We consider a 2-valued non-deterministic connective $${\wedge \!\!\!\!\!\vee }$$ defined by the table resulting from entry-wise union of tables conjunction and disjunction. Being half disjunction we named it platypus. The value is not completely determined input, contrasting with usual notion Boolean connective. call any based on multi-functions over set. In this way, non-determinism allows for...

This paper explores derivative operations of the Boolean differential calculus for lattices of Boolean functions. Such operations are needed to design circuits with short delay and low power consumption [3] as well as to calculate minimal complete sets of fitting test patterns [4]. It will be shown that each derivative operation of a lattice of Boolean functions creates again a lattice of Boole...

This paper presents a new type of neuron, called Boolean neuron. We suggest algorithms for decomposition of Boolean functions sets based on Boolean neural networks that include only Boolean neurons. The advantages of these neural networks consist in the reduction of memory space and computation time in comparison to the representation of Boolean functions by usual neural networks. The Boolean n...