- The program
- Compatibility
- Input examples
- Usage
- Infix notation
- Polish notation
- Alpha graphs: an extremely short introduction
- Feedback

The sole purpose of this program is generating, and displaying, Alpha Graphs under Symbian. Alpha Graphs are the propositional subset of Charles Sanders Peirce's logical system called Existential Graphs.

The program will work with a number of fairly recent Nokia mobile phones, especially (but not restricted to) those with a touch-pad. Trying out the program on a Symbian phone of your choice won't do any harm; if it proves not to work with the respective phone, just uninstall it, and, optionally, hope for a future version.

The program supports all usual connectives of classical logic, that is negation, conjunction, (inclusive) disjunction, conditional (material implication), biconditional (material equivalence), exclusive disjuncton (XOR), the Peirce operator (NOR), the Sheffer operator (NAND), as well as the constants 1 and 0 denoting truth and falsehood, respectively.

The program has been tested running e.g. on the following Nokia devices: 5230, 5630 XpressMusic, 5800 XpressMusic, 6220 classic, 6700, 6710 Navigator, E51, E52, E63, N86, N97, N97 mini, X6

The following Nokia devices are known to run this program with the single exception that they do not show the "Input" and "Examples" menus, meaning that you have to enter your propositions using the keyboard: N78, N81, N96

The following Nokia devices are known *not* to run this program:
5700,
6110,
6120 classic,
E61,
N73,
N80,
N93

Infix notation | Polish notation |
---|---|

P->(Q->P) | CpCqp |

(P->Q)->P | CCpqp |

~P v Q | ANpq |

(P & Q) v (P & R) | AKpqKpr |

(P & (Q v P)) & R | KKpAqpr |

((P>(Q>R))>((P>Q)>(P>R))) | CCpCqrCCpqCpr |

P!P | NApp |

(P!Q)!(P!Q) | NANApqNApq |

(P!P)!(Q!Q) | NANAppNAqq |

The main component of the user interface is the text field where the user may enter a single proposition, be it in infix notation (the somewhat standard way of writing down propositions), or in Polish notation (the cool prefix notation developed by Lukasiewicz in the 1920s).

- When using a device with a full keyboard, you will probably enter the proposition using the keyboard.
- On a touch-style device, you will usually make use of the visual buttons labelled "P", "Q", and so on. There are buttons for a few propositional letters, and for the most important connectives. The blue button labelled "C" is for deleting the most recently entered character. The green button, finally, will submit your proposition causing the alpha graph to be generated.
- When using a device with a typical phone keyboard, you probably will prefer entering your proposition by selecting the respective entries in the options menu. The menu item "Propositions" will allow you to choose a propositional letter. The item "Connectives" offers a list of available connectives. The item "Brackets" will allow you to enter a bracket.

When finished entering, an alpha graph will be generated from the proposition when you either select the green touch-button (mentioned above), or when you select the respective item from the "Options" menu.

Note: Your browser may be unable to properly display some of the logical connectives used below. Of course this restriction will not apply to the program when installed and running on your personal computing device.

- Propositional constants
- A through U, and W through Z, case insensitive; note that the letter "v" is reserved for disjunction (see below) and may not be used for a propositional constant.
- Negation
- ~ (tilde), - (dash), ¬
- Conjunction
- & (ampersand), ^, ∧
- Disjunction
- v (the lower-case letter), |, ∨
- Conditional
- >, ->, =>, -->, ==>, →
- Biconditional
- =, ↔
- XOR
- %
- Peirce operator (NOR)
- ! (exclamation mark), ↓
- Sheffer operator (NAND)
- upside-down exlamation mark, ↑
- Brackets
- As usual, the rounded brackets, (, and ), may be used for grouping expressions.
- Spaces
- In order to improve readability, the user may freely add space characters into their proposition.

Propositions in Polish notation are restricted to Lukasiewicz's own connectives N, K, A, C, and E. You have to user lower-case letters as propositional constants, but not the letter "v", since it denotes infix disjunction (see above).

For one thing (and as far as it concerns this program), alpha graphs are a graphical notation for propositional logic. In this respect, alpha graphs use only two connectives: conjunction and negation. Since all classical truth functions can be expressed using the truth functions of classical conjunction and negation, it is effectively possible to express any expression of classical propositional logic by an alpha graph.

- For expressing the conjunction of two propositions, you simply write both of them down. For example, "PQ" expresses the conjunction of the two atomic propositions "P", and "Q".
- To negate a proposition, you enclose it with a line building up e.g. a circle, an oval, a square, or indeed any closed geometrical figure you like (for technical reasons, this program uses rectangles). A variant proposed by Peirce himself is bracketing: Here you put the proposition to negate between brackets, making the brackets "simulate" a closed figure. So, if you want to negate "P", you write down "P" and draw e.g. a circle around it - or you write down "(P)".
- For the conditional "If P, then Q", Peirce uses the diagram corresponding to "(P(Q))", literally meaning "It is not the case that both P is true, but Q is false". Note that, indeed, P→Q is equivalent to ¬(P&¬Q).
- The alternative disjunction "P, or Q, or both" is written as "((P)(Q))" (or, rather, drawn as the corresponding diagram), literally meaning "It is not the case that both P, and Q, is false".

Though this short introduction should suffice to provide an understanding of the alpha graphs as a logical notation (and, hence, of the Alpha Graph Program), it does justice neither to Peirce's motivation (both philosophical and didactical), nor to the formal aspects of his graphical logic, since, for the other thing, what Peirce did was a formally complete graphical calculus. For an overview of these aspects, you might see my German Wikipedia article Existential Graphs. At the time of writing this, the article in the English Wikipedia is shorter and lacks depth, but provides both a first overview, and a number of references.

Your feedback, questions, and support will be most welcome. Please direct your verbal feedback to gottschall@gmx.de.

2012-09-07 09:58:02

gottschall@gmx.de