Definition

Noun: A logical relation is a connection or association between two or more propositions, statements, or concepts based on the principles of logic. It describes how the truth, validity, or meaning of one proposition is connected to or dependent on another.

Usage

The term "logical relation" is used primarily in formal contexts such as philosophy, mathematics, computer science, and linguistics to analyze the structure of arguments and statements. - It is used to discuss the formal connections between ideas. - It often appears in discussions about deductive reasoning, set theory, or database design.

Examples

• In philosophy, understanding the logical relation between premises is essential for evaluating the validity of an argument.
• The database schema defines the logical relations between different tables of information.
• The study focused on the logical relations of implication and equivalence within the formal system.

Advanced Usage

• In Formal Logic: A logical relation can be specifically defined, such as entailment, contradiction, or contrariety. For example, "The logical relation of holds when the truth of proposition P guarantees the truth of proposition Q."
• In Model Theory: Logical relations are studied as connections between structures and the sentences true in them.

Variants and Related Words

• Relation (n): The way in which two or more concepts, objects, or people are connected.
• Logical connective (n): A symbol or word used to connect propositions (e.g., AND, OR, IF...THEN) to form more complex ones, thereby creating a logical relation.
• Entailment (n): A specific type of logical relation where one set of propositions logically necessitates another.

Synonyms

• Logical connection
• Formal relation
• Inferential relationship

Antonyms

• Illogical connection
• Contradiction (when referring to a specific type of opposing logical relation)

Related Phrases and Concepts

• Logical operator: A function or symbol (like ∧ for AND) that creates a compound statement from simpler ones, establishing a logical relation.
• Truth-functional relation: A logical relation where the truth value of a compound statement is determined solely by the truth values of its parts.
• To stand in a logical relation: This phrase describes the state of propositions being connected logically.
  • The two hypotheses stand in a logical relation of mutual exclusivity.

Noun

1. a relation between propositions