Class Preserving Monotonic and Dual Monotonic Language Learning

In the present paper strong{monotonic, monotonic, weak{monotonic as well as dual strong{monotonic, dual monotonic and dual weak{monotonic reasoning is studied. We investigate the power of all types of monotonic and dual monotonic inference from positive as well as from positive and negative data in the context of algorithmic language learning theory, thereby obtaining strong hierarchies. Strong{monotonicity describes the requirement to only produce better and better generalizations. Monotonic learning re ects the demand that for any two guesses the one output later has to be at least as good as the previous one with respect to the language to be learnt. Weak{monotonicity is the analogue of cumulativity in learning theory. Dual strong{monotonic learning expresses the concept to generate a chain of descending specializations converging in the limit to the target language. Dual monotonicity describes the same goal with respect to the target language and dual weak{monotonic learning is the dual analogue of cumulativity.