The Truth-table Widget happens to be called Truth-table Widget due to its sole purpose being the generation, and proper display, of truth-tables. The widget works with MacOS 10.4.3 and later. It is small and does not require a live connection to the Internet.

The Truth-table Widget, being so called due to it being a widget displaying truth-tables, 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.

Mac OS X 10.4 Tiger is required. If you're using Safari, click the download link. When the widget download is complete, Show Dashboard, click the Plus sign to display the Widget Bar and click the widget's icon in the Widget Bar to open it. If you're using a browser other than Safari, click the download link. When the widget download is complete, unarchive it and place it in /Library/Widgets/ in your home folder. Show Dashboard, click the Plus sign to display the Widget Bar and click the widget's icon in the Widget Bar to open it.

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

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

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

P->Q->P | CCpqp |

~P v Q | ANpq |

P & Q v P & R | AKpqKpr |

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

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

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

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

P!P | NApp |

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

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

The user interface of the Truth-table Widget consists of a sole 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). After entering the proposition, all the user needs to do is depressing the Enter key smoothly, but firmly. No more than one or two blinks of an eye later, the truth-table gets displayed properly.

Note: Your browser may be unable properly to display some of the logical connectives used below. Of course this restriction will not apply to the Truth-table widget 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.
- Operator precedence
- The precedence of the operators is the following: (1) Negation (first); (2) conjunction and NAND; (3) disjunction, XOR, and NOR; (4) conditional; and (5) biconditional (last). Operators of the same precedence that are not grouped with brackets will be evaluated from left to right.

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).

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

2012-10-27 13:58:02

gottschall@gmx.de