Predicate Logic Sentence

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:
- Person(x).
- Parent(x,y).
- Person(Socrates). (A Ground Fact).
- Grandparent(x,y) :- Parent(x,y), Parent(y,z), person(x), person(y), person(z).
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

(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.

(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.

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

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