Mereological vagueness and quantum information

Qualitative representations of mereological structures in Artificial Intelligence are generally based on a set of mutually exclusive and collectively exhaustive crisp (RCC5) relations. The amount of information carried by each element in this set of (crisp) relations is determined by the number of bits (N) required to distinguish all members of the set. This paper posits that mereological vagueness can arise if mereological relations are limited in the amount of information they can carry. Consequently, a comprehensive set of vague mereological relations is introduced, where each relation in this set can only carry 0 < n < N bits of information. In this framework, mereological information is treated as quantum information, with quantum bits (qubits) distinguishing relations subject to ontic vagueness. The main contribution is the thorough examination of mereological relations within a 3 qubit quantum system. Quantum bits are not represented as vectors in a Hilbert space but as cells in (granular) partitions. This paper is the companion to the author's quantized-mereology framework and develops its entangled-state layer: the combination of three simultaneous elementary questions, the families of entangled information states, the probability distribution for possible observations and the dynamics induced by sequences of non-simultaneous questions.