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Projects archive / Monotone boolean functions in 4 variables

Code:fdl4Beynon2002
Title:Monotone boolean functions in 4 variables
Authors:Meurig Beynon, Bibi Hussain
Date:19-Aug-2002
Type:model
Funding:Acad - Academic research
Short description:Modelling FDL4 by decreasing families of subsets
EM Technologies:tkeden, %eden, %donald, %scout, %eddi
Keywords:tutorial, education
empublic references:fdl3Hussain2001
EMpress references:
Web site references:
Previous locations:
Tour:README.txt

This model generalises a model developed by Bibi Hussain in her third year project in 2000-2001 (viz. fdl3Hussain2001). (The DoNaLD specification of the Hasse diagram for FDL4 was constructed by Hussain based on the work done by John Buckle in his PhD thesis.) The model illustrates the construction of two types of lattice: boolean lattices (as represented by the powerset B4 of a 4 element set) and free distributive lattices [FDLs] (as represented by the 166 monotone boolean functions with 4 arguments - or equivalently propositions involving 4 variables and the connectives AND and OR). The model animates set union and intersection in B4, and displays the correspondence between elements of FDL4 and decreasing subsets of B4. Each decreasing family of subsets X determines a unique monotone boolean function that takes the value 0 on all the characteristic vectors associated with sets in X. The functionality of the model generalises that of Hussain's model of FDL3 in that the values of x and y entered in the interface can refer to elements in FDL4 as well as subsets of B4. Following John Buckle (and modulo the reconfiguration of the Hasse diagram by inversion and L to R reflection that is introduced in Beynon's model), the elements of FDL4 are labelled as a1, a2, b2, c2, d2, a3, b3, c3, d3, e3, f3, a4, ... etc according to their position in R to L order and the level (from 1 to 15) at which they appear in FDL4. The code of an element can be entered as a value for x and y through the interface, and the corresponding elements, together with their union and intersection, will be displayed in FDL4 subject to pressing the "Enter x and y values" button and clicking in the FDL4 window.

fdl4Beynon2002 is available locally within DCS at /dcs/emp/empublic/projects/fdl4Beynon2002
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README.txt 7347 08:45 PM Aug 29 2002 04:05 PM Dec 15 2014
README.txt~ 7347 05:47 PM Aug 19 2002 04:05 PM Dec 15 2014
README.xml 2363 05:46 PM Aug 19 2002 04:05 PM Dec 15 2014
Run.e 298 08:31 PM Aug 17 2002 04:05 PM Dec 15 2014
addattrfdl4.e 29154 09:27 PM Aug 15 2002 04:05 PM Dec 15 2014
attrfdl4.e 32138 04:59 PM Aug 07 2002 04:05 PM Dec 15 2014
buildfdl4.e 2033 01:00 PM Jul 27 2002 04:05 PM Dec 15 2014
currelttxt.e 539 10:39 AM Aug 16 2002 04:05 PM Dec 15 2014
eltlocate.e 2175 08:00 PM Jul 29 2002 04:05 PM Dec 15 2014
fdl4.e 5779 08:03 AM Aug 18 2002 04:05 PM Dec 15 2014
fdlscreenshot.gif 29394 05:34 PM Aug 19 2002 04:05 PM Dec 15 2014
ixfdl4.e 3040 08:51 AM Aug 18 2002 04:05 PM Dec 15 2014
lattice4.e 5975 04:14 PM Jul 30 2002 04:05 PM Dec 15 2014
loadfdl4.e 2363 08:50 AM Aug 18 2002 04:05 PM Dec 15 2014
locixfdl4.e 2139 09:39 PM Jul 29 2002 04:05 PM Dec 15 2014
makembf.e 1028 10:10 AM Aug 14 2002 04:05 PM Dec 15 2014
newmakembf.e 1326 10:51 AM Aug 14 2002 04:05 PM Dec 15 2014
probnotes.txt 743 09:01 PM Jul 29 2002 04:05 PM Dec 15 2014
v2fdl4.e 16794 10:26 PM Jul 29 2002 04:05 PM Dec 15 2014
wmbFDL4diagram.d 19774 10:50 AM Aug 18 2002 04:05 PM Dec 15 2014
wmbsupp.e 1756 10:36 AM Aug 16 2002 04:05 PM Dec 15 2014
xypanel4.s 6919 08:36 AM Aug 18 2002 04:05 PM Dec 15 2014

empublic system initially created by Ashley Ward with assistance from Chris Roe and Meurig Beynon.