Human languages include adjuncts, which are grammatically optional
elements. Some adjuncts can also be repeated indefinitely. I
consider four learnable classes of languages and ask whether
these classes include optional and repeated elements, and what
input a learner requires in order to generalise from finite to
indefinite repetition.

Keywords: adjunct, adjective, optionality, repetition, learnability, PDFA, 0-reversible, n-gram, substitutable context free

• N-gram learners:
  
  
  
  • For an n-gram learner to learn a language with a string
    x that
    can be repeated indefinitely in some context, the learner must
    encounter, in that context, x, xx, xxx,... up to n
    divided by the length of x, +2, x's.
    
  
  

• 0-reversible learners:
  
  
  
  • For a 0-reversible learner to learn a language with a string
    x that is optional and
    can be repeated indefinitely in some context, the learner must
    encounter, in that context, n x's and n+1 x's for
    some n. For example, if the learner encounters The red red
    red rose and The red red red red rose, it will conclude
    not only that, say, The red red red red red red rose is
    grammatical, but also that The rose is.
    
  
  
  
  
• Substitutable context free learners:
  
  
  
  • Just like for 0-reversible learners, for a substitutable learner to learn a language with a string
    x that is optional and
    can be repeated indefinitely in some context, the learner must
    encounter, in that context, n x's and n+1 x's for
    some n.
    
  
  
• Clark & Thollard's PDFA learner
  
  
  
  • Repetition and optionality are both learnable
    
  • No mutual entailment in normal cases
    
  
  

  
  In human language, not all repeatable elements are optional,
  and not all optional elements are repeatable. However, this work
  does not yet include learners for human-like languages; stay
  tuned!
  

• Slides ISAIM 2014: Learning repetition and optionality


• SCiL 2020 talk: Adjuncts, Repetition, and Learnability

                
@incollection{fowlie2014learning,
  title={Learning Adjuncts},
  author={Meaghan Fowlie},
  booktitle={Connectedness: papers by and for {S}arah {V}an{W}agenen},
  series={UCLA Working Papers in Linguistics},
  editor={Carson Schutze and Linnaea Stockall},
  volume={18},
  pages={},
  year={2014}
}
            

                
@phdthesis{fowlie2017slaying,
  title={Slaying the Great Green Dragon: Learning and modelling iterable ordered optional adjuncts},
  author={Fowlie, Meaghan},
  year={2017},
  school={UCLA}
}