Next character prediction (list)?

[jabowery]

Recognizing this may be beyond the intended scope of the maxsynth ILP approach to program synthesis:

Muggleton does, in "Inductive Logic Programming: Theory and Methods" , reference Solomonoff Induction as foundational. Bearing in mind the critical difference between Rissanen's Turing INcomplete MDL codes, and the Turing Complete basis for Kolmogorov Complexity used by Solomonoff, what might a "next character prediction" based on ILP look like?

For example, the following is non-working code for a problem generator that reads in a 100M snapshot of Wikipedia for a list problem:

(maxsynth) jabowery@jaboweryML:~/devel/maxsynth$ cat ilpexp/problem/list/wiki/wiki.py 
import random
from ..list import ListProblem, gen_list
wikistr = open('/mnt/BulkData/home/jabowery/dev/sequitur/data/enwik8').read()
context = 1000
pred_len = 1
def gen_pos():
    pos = random.randint(0,len(wikistr)-1-context-pred_len)
    x = list(wikistr[pos:pos+context+1])
    y = x[-pred_len:]
    x = x[:-pred_len]
    return f'f({x},{y})'

def gen_neg():
    while True:
        pos = random.randint(0,len(wikistr)-1-context-pred_len)
        x = list(wikistr[pos:pos+context+1])
        pos = random.randint(0,len(wikistr)-1-context-pred_len)
        y = wikistr[pos:pos+pred_len]
        x = x[:-pred_len]
        return f'f({x},{y})'

WIKI = 'wiki'

class Wiki(ListProblem):
    def __init__(self, noise_level=0):
        super().__init__(WIKI, gen_pos, gen_neg, WIKI, noise_level)

[andrewcropper]

Richard Evans uses ILP to do character prediction:

Richard Evans, José Hernández-Orallo, Johannes Welbl, Pushmeet Kohli, Marek J. Sergot:
Making sense of sensory input. Artif. Intell. 293: 103438 (2021)

Available here: https://arxiv.org/pdf/1910.02227.pdf