What is the definition of the understanding of (written) natural language and how can we test or measure this understanding? What is understanding of the symbolic knowledge be it encoded in any form? This question is about symbolic knowledge, not about aesthetic and art.

Natural language understanding is neglected part of natural language processing in computer science. Exact definitions and tests of understanding are necessary for producing artificial general intelligence (AGI) - e.g. https://link.springer.com/chapter/10.1007/978-3-319-41649-6_13 article argues that artificial general intelligence (e.g. software piece) should learn and self-modify itself but such development is possible only if AGI can estimate the quality/fitness of the new self-modification - whether this self-modification is better than existing version of AGI and whether this self-modification can be applied? Obviously - if we want to apply machine learning and AGI to understanding of the natural language then we should be able to test and measure the understanding.

There is article https://link.springer.com/chapter/10.1007/978-3-319-41649-6_11 about understanding specifically but it is somehow narrow minded to the particular QA task. Maybe cognitive science have better tests?

For the reference - there are some AGI systems of "cognitive architectures" under development (wikipedia has list of them) - like OpenCog, NARS, Soar and some others.

So - if we can define and measure understanding, how machines understand knowledge then we can come closer to AGI.

Philosophy has been the source of ideas for mathematics and computer science for long time. E.g. Goedels incompleteness theorems are more or less just mathematical encoding of the liar's paradox. If we can define understanding philosophically then we can also use this notion in computer science and artificial intellifence specifically.

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    Are you familiar with the work of Schank? fbi.h-da.de/fileadmin/personal/b.harriehausen/NLP/NLP_SS07/… – MmmHmm Mar 11 '17 at 11:49
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    Isn't Schmidhuber great? – MmmHmm Mar 11 '17 at 11:49
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    Erklaren meaningfully is one "test" of verstehen however, like the Turing test, interpretation of the test data it is within a subjective boundary, though with sufficient computational force, an adequate simulation could be achieved in an efficient time window. – MmmHmm Mar 11 '17 at 11:52
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    IT reads like you have considered these boundary conditions as well: cogprints.org/7150/1/ – MmmHmm Mar 11 '17 at 11:54
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    This is sometimes called "competence" (e.g. Chomsky) – Joseph Weissman Mar 11 '17 at 12:45

In computational semantics, the meanings of sentences are sometimes represented using discourse representation theories, which represent the meanings of sentences using logical predicates.

This approach has been used in artificial intelligence to implement natural language understanding systems such as Attempto Controlled English.

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