Quantifiers in First-Order Logic
Universal Quantifier (∀)
- Meaning: Denotes that a statement holds for all objects in the domain.
- Example: ∀xP(x) means “for all x, P(x) is true”, indicating that property P holds for all objects x in the domain.
Existential Quantifier (∃)
- Meaning: Denotes that a statement holds for at least one object in the domain.
- Example: ∃xP(x) means “there exists an x such that P(x) is true”, indicating that there is at least one object x in the domain for which property P holds.
Syntax and Semantics of First-Order Logic in AI
First-order logic (FOL), also known as first-order predicate logic, is a fundamental formal system used in mathematics, philosophy, computer science, and linguistics for expressing and reasoning about relationships between objects in a domain. In artificial intelligence (AI), first-order logic (FOL) serves as a cornerstone for representing and reasoning about knowledge. Its syntax and semantics provide a robust framework for encoding information in a precise and structured manner, enabling AI systems to perform tasks such as automated reasoning, planning, and natural language understanding.
This article provides an in-depth overview of FOL’s syntax, semantics, and applications in AI.
Table of Content
- Syntax of First-Order Logic
- Quantifiers in First-Order Logic
- Well-Formed Formulas (WFFs) in First-Order Logic
- Semantics of First-Order Logic
- Satisfaction in First-Order Logic
- Validity in First-Order Logic
- Applications of First-Order Logic in AI
- Conclusion