predicate symbol (english) - meaning, definition, translation, pronunciation

Part of Speech

Predicate symbol is primarily used as a noun in the context of mathematics and logic.

Phonetic Transcription

/pˈrɛdɪkət sɪmbəl/

Meaning and Usage

A predicate symbol refers to a symbol used in formal logic and mathematics to denote a property or relation that a subject can have. In predicate logic, it expresses assertions about objects or subjects. Typically, it serves as a function that takes one or more arguments and returns a truth value (true or false).

The term is predominantly associated with formal languages, specifically in mathematical logic, and is more frequently encountered in written contexts, such as textbooks, academic papers, and logic discussions.

Example Sentences

1. The predicate symbol 'P(x)' indicates that property P holds for the element x.

2. Символ предиката 'P(x)' указывает на то, что свойство P принадлежит элементу x.

3. In logic, each predicate symbol must be defined to clarify its meaning.

4. В логике каждый символ предиката должен быть определён, чтобы уточнить его значение.

5. The choice of a predicate symbol influences the structure of the logical system.

6. Выбор символа предиката влияет на структуру логической системы.

Idiomatic Expressions

While "predicate symbol" itself is not commonly found in idiomatic expressions, understanding how predicate symbols function can enrich comprehension of other mathematical or logical terms involving predicates. However, related expressions may emerge in discussions of logic or mathematics, such as:

1. Predicate calculus is a powerful framework for formal reasoning.

2. Предикатное исчисление — это мощная основа для формального рассуждения.

3. In programming, a predicate function checks conditions and returns true or false.

4. В программировании предикатная функция проверяет условия и возвращает истину или ложь.

5. Understanding the predicate relationship between variables can significantly simplify proofs.

6. Понимание предикатной связи между переменными может значительно упростить доказательства.

Etymology

The term predicate originates from the Latin word praedicatum, which means "something asserted or affirmed." It has evolved through Middle English before becoming used in modern formal logic and mathematics. The word symbol comes from the Greek symbolon, meaning "token" or "sign."

Synonyms and Antonyms

Synonyms: - Assertion symbol - Relation symbol - Property symbol

Antonyms: - Subject symbol (in the context of predicate logic) - Object

In summary, the term "predicate symbol" plays a crucial role in the fields of logic and mathematics, allowing the expression of properties and relations succinctly and precisely through formal notation and definitions.