# Predicate Logic System

A Predicate Logic System is a Formal Logic System that deals with finding logical relations between sentences in which predicates are distributed through ranges of subjects by means of quantifiers.

**AKA:**Logic Of Quantifiers, Predicate Calculus, Predicate Logic, Predicate Logic Calculus.**Context:**- It ranges from being Lower Predicate Logic System to being a Higher-Order Predicate Logic System.
- It can be part of deductive logic system composed of a predicate logic language and predicate logic operations (that allows the representation of Logic Terms, rredicates and of quantification over variables).

**Example(s):****Counter-Example(s):****See:**Symbolic Logic System, Logic, Calculus, Proposition, Truth-Functional Operator, Universal Quantifier, Existential Quantifier.

## References

### 2018

- (Schagrin & Hughes, 2018) ⇒ Morton L. Schagrin, and G.E. Hughes (November 02, 2018). Formal logic: https://www.britannica.com/topic/formal-logic/The-predicate-calculus Retrieved: 2019-06-09. In: Encyclopaedia Britannica.
- QUOTE: Propositions may also be built up, not out of other propositions but out of elements that are not themselves propositions. The simplest kind to be considered here are propositions in which a certain object or individual (in a wide sense) is said to possess a certain property or characteristic; e.g., “Socrates is wise” and “The number 7 is prime.” Such a proposition contains two distinguishable parts: (1) an expression that names or designates an individual and (2) an expression, called a predicate (...) Predicates with two or more arguments stand not for properties of single individuals but for relations between individuals. Thus the proposition “Tom is a son of John” is analyzable into two names of individuals (“Tom” and “John”) and a dyadic or two-place predicate (“is a son of”), of which they are the arguments; and the proposition is thus of the form ϕxy. Analogously, “… is between … and …” is a three-place predicate, requiring three arguments, and so on. In general, a predicate variable followed by any number of individual variables is a wff of the predicate calculus.

### 2017

- (Encyclopaedia Britannica, 2017) ⇒ The Editors of Encyclopaedia Britannica (April 13, 2017). Predicate calculus: https://www.britannica.com/topic/predicate-calculus Retrieved: 2019-06-09.
- QUOTE: Predicate calculus, also called Logic Of Quantifiers, that part of modern formal or symbolic logic which systematically exhibits the logical relations between sentences that hold purely in virtue of the manner in which predicates or noun expressions are distributed through ranges of subjects by means of quantifiers such as “all” and “some” without regard to the meanings or conceptual contents of any predicates in particular. Such predicates can include both qualities and relations; and, in a higher-order form called the functional calculus, it also includes functions, which are “framework” expressions with one or with several variables that acquire definite truth-values only when the variables are replaced by specific terms. The predicate calculus is to be distinguished from the propositional calculus, which deals with unanalyzed whole propositions related by connectives (such as “and,” “if . . . then,” and “or”).

### 2009a

- (WordNet, 2009) ⇒ http://wordnetweb.princeton.edu/perl/webwn?s=predicate%20calculus
- QUOTE: S: (n) predicate calculus, functional calculus (a system of symbolic logic that represents individuals and predicates and quantification over individuals (as well as the relations between propositions))

### 2009b

- (Wiktionary, 2009) ⇒ http://en.wiktionary.org/wiki/predicate_calculus
- QUOTE: (logic) The branch of logic that deals with quantified statements such as "there exists an x such that..." or "for any x, it is the case that...", where x is a member of the domain of discourse.

### 2009c

- (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Predicate_logic
- In mathematical logic, predicate logic is the generic term for symbolic formal systems like first-order logic, second-order logic, many-sorted logic or infinitary logic. This formal system is distinguished from other systems in that its formulas contain variables which can be quantified. Two common quantifiers are the existential ∃ and universal ∀ quantifiers. The variables could be elements in the universe, or perhaps relations or functions over the universe. For instance, an existential quantifier over a function symbol would be interpreted as modifier "there is a function".
- In informal usage, the term "predicate logic" occasionally refers to first-order logic. Some authors consider the predicate calculus to be an axiomatized form of predicate logic, and the predicate logic to be derived from an informal, more intuitive development. [1]