functional calculus
Học thuậtThân thiện
Definition
Noun: A system of symbolic logic that extends propositional logic by including the representation of individuals, predicates, quantification over individuals (using symbols like ∀ for "all" and ∃ for "there exists"), and the logical relations between such quantified propositions. It is a formal system for analyzing the logical structure of statements about objects and their properties.
Examples of Usage
- Modern mathematics relies heavily on the functional calculus for formulating precise definitions and proofs.
- The philosopher used functional calculus to analyze the logical form of the statement "All humans are mortal."
- A key difference between propositional logic and functional calculus is the latter's ability to express statements about "some" or "all" members of a domain.
Advanced Usage
- First-order functional calculus: Often synonymous with "first-order logic," it is the most commonly studied system, where quantification is allowed only over individuals, not over predicates or sets.
- Higher-order functional calculus: A more expressive system that permits quantification over predicates and functions themselves (e.g., "There is a property that all great leaders share").
Variants and Related Words
- Predicate calculus: A term often used interchangeably with .
- First-order logic (FOL): The standard, foundational system of functional calculus.
- Quantification: The part of functional calculus dealing with symbols like ∀ (universal quantifier) and ∃ (existential quantifier).
Synonyms
- Predicate logic
- Quantification theory
Related Phrases
- Domain of discourse: The collection of individuals over which the variables in a functional calculus range.
- Bound variable: A variable that is within the scope of a quantifier.
- Open sentence: A logical formula in functional calculus that contains at least one free variable.
Noun
- a system of symbolic logic that represents individuals and predicates and quantification over individuals (as well as the relations between propositions)