Namespaces
Variants
Actions

Difference between revisions of "Predicate symbol"

From Encyclopedia of Mathematics
Jump to: navigation, search
(more Tex)
(define n-ary)
Line 2: Line 2:
 
''predicate letter''
 
''predicate letter''
  
A notation for some concrete predicate or relation. E.g., the symbol $\leq$ often denotes the order relation on the real numbers; it is a $2$-place predicate. In the formal structure of a language, the symbols denoting predicates must be used, in a well-defined way, for constructing expressions of the language. In particular, if $P$ is an $n$-place predicate symbol, then the following rule should be among the syntactic rules for forming expressions in the formalized language:  "If $t_1,\ldots,t_n$ are terms, then $P\,t_1\ldots t_n$ is a formula" . Thus, predicate symbols are syntactically used to form formulas, and semantically denote predicates.
+
A notation for some concrete predicate or relation. E.g., the symbol $\leq$ often denotes the order relation on the real numbers; it is a $2$-place predicate. In the formal structure of a language, the symbols denoting predicates must be used, in a well-defined way, for constructing expressions of the language. In particular, if $P$ is an $n$-place (or $n$-ary) predicate symbol, then the following rule should be among the syntactic rules for forming expressions in the formalized language:  "If $t_1,\ldots,t_n$ are terms, then $P\,t_1\ldots t_n$ is a formula" . Thus, predicate symbols are syntactically used to form formulas, and semantically denote predicates.
  
 
====References====
 
====References====
Line 13: Line 13:
  
 
====Comments====
 
====Comments====
A predicate symbol is also called a relation symbol.
+
A predicate symbol is also called a ''relation symbol''.
  
 
====References====
 
====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  Yu.I. Manin,  "A course in mathematical logic" , Springer  (1977)  (Translated from Russian)</TD></TR></table>
+
<table>
 +
<TR><TD valign="top">[a1]</TD> <TD valign="top">  Yu.I. Manin,  "A course in mathematical logic" , Springer  (1977)  (Translated from Russian)</TD></TR>
 +
</table>

Revision as of 06:46, 18 October 2016

predicate letter

A notation for some concrete predicate or relation. E.g., the symbol $\leq$ often denotes the order relation on the real numbers; it is a $2$-place predicate. In the formal structure of a language, the symbols denoting predicates must be used, in a well-defined way, for constructing expressions of the language. In particular, if $P$ is an $n$-place (or $n$-ary) predicate symbol, then the following rule should be among the syntactic rules for forming expressions in the formalized language: "If $t_1,\ldots,t_n$ are terms, then $P\,t_1\ldots t_n$ is a formula" . Thus, predicate symbols are syntactically used to form formulas, and semantically denote predicates.

References

[1] S.C. Kleene, "Introduction to metamathematics" , North-Holland (1951)
[2] Yu.L. Ershov, E.A. Palyutin, "Mathematical logic" , Moscow (1970) (In Russian)


Comments

A predicate symbol is also called a relation symbol.

References

[a1] Yu.I. Manin, "A course in mathematical logic" , Springer (1977) (Translated from Russian)
How to Cite This Entry:
Predicate symbol. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Predicate_symbol&oldid=39423
This article was adapted from an original article by V.N. Grishin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article