Chaining operators and relations

When you have several terms with operators in between, some kind of associativity is normally implied, so that the expression can be evaluated as a sequence of binary operations:

\[ a \cdot b \cdot c = (a \cdot b) \cdot c \]

That isn't usually the case when terms are joined with relation symbols :

Let \(a=1\), \(b=2\), \(c=3\).

\( (a \lt b) \lt c = \text{True} \lt c \)

Doesn't make sense!

It doesn't make sense to evaluate this as a sequence of binary operations. Instead, a chain of \(n\) relations could be interpreted as a set of \(n\) statements:

\[ a \lt b \lt c \iff (a \lt b) \wedge (b \lt c) \]