Changes

x \operatorname{'s~Instance}    & = &

x \operatorname{'s~Instance}    & = &

\operatorname{Instance~of}\ x  & = &

\operatorname{Instance~of}\ x  & = &

\operatorname{Object~below}\ x, \\

\operatorname{Object~below}\ x. \\

\end{array}</math>

\end{array}</math>

|}

|}

A symbol like "''x''&nbsp;<math>\lessdot</math>" or "''x''&nbsp;<math>\gtrdot</math>", with extra spaces or dots being optional, is called a ''catenation'', where "''x''" is the ''catenand'' and "<math>\lessdot</math>" or "<math>\gtrdot</math>" is the ''catenator''.  Due to the fact that "<math>\lessdot</math>" and "<math>\gtrdot</math>" indicate dyadic relations, the significance of these so-called ''unsaturated'' catenations can be rationalized as follows:

A symbol like <math>x \lessdot</math> or <math>x \gtrdot</math>, with extra spaces or dots being optional, is called a ''catenation'', where <math>x\!</math> is the ''catenand'' and <math>\lessdot</math> or <math>\gtrdot</math> is the ''catenator''.  Due to the fact that <math>^{\backprime\backprime} \lessdot ^{\prime\prime}</math> and <math>^{\backprime\backprime} \gtrdot ^{\prime\prime}</math> indicate dyadic relations, the significance of these so-called ''unsaturated'' catenations can be rationalized as follows:

:{|

{| align="center" cellpadding="8"

| ''x'' <math>\lessdot</math>

|

| =

<math>\begin{array}{lllll}

| ''x'' is the Instance of what?

x \lessdot                                 & = &

| =

x\ \operatorname{is~the~Instance~of~what?} & = &

| ''x''&rsquo;s Property&nbsp;,

x \operatorname{'s~Property},             \\

x \gtrdot                                 & = &

| ''x'' <math>\gtrdot</math>

x\ \operatorname{is~the~Property~of~what?} & = &

| =

x \operatorname{'s~Instance}.             \\

| ''x'' is the Property of what?

| =

| ''x''&rsquo;s Instance&nbsp;.

|}

|}