# Writing Symbols (and Alternative Symbols)

###### 12/15/20

We may wish to use a computer to write logical symbols, both for entry into exercises and to produce web pages of Notes.

Additionally not all logicians, and logical texts, use the same symbols for the logical connectives. [In fact, pretty well every logical text is slightly different from every other one, usually in small details of the symbols or rules. This is truly a pain, and unnecessary (and pathetic). Imagine what would happen in mathematics if each text used a different symbol for the addition '+' sign, or for the integration sign!]

Here are some common symbols and alternatives.

'not' : ∼ (the 'tilde'), ¬ (looks like the top right corner of a box)

'and': ∧,& (the ampersand), . (just a period)

'or': ∨ (usually just this, vel)

'implication': ⊃ , →

'equivalence': ≡, ↔

'existential quantifier': ∃, ∑

'universal quantifier':∀, ∏

'therefore': ∴, ⊦ (this 'assertion' symbols actually means something slightly different, but often appears in this context)

'necessary': □

'possible': ◊

'lambda': λ

'member of': ε

'not member of': ∉

'epsilon [large]': Ε      /*We prefer the above 'member of' for set theory, but the system will read this.*/

'epsilon [small]': ε      /*We prefer the above 'member of' for set theory, but the system will read this.*/

'subset': ⊂

'union': ∪

'intersection': ∩

'cartesian product': ×

/*For multiplication in arithmetic we use the period, for example (a.b). For set theory you need to use this symbol for cross product. Upper or lower case exe ie 'X' or 'x' will not work. Upper X is a proposition or predicate, lower x is a variable, so Xx is a well formed formula (but it has no connection with cross product) .*/

'empty set': ∅

'power set' : ℘

'universe set: Ü     /*Ü umlaut (type option-U upper-case-U)*/

So, in a logic book, you might see (A&B)→C and that is just the same as (A∧B)⊃C.

For the logic symbols, we're going to choose one or more Unicode symbols ( 'Unicode... the most widely adopted software standard in the world...'). but web browsers use html so the question arises of Unicode to html conversion. As the development on web browsers continues, and html 4.0, more and more Unicode symbols are available, in fact all the 'mathematical' and 'logic' symbols are available on all modern browsers (see the wonderful Alan Wood) .

These logical symbols do have html codes, and here is what they are

'not' : &sim; (the 'tilde'), &not; (looks like the top right corner of a box)
'and': &and;,&amp; (the ampersand), . (just a period)
'or': &or; (usually just this, vel)
'implication': &sup; , &rarr;
'equivalence': &equiv;, &harr;
'existential quantifier': &exist;, &sum;
'universal quantifier':∀, &forall; &prod;
'therefore': &there4;, ⊦ (this 'assertion' symbols actually means something slightly different, but often appears in this context)
'necessary': &#9633;
'possible': &loz;
'lambda': &lambda;

'member of' or 'element of': &#8712; &isin;
'not member of': &notin;
'union': &#8846;
'intersection': &#8845;
'subset': &#8834;
'cross or Cartesian product': &#215;
'empty set': &#8709;
'power set': &weierp;

So, if you know about html, can use an html editor etc., if, for example, you insert into the html of a web page '&there4;' you will get (if your browser can do it) ∴

Wikipedia have a table of logical symbols

[There is a little trick/elegance that the SoftOption software uses. It will try to make sense of what you write, if it can, to the extent that if you use the 'wrong' symbol for, say, negation (ie a symbol for negation but not the one your system uses) the software will read it and understand-- and when the software writes to you it will use your symbols. In a sense that is, garbage in garbage not out.]