logical system

Thân thiện

A student draws a logical system on the whiteboard.

Definition

Noun: A formal, structured framework of principles and rules used for valid reasoning and deduction. It provides a consistent method to derive conclusions from premises.

Examples

• Mathematicians rely on a logical system to prove theorems from basic axioms.
• The development of a new logical system can change how we approach problems in computer science.
• In philosophy, different logical systems are analyzed for their strengths and limitations in representing truth.

Advanced Usage

• "Within the logical system of...": Used to specify that a conclusion or argument is valid according to a particular framework.
  • The statement is a tautology within the logical system of classical propositional calculus.
• "The axioms of a logical system": Refers to the foundational, self-evident statements upon which the system is built.
  • Changing even one of the axioms can create an entirely different logical system.

Variants and Related Words

• Formal system: A closely related term often used interchangeably, emphasizing the syntactical rules for manipulating symbols.
• System of logic: A synonymous phrase.
• Logic: The broader study of reasoning, of which a logical system is a specific, formalized instance.

Synonyms

• Formal logic
• Deductive system
• Calculus (in a technical sense, e.g., "predicate calculus")

Related Phrases

• Soundness of a logical system: The property that the system's rules only allow the derivation of true conclusions from true premises.
• Completeness of a logical system: The property that all true statements expressible in the system can be derived using its rules.

Học thuật

Noun

1. a system of reasoning

Từ đồng nghĩa

• logic
• system of logic