tiên đề hoá

Definition

1. Verb:
   • To axiomatize: The primary meaning of "tiên đề hoá" is to formulate or organize a theory, system of knowledge, or set of statements into a formal structure based on axioms. This involves identifying a set of self-evident or assumed starting principles (axioms) from which other truths can be logically derived.

Usage Examples

• Verb:
  • Các nhà toán học đã tiên đề hoá hình học Euclid. (Mathematicians have axiomatized Euclidean geometry.)
  • Mục tiêu là tiên đề hoá lý thuyết lượng tử. (The goal is to axiomatize quantum theory.)
  • Việc tiên đề hoá một lĩnh vực nghiên cứu có thể làm sáng tỏ các giả định cơ bản của nó. (Axiomatizing a field of study can clarify its fundamental assumptions.)

Advanced Usage

• The process of "tiên đề hoá" is central to formal logic, mathematics, and theoretical computer science, where it provides a rigorous foundation for deductive reasoning.
• It implies a movement from informal or empirical knowledge to a strictly formal, logical system.

Variants and Related Words

• Tiên đề (n): axiom, postulate. A statement that is accepted as true without proof, serving as a starting point.

  • Một tiên đề của hình học là qua hai điểm chỉ kẻ được một đường thẳng. (An axiom of geometry is that only one straight line can be drawn through two points.)

• Hệ tiên đề (n): axiomatic system, axiom system. A set of axioms from which theorems are derived.

  • Hệ tiên đề của Peano mô tả các số tự nhiên. (Peano's axiomatic system describes the natural numbers.)

Synonyms

• To formalize: To give a definite form or structure, often involving logical rules.
• To systematize: To arrange according to a system.

Related Concepts

• Suy diễn (n): deduction, inference. The process of reasoning from axioms or general principles to specific conclusions.
• Định lý (n): theorem. A statement that has been proven on the basis of axioms.