Monotone boolean functions in 3 variables
Modelling FDL3 by decreasing families of subsets
This model was developed by Bibi Hussain in her third year project in 2000-2001. It illustrates the construction of two types of lattice: boolean lattices (as represented by the powerset B3 of a 3 element set) and free distributive lattices [FDLs] (as represented by monotone boolean functions with 3 arguments or equivalently propositions involving 3 variables and the connectives AND and OR). The model animates set union and intersection in B3, and displays the correspondence between elements of FDL3 and decreasing subsets of B3. 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.
Final year project