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.
Table of Contents
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.
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