Chapter 4 Symbols and formulas

Logical formulas are entered in LATEX math mode, which LATExml converts to MathML. Depending on whether MathJax is loaded, the output, both visual and for screen readers, may be different. Without MathJax, ChromeVox does not read out formulas and symbols.

First of all, there are symbols for sentence letters and predicates, which are uppercase math letters like $A$ , $B$ , or $P$ . Sometimes the have subscripts like $A_{1}$ or $B_{n}$ . Sometimes these are typeset in a script font, e.g., as $\mathcal{A}$ but screen readers probably don’t distinguish between regular and script letters. (ChromeVox does, though, reading $A$ as “upper A” and $\mathcal{A}$ as “script upper A”.)

Then there are the logical operators:

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logical not: $\neg$ ,
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logical or: $\vee$ ,
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logical and: $\wedge$ ,
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the conditional: $\rightarrow$ ,
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the biconditional: $\leftrightarrow$ ,
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the contradiction symbol: $\bot$ ,
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the universal quantifier: $\forall$ ,
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the existential quantifier: $\exists$ , and
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the equals sign: $=$ .

Further symbols are:

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the therefore symbol: $\therefore$ ,
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the proves single turnstile: $\vdash$ ,
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the entailment double turnstile: $\vDash$ (as well as their negated versions: $\nvdash$ and $\nvDash$ ), and
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the modal box: $\Box$ ,
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the diamond: $\Diamond$ .

These combine into formulas like $(A\wedge B)\rightarrow(\neg C\vee\Box D)$ or $\forall x[P(a,b,x)\rightarrow(x=a\vee Q(x))]$ .

Ellipses can occur between formulas as text: $A_{1}$ , …, $A_{n}$ or as math: $P(x_{1},\dots,x_{n})$ . They should be pronounced by screen readers in both cases.

Logicians like to be pedantic about use and mention, so often letters and formulas are enclosed in single or double quotation marks. For instance, we mention the formula ‘ $A\wedge B$ ’ using single quotation marks or “ $A\land B$ ” using double quotation marks. Screen readers may in particular have difficulty at the end of a sentence where they read out the closing quotation mark and the sentence-ending period like ‘ $A\land B$ ’.

Sometimes it is important that quotation marks are pronounced as when we want to emphasize that ‘Alex’ and “Dana” are names and even that “‘Alex”’ is a name of the name ‘Alex’.

Sometimes formulas are set off from the main text as ‘displays’, e.g., the formula

A\wedge B

is displayed on a line by itself. Screen readers may have trouble with the sentence ending period when a displayed formula ends a sentence, like this one:

A\vee B.

Displayed formulas can also have embedded text like:

A\text{ and }B

LATEX can also produce displayed formulas that are broken across lines, like

(A\wedge B)\rightarrow{}\\ (A\vee B),

(using the multline environment) or formulas that are aligned like

	$\displaystyle(A\wedge B)$	$\displaystyle\rightarrow(A\vee B)$
	$\displaystyle(A\vee B)$	$\displaystyle\rightarrow(A\wedge B)$

(using the align environment). (MathJax on Firefox/Linux does not display the last one if “math renderer” output is set to SVG but does display it in CHTML. ChromeVox only reads the arrows and right sides of these equations.)