PeterBurbery/BooleanLogic

(1.23.0) current version: 1.24.0 »

Work with logical functions and boolean values

Contributed By: Peter Cullen Burbery

This paclet contains helpful functions for boolean logic. I give credit to the authors of FindBooleanAlternative, Stephen Wolfram and Nikolay Murzin. I want to compile helpful functions for logic into one place.

Installation Instructions

To install this paclet in your Wolfram Language environment, evaluate this code:
PacletInstall["PeterBurbery/BooleanLogic"]

Details

The picture has William of Ockham in the center, who formulated what is now known as De Morgan's Laws. William of Ockham was a theologian who formulated Ockham's razor and studied ternary logic.

Paclet Guide

Examples

Basic Examples (13) 

Find an alternative form of p implies q and r with xor and nand:

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Out[1]=

Find seven other alternatives:

In[2]:=
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Out[2]=

Make a Venn diagram for b, c, and d:

In[3]:=
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Out[3]=

Add the input e to the Venn Diagram:

In[4]:=
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 b \[Xor] (c \[And] d \[Or] e)]
Out[4]=

VennDiagram can accept up to 5 variables:

In[5]:=
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Out[5]=

Make a Venn diagram using BooleanFunction as input:

In[6]:=
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 BooleanFunction[RandomInteger[2^(2 4)], 4][b, c, d, e]]
Out[6]=

Create a Venn diagram by using sets as input:

In[7]:=
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    c, e, g}}]
Out[7]=

Create a Venn diagram by using Not and Or canonical normal form as input:

In[8]:=
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Out[9]=

Find information on a boolean function's structure:

In[10]:=
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Out[10]=

Find information on the output given true inputs and false inputs, including whether the problem is satisfiable. This is helpful when working on the NP-complete problem 3SAT:

In[11]:=
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Out[11]=

Evaluate the NP complete 17SAT problem:

In[12]:=
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Scaled[0.15`]], Rule[ImageSize, 10], Rule[ImageSize, List[Automatic, 35]]]], StyleBox[RowBox[List["BooleanTruthInputData", " "]], Rule[ShowAutoStyles, False], Rule[ShowStringCharacters, False], Rule[FontSize, Times[0.9`, Inherited]], Rule[FontColor, GrayLevel[0.1`]]]]], Rule[GridBoxSpacings, List[Rule["Columns", List[List[0.25`]]]]]], Rule[Alignment, List[Left, Baseline]], Rule[BaselinePosition, Baseline], Rule[FrameMargins, List[List[3, 0], List[0, 0]]], Rule[BaseStyle, List[Rule[LineSpacing, List[0, 0]], Rule[LineBreakWithin, False]]]], RowBox[List["PacletSymbol", "[", RowBox[List["\"PeterBurbery/BooleanLogic\"", ",", "\"BooleanTruthInputData\""]], "]"]], Rule[TooltipStyle, List[Rule[ShowAutoStyles, True], Rule[ShowStringCharacters, True]]]], Function[Annotation[Slot[1], Style[Defer[PacletSymbol["PeterBurbery/BooleanLogic", "BooleanTruthInputData"]], Rule[ShowStringCharacters, True]], "Tooltip"]]], Rule[Background, RGBColor[0.968`, 0.976`, 0.984`]], Rule[BaselinePosition, Baseline], Rule[DefaultBaseStyle, List[]], Rule[FrameMargins, List[List[0, 0], List[1, 1]]], Rule[FrameStyle, RGBColor[0.831`, 0.847`, 0.85`]], Rule[RoundingRadius, 4]], PacletSymbol["PeterBurbery/BooleanLogic", "BooleanTruthInputData"], Rule[Selectable, False], Rule[SelectWithContents, True], Rule[BoxID, "PacletSymbolBox"]][
  BooleanFunction[RandomInteger[2^(2 17)], 17]] // Short[#, 9] &
Out[12]=

Generate a truth table for a function with 4 inputs:

In[13]:=
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  b \[Xor] c \[Or] d \[And] e] // TraditionalForm
Out[13]=

Use 1 and 0 in place of true and false, respectively:

In[14]:=
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Out[14]=

Publisher

Peter Burbery

Compatibility

Wolfram Language Version 13.1

Version History

  • 1.24.0 – 29 September 2022
  • 1.23.0 – 29 September 2022
  • 1.22.0 – 29 September 2022
  • 1.21.0 – 29 September 2022
  • 1.20.0 – 29 September 2022
  • 1.19.0 – 29 September 2022
  • 1.18.0 – 29 September 2022
  • 1.17.0 – 29 September 2022
  • 1.16.0 – 28 September 2022
  • 1.15.0 – 28 September 2022
  • 1.14.0 – 27 September 2022
  • 1.13.0 – 27 September 2022
  • 1.12.0 – 19 September 2022
  • 1.11.0 – 19 September 2022
  • 1.10.0 – 19 September 2022
  • 1.9.0 – 19 September 2022
  • 1.8.0 – 19 September 2022
  • 1.7.0 – 19 September 2022
  • 1.6.0 – 19 September 2022
  • 1.5.0 – 19 September 2022
  • 1.4.0 – 18 September 2022
  • 1.3.0 – 18 September 2022
  • 1.2.0 – 17 September 2022
  • 1.1.0 – 17 September 2022
  • 1.0.0 – 17 September 2022

License Information

MIT License

Paclet Source

Source Metadata

See Also