Difference between revisions of "Predicate symbol"
From Encyclopedia of Mathematics
(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
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