Full does not imply strong, does it?

Algebra Universalis Full does not imply strong , does it ?

We give a duality for the variety of bounded distributive lattices that is not full (and therefore not strong) although it is full but not strong at the finite level. While this does not give a complete solution to the “Full vs Strong” Problem, which dates back to the beginnings of natural duality theory in 1980, it does solve it at the finite level. One consequence of this result is that altho...

Superintelligence Does Not Imply Benevolence

Asmachines become capable ofmore autonomous and intelligent behavior, will they also display more morally desirable behavior? Earth’s history tends to suggest that increasing intelligence, knowledge, and rationality will result in more cooperative and benevolent behavior. Animals with sophisticated nervous systems track and punish exploitative behavior, while rewarding cooperation. Humans form ...

Does ‘Ought’ Imply ‘Can’? And Did Kant Think It Does?

Count(q) Does Not Imply Count(p)

I solve a conjecture originally studied by M. Ajtai. It states that for different primes q, p the matching principles Count(q) and Count(p) are logically independent. I prove that this indeed is the case. Actually I show that Count(q) implies Count(p) exactly when each prime factor in p also is a factor in q. 1 The logic of elementary counting “She loves me, she loves me not, she loves me,. . ....

Diversity does not Necessarily Imply Adaptability

Dynamic optimiser design currently assumes that diversity is a desirable property towards achieving adaptability, as a population-based optimiser contains an implicit memory. This paper examines the applicability of this assumption. Population-based algorithms of different size are tested against optimisers using a single solution. Results presented here suggest that this view is somewhat simpl...