Changes

I am going to revert to my customarily sloppy workshop manners and refer to propositions and proposition expressions on rough analogy with functions and function expressions, which implies that a proposition will be regarded as the chief formal object of discussion, enjoying many proposition expressions, formulas, or sentences that express it, but worst of all I will probably just go ahead and use any and all of these terms as loosely as I see fit, taking a bit of extra care only when I see the need.

I am going to revert to my customarily sloppy workshop manners and refer to propositions and proposition expressions on rough analogy with functions and function expressions, which implies that a proposition will be regarded as the chief formal object of discussion, enjoying many proposition expressions, formulas, or sentences that express it, but worst of all I will probably just go ahead and use any and all of these terms as loosely as I see fit, taking a bit of extra care only when I see the need.

Let <math>Q\!</math> be a proposition with an unspecified, but context-appropriate number of variables, say, none, or <math>x,\!</math> or <math>x_1, \ldots, x_k,\!</math> as the case may be. (To be more precise, I should have said "sentence <math>Q\;\!</math>".)

Let <math>Q\!</math> be a propositional expression with an unspecified, but context-appropriate number of variables, say, none, or <math>x,\!</math> or <math>x_1, \ldots, x_k,\!</math> as the case may be.

:* Strings and graphs sans labels are called ''bare''.

:* Strings and graphs that have no labels are called ''bare''.

:* A bare terminal node, "o", is known as a ''stone''.

:* A bare terminal node, symbolized by a small circle <math>\circ</math> in text, is known as a ''stone''.

:* A bare terminal edge, "|", is known as a ''stick''.

:* A bare terminal edge, symbolized by a vertical bar <math>\vert</math> in text, is known as a ''stick''.

Let the ''replacement expression'' of the form ''Q''[o/''x''] denote the proposition that results from ''Q'' by replacing every token of the variable ''x'' with a blank, that is to say, by erasing ''x''.

Let the ''replacement expression'' of the form ''Q''[o/''x''] denote the proposition that results from ''Q'' by replacing every token of the variable ''x'' with a blank, that is to say, by erasing ''x''.