Is 'Hjsuidj***7348672' a wffl?

An atomic formula is a sequence of three symulus: A variable or constant, a relation, and a variable or constant.

A1: Ø = Ø       F1: ¬ (P)                        'A sequence of symbols' is not a wffl.
A2: Ø = E        F2: (P) ⇒ (Q)                ' ¬ (Ø = Ø) ' is a wffl. It is a sequence of
A3: E = Ø        F3: (P) ∨ (Q)                symulus composed using A1 and F1.
A4: X = Y        F4: (P) ∧ (Q)
A5: Ø ∈ Ø       F5: (P) ⇔ (Q)
A6: Ø ∈ R       F6: ∀X (P)
A7: S ∈ Ø       F7: ∃X (P)
A8: W ∈ A

Only a string of symulus built from atomic formula and rules F1 - F7 is a wffl.

Rules F1 - F7 are called compound formulae
             P and Q are the components of each compound formula

Rules F1 - F5 are called propositional forms.
            ONLY sequences of symbols built from F1 - F5 are propositional forms.
            P and Q are also propositional forms.

P and Q are propositional variables.
           The variable X is not a propositional variable.
                                X is an operator variable because it follows a quantifier.
If X did not follow a quantifier,
                        then X would be called an individual variable.

A logical formula is either a wffl or a propositional form. Finally, a proposition is a logical formula that has a truth value.

Warning: This Post is Boring. Reader Discretion is Advised

Definition2: Every atomic formula is a well-formed formula (Pronounced whiff). Additionally, for all wff's P and Q, and for every variable X, the following formulae are also wff's:

            Formula           Translation
F1    ¬ (P)                    not P
F2       (P) ⇒ (Q)         P implies Q
F3       (P) ∨ (Q)         P or Q
F4       (P) ∧ (Q)         P and Q
F5       (P) ⇔ (Q)         P is equivalent to Q
F6       ∀X (P)             For each X, P
F7        ∃X (P)            There exists an X such that P

Remember, they're just symulus.

ф○● ○ф● ○●ф

Take your pick: (Pre)fix, (In)fix, Or (Post)fix notation. They are all equivalent. 

Examples

Prefix: =XY        Infix: X=Y        Postfix: XY=

In some contexts, I use prefix notation because it places emphasis on the relation.

Postfix notation mirrors the order computers perform operations.

Finally, infix notation is what I use most. It's what I grew up on.

These are simple examples. Future posts will show formulae of greater complexity.  

(α)lpha(β)et

αβ are the first two letters of the Greek alphabet. Say alpha. Now say beta. 'α' is pronounced alpha and 'β' is pronounced beta. I can't imagine where 'alphabet' came from. Below is the current list of symbols I use.

Ø , ∈ , = , ∀ , ∃ , ○ , ● , ¬ , ∧ , ∨ , ⇒ , ⇔ , ( , ) , [ , ] , { , } , (Variables)

      Constant:                               Relations:                                      Quantifiers: 

             Ø  ( the empty set )              ∈  ( is an element of )                 ∀ ( for each ) 

                                                              =  ( equals )                                   ∃  ( there exists )
       
     Connectives:                           Grouping Symbols:                            Values:
             ¬ ( not )                                     (     ( left parenthesis )                   ○  ( true )
             ∧ ( and )                                    )    ( right parenthesis )                 ●  ( false )
             ∨ ( or )                                      [      ( left bracket )                  
             ⇒ ( implies )                             ]      ( right bracket )                 Variables:
            ⇔ ( is equivalent to )              {     ( left brace )                             Any symbols not listed
                                                                 }     ( right brace )                           here are variables.                                                                                                                                       Scripts allowed
    

Nothing Is A Thing

∅ = { x | ¬ (x = x)}:   The empty set equals the set of all x, such that, it is not the case that x equals x.

Ever been on a bus with a passenger blabbing on and on about just a bunch of nothing? I call those people bags-of-wind. In other words, there's nothing but air in there. Which is a lot like the empty set just without the wind. As for myself, other passengers should call me a Platonist.

{[(is true) is a predicate] is a proposition} is TRUE!

Anything can be a subject. So long as you can talk about it, then it's a subject. It can be a subject even if what you are saying about it is false. A predicate is different. The subject is talked about and the predicate does the talking. Put them together and you get a proposition. Read 1 - 10

Note: ' ○ ' is not used as a predicate in future posts.
1.      {[( is true ) is a predicate] is a proposition} is true.

2.       ' ○ ' is a predicate. 

3.       ' is awesome ' is also a predicate. 

4.       ○ ( David is awesome ).

5.       If ' A ' represents ' is awesome ', then ○ ( A David ). 

6.       Simplify my name to just ' d '. 

7.       So, ○(Ad). 

8.       ○{[(○) is a predicate] is a proposition} says precisely the same thing (1) says. 

9.       In other words, ' ○ ' represents the predicate ' is true '. 

10.     Conversely, ' ● ' means ' is false '.

( Take note that ' (Ad) ' is the subject of ' ○(Ad) '. A proposition can be a subject.)

I define my own terms and rules. The way I symbolize from English to predicate logic is to always order from left to right the predicate symbol with its corresponding subject symbol. Letter predicate symbols are capitalized. The subject symbol is always lowercase. Go through the above list again now that you know the predicate/subject order and capitalization rules. 

In conclusion, Ad. (Remember: ' Ad ' means ' David is awesome ') 

Random Comment: Following set rules from start to finish is a good way to attract mathematician eyeballs.

Imagine a Frog

Did you imagine a frog? When I look at ' frog ' I imagine a picture of a frog but when I look at ' P4ÆØ ' no previously programmed or knee-jerk response occurs in my mind. Redefine the symulus 'ÆØ ' to mean dog, ' ? ' to mean friend, and ' # ' to mean haired. The following sentences use each word's new representation.

I took my ÆØ for a walk this morning.

I ran into a ? and she has two ÆØ's.

Molly is a shaggy # ÆØ but Tank is a short # ÆØ.

If the symulus normally used to write English are replaced as they are above, then the average reader will experience a delayed symulus-to-symbolate response when compared to the normally used collection of symulus. Also, as the diversity and number of replacements increase, a delayed symulus-to-symbolate response will also increase. Do you agree?

Foreign symulus are easier to see as independent entities existing in and of themselves or in other words symbola. While familiar symulus are easier to think of as their corresponding symbolate. Regardless, the mind must travel from symulus to symbola to symbolate. Any multilingual speaker can attest to the truth of these assertions.