Sentence examples for relation symbols from inspiring English sources

The symbols of this middle group include the nonlogical constants of the language, such as relation symbols, function symbols and constant individual symbols.

And suppose we have a first-order language formed in the usual way, with relation symbols, \(R_1\), …, \(R_n\) whose arities match those of the given relations.

Consider the following formula, where \(S\) is a two-place relation symbol interpreted by \ \bS\), and \(E\) and \(O\) are auxiliary one-place relation symbols.

A valuation \ v\) in this structure is a mapping from individual variables to members of \ \bD\) and from auxiliary relation symbols to partial relations on \ \bD\).

Let us consider a first-order language L, with connective &, ∨, and ¬, quantifiers ∀ and ∃, the equals sign =, variables, and some stock of names, function symbols and relation symbols.

Among the relation symbols we still have \(E\), which now is of type \(\langle O\rangle\), and we have \, of type \(\langle O,O \rangle\).

Thus, if F is a sentence containing equality, a sentence G can be adjoined to it that embodies the special properties of identity relevant to the sentence F. The conjunction of F and G can then be treated as a sentence not containing equality (i.e., "=" can be treated as an arbitrary relation symbol).

He has a relation symbol expressing 'x is dependent on y'.

Here an 'I-predicable' is a binary relation symbol '=' satisfying (W).

In the following, \(P\) is an auxiliary relation symbol of arity 0, that is, a propositional letter.

The formal language of set theory is the first-order language whose only non-logical symbol is the binary relation symbol $\in $