The Lattice Computing (LC) Paradigm

The notion of Cyber-Physical Systems (CPSs) has been introduced to account for technical devices with both sensing and reasoning abilities including a varying degree of autonomous behaviour. There is a need for supporting CPSs by mathematical models that involve both sensory data and cognitive data towards improving CPSs effectiveness during their interaction with humans. However, a widely acceptable mathematical modelling framework is currently missing. In the aforementioned context, the Lattice Computing (LC) paradigm is proposed for mathematical modelling in CPS applications based on lattice theory by unifying rigorously numerical data and non-numerical data; the latter data include (lattice ordered) logic values, sets, symbols, graphs and other. More specifically, the “cyber” components of a CPS involve nonnumerical data, whereas the “physical” components of a CPS involve numerical data. A promising advantage of LC is its capacity to compute with semantics represented by a lattice (partial) order relation