Changes

While working with expressions solely in propositional calculus, the use of plain parentheses to represent logical connectives is simplest to write and easiest to read for both human and machine parsers.  In the present text I preserve this form of expression in tables and set-off displays, but in contexts where parentheses are needed for functional notation I will use a distinctive font for logical operators.

While working with expressions solely in propositional calculus, the use of plain parentheses to represent logical connectives is simplest to write and easiest to read for both human and machine parsers.  In the present text I preserve this form of expression in tables and set-off displays, but in contexts where parentheses are needed for functional notation I will use a distinctive font for logical operators.

The briefest expression for logical truth is the empty word, usually denoted by <math>\varepsilon\!</math> or <math>\lambda\!</math> in formal languages, where it forms the identity element for concatenation.  To make it visible in this text, I denote it by the equivalent expression "<math>((~))\!</math>", or, especially if operating in an algebraic context, by a simple "<math>1\!</math>".  Also when working in an algebraic mode, I use the plus sign "<math>+\!</math>" for exclusive disjunction.  Thus, we may express the following paraphrases of algebraic forms:

The briefest expression for logical truth is the empty word, usually denoted by <math>\varepsilon\!</math> or <math>\lambda\!</math> in formal languages, where it forms the identity element for concatenation.  To make it visible in this text, it may be denoted by the equivalent expression "<math>((~))\!</math>", or, especially if operating in an algebraic context, by a simple "<math>1\!</math>".  Also when working in an algebraic mode, the plus sign "<math>+\!</math>" may be used for [[exclusive disjunction]].  For example, we have the following paraphrases of algebraic expressions by bracket expressions:

<center>

<center>

</center>

</center>

It is important to note that the last expressions are not equivalent to the triple bracket expression <math>(x, y, z).\!</math>

It is important to note that the last expressions are not equivalent to the triple bracket <math>(x, y, z).\!</math>

<font face="courier new">

<font face="courier new">