Abstract It is often useful to be able deal with locales in terms of presentations their underlying frames, or equivalently, the geometric theories which they classify. Given a presentation for locale, its sublocales can obtained by simply appending additional relations, but case quotient more subtle. We provide simple procedures obtaining open quotients, proper quotients general triquotients f...

Intelligent cooperative multiagent systems are applied for solving a large range of real-life problems, including in domains like biology and healthcare. There are very few metrics able to make an effective measure of the machine intelligence quotient. The most important drawbacks of the designed metrics presented in the scientific literature consist in the limitation in universality, accuracy,...