According to Kardashev Scale, can a Type I Civilization be able to develop artificially intelligent system that surpasses it's own intelligence to match the intelligence of higher civilizations in the hierarchy?
According to the Church-Turing thesis any future computer can be simulated on a Turing machine. Imagine Deep Thought, the Multicorticoid Perspecutron Titan Muller, Milliard Gargantubrain, Hactar, mighty supercomputers of old, machines of renown. They all could be simulated on a Raspberry Pi, given enough time and memory (cloud based?).
So how could an already-intelligent system be enhanced to bring forth more intelligent behavior? Sure, bigger knowledge bases add to problem-solving capabilities. Douglas R. Hofstadter put the ability to detect analogies into the center of thinking. This could be achieved by pattern-matching: more processing power, more computer cores, more parallelity.
In general every future intelligence system surfaces the previous, mainly because of more knowledge addition due to future researches and development which may be apply to every future system.
If we assume that it is possible that a civilization can design AI that surpasses the intelligence of that civilization, then it would be an evolutionary process because that AI will surely be able to do the same.
See the recommendation of Rachit S Garg for the Artificial Intelligence scale similar to Kardashev's.
To answer your question, the first step is to find equivalent measure units.
Kardasev's scale for technological level of civilization uses astronomy and the levels are the planet (I), the planetary system (II), and the galaxy (III).
Then for the scale of the artificial intelligence level of civilization
- the basic unit (1) is ... what? : an "individual"!
- The next level (2) would be the intelligence of a "collective"/"team" = "a 'swarm' of humans". (see https://en.wikipedia.org/wiki/Swarm_intelligence)
- Next (3) we have the level of the intelligence of a planet civilization (humans / extraterrestrial beings),
- the level (4) of the intelligence of a planetary system civilization,
- the level (5) of the intelligence of a galaxy civilization, and
- the level (6) of super-being (human / extraterrestrial) intelligence.
We can see from the proposed AI scale that:
- The first gigantic step (our level 1) is the "Type II AI" (General AI) and is not achieved yet!
- Currently The Mankind works simultaneously for the levels 1, 2, and 3 (for examples of human level 3: IOT).
- The Kardashev's level 1 equivalent is our level 3.
- The Kardashev's level 2 equivalent is our level 4.
- The Kardashev's level 3 equivalent is our level 5.
I suppose that having obtained our level 1 AI (an "individual" intelligence equivalent) the levels 2 and 3 will be much easier to attain. As for the level 4 and/or 5 they could be very difficult as we must possibly blend with strange (from our point of view) extraterrestrial civilizations.
- Can a Civilization (any level) develop an AI system that surpasses his intelligence? Is more than possibly, is certainly! Think only to the non-human senses (animal or artificial) which are already in use!
- Can a Civilization (any level) develop an AI system that matches a superior level? It depends! If it is necessary to blend two different kinds of civilizations none of the two can do it by herself.