate symbols, which map individuals to truth values
• greater(5, 3)
• green(Grass)
• color(Grass, Green)

Quantifiers

• Universal quantification
• (∀x) dolphin(x) ➝ mammal(x)
• Existential quantification
• (∃x) mammal(x) ∧ lays-eggs(x)

# Hyungyong Kim's FOL model for Molecular biology#

• Objects: Molecule, DNA, RNA, Protein, TATA box, Chemical
• Predicates
• is-a(x, y), is-part-of(x, y)
• replicate(x), transcribe(x, y), translate(x, y)
• activate(x, y), repress(x, y)
• bind(x, y)
• catalyze(x, from, to)
• Facts
• is-a(DNA, Molecule), is-part-of(Promoter, DNA)
• is-a(mRNA, RNA)
• replicate(DNA, DNA), transcribe(DNA, mRNA), translate(mRNA, Protein)
• Rules for molecular biology relations
• (∀x,y) transcribe(x, y) ⟷ reverse-transcribe(y, x)
• (∀x,y) regulate(x, y) ∧ more-express(y) ➝ activate(x, y)
• (∀x,y) bind(x, y) ⟷ bind(y, x)
• Queries
• activate(aGene, bGene)

--> type과 instance를 분리할 필요가 있음.