logical system
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.
Noun
-
a system of reasoning
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