# Predicate Logic Sentence

(Redirected from Predicate Function)

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A Predicate Logic Sentence is a Logic Sentence with a Fixed Set of Predicate Formula Arguments that can be composed of Constants or Variables.

**AKA:**Predicate, Predicate Function, Predicate Sentence, Predicate Formula Sentence, Predicate Formula.**Context:**- It can be a Ground Fact, if its Argument are all Constants.
- It can be a Well-Formed Formula (or an Ill-Formed Formula).
- It can be associated to a Predicate Logic Language (from a Predicate Logic System).

**Example:****Counter-Example(s):**- 5 - 1 = 4, a Mathematical Sentence.
- “
*The floor is dry.*”, a Natural Language Sentence.

**See:**Propositional Logic Sentence, Relation, Horn Clause, Boolean-Valued Function, Indicator Function.

## References

### 2016

- (Wikipedia, 2016) ⇒ https://en.wikipedia.org/wiki/Predicate_(mathematical_logic) Retrieved:2016-5-19.
- In mathematics, a
**predicate**is commonly understood to be a Boolean-valued function*P*:*X*→ {true, false}, called the predicate on*X*. However, predicates have many different uses and interpretations in mathematics and logic, and their precise definition, meaning and use will vary from theory to theory. So, for example, when a theory defines the concept of a relation, then a predicate is simply the characteristic function or the indicator function of a relation. However, not all theories have relations, or are founded on set theory, and so one must be careful with the proper definition and semantic interpretation of a predicate.

- In mathematics, a

### 2011

- (Sammut & Webb, 2011) ⇒ Claude Sammut, and Geoffrey I. Webb. (2011). “Predicate.” In: (Sammut & Webb, 2011) p.781
- QUOTE: A predicate or predicate symbol is used in logic to denote properties and relationships. Formally, if P is a predicate with arity n, and t1, …, tn is a sequence of n terms (i.e., constants, variables, or compound terms built from function symbols), then P(t1, …, tn) is an atomic formula or atom. Such an atom represents a statement that can be either true or false. Using logical connectives, atoms can be combined to build well-formed formulae in first-order logic or clauses in logic programs.

### 2009

- CYC Glossary http://www.cyc.com/cycdoc/ref/glossary.html
- predicate: Predicates are represented in CycL by constants that are sometimes referred to as "CycL predicates" or, more casually, as "predicates." Like CycL functions (the other kind of relation-denoting constants), CycL predicates can be used as the leading term (after the initial parenthesis) in CycL expressions. When a CycL predicate is applied to the right number and type of arguments, the expression formed is a CycL formula--a formula expressing a proposition about something. In contrast, expressions formed with functions as arg 0 (in the leading position) are terms and so do not express propositions.

- http://www.cs.utexas.edu/~novak/reso.html
- http://www.cs.utexas.edu/~novak/resosol.html

### 2008

- www.pcai.com/web/glossary/pcai_p_s_glossary.html
- A function that returns either a true or false value.