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Three Dogmas, a Puzzle and its Solution

Paper · 2023 · Elnaserledinellah Mahmood Abdelwahab

Summary

The paper argues that the founders of modern logic (Frege, Russell, Tarski) built formal languages on assumptions about natural language that linguists dispute. The author tests four such assumptions against established principles of Arabic grammar and semantics and claims to refute each: that words name objects, that copular "ToBe" sentences state identity, that indefinite descriptions only become meaningful when rewritten as existential quantifiers, and that symbols carry no meaning apart from an interpretation. From this, the author concludes that semantic axioms taken from mathematical logic should not serve as the model of meaning for Arabic syntax. The second half moves to computation. Arabic parsing is said to rely on "meaning-particles", syntactic markers that make words, phrases and sentences quick to recognise. The author identifies analogous particles in 3CNF formulas and uses them inside 3SAT solvers to impose structural conditions intended to keep Free Binary Decision Diagrams (FBDDs) from growing exponentially. Supporting evidence comes from multiplication circuits. The claim of efficient SAT handling is extraordinary, and the excerpt does not show independent verification.

Key points

  • Published in J. Acad. (N.Y.) 2023, Vol. 12,1:3-101 (99 pages), Theoretical Computer Science; also on arXiv as 2310.19123.
  • Part A sets each "dogma" of logic against an Arabic "anti-dogma", covering:
    • naming, sense and reference;
    • the verb "ToBe";
    • Russell's indefinite descriptions;
    • the link between grammar and meaning;
    • quantification anomalies and apparent paradoxes.
  • Part B explains why language recognition is NP-complete and links CNF formulas to truth tables and Binary Decision Diagrams. It notes that finding a literal ordering is itself NP-complete and poses the resulting "puzzle": can an optimal ordering be found efficiently?
  • Part C proposes a satisfaction procedure built from four parts:
    • the s.l.o. condition;
    • a Renaming Algorithm;
    • a Renaming and Ordering Algorithm;
    • a step called PR'.
  • The author argues that known exponential lower bounds on FBDD size do not contradict the results, and reports experiments on multiplication circuits.

Interesting ideas

  • I1. Grammatical marker words ("meaning-particles") can serve as cheap anchors that narrow the search when recognising phrases and sentences, rather than leaving the parser to treat every position alike.
  • I2. A copular sentence need not express identity between two referents; often it predicates a property or a class membership of the subject.
  • I3. An indefinite description can be kept as a meaningful unit in its own right rather than immediately rewritten as an existential quantifier.
  • I4. Rename and reorder variables according to structural conditions of the input, so that a decision diagram stays small, rather than accepting an arbitrary ordering.
  • I5. When claiming an efficiency result, explicitly explain why it does not conflict with known lower bounds, and test it on a family known to be hard (here, multiplication circuits).

For Mova

How these ideas could serve Mova, our small open language model — its files, stages and tests:

  • I1 (tree): Particles and function words (auxiliaries, determiners, subordinators) could act as early hard anchors in the perceptron parser, pruning candidate heads before costlier scoring.
  • I2 (frames): When prag builds a frame from a "be" clause, it could choose among identity, attribution and class-membership readings explicitly, instead of always linking two entities as equal.
  • I3 (world): Indefinite noun phrases could introduce provisional, underspecified entities in the world of the text, to be resolved or merged later by coreference instead of being fixed at once.
  • I4 (learn): Self-induced repair rules or knowledge-graph lookups could be ordered by structural dependencies to keep intermediate search spaces bounded, with that size logged as an explainable diagnostic.
  • I5 (learn): Evaluation could include a deliberately hard negative-control set where a method is expected to fail, together with a written argument for why any reported gain is not an artifact.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Institutions

Also on the byline: GridSAT Stiftung.

📚 Shelves 5The field of science this work belongs to (OpenAlex fields).Computer Science · 9,086 worksArtificial Intelligence · 8,889 worksArts and Humanities · 9,296 worksLanguage and Linguistics · 9,206 worksComputational Theory and Mathematics · 116 works

🧭 Topics 1Research subjects and languages the work is about.Semitic languages · 1,484 works

Cite

Cite as Elnaserledinellah Mahmood Abdelwahab. 2023. Three Dogmas, a Puzzle and its Solution. arXiv:2310.19123 · J. Acad. (N.Y.) 2023, Vol. 12,1:3-101.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.48550/arxiv.2310.19123 · arXiv 2310.19123

@misc{abdelwahab2023three,
  title = {{Three Dogmas, a Puzzle and its Solution}},
  author = {Elnaserledinellah Mahmood Abdelwahab},
  year = {2023},
  doi = {10.48550/arxiv.2310.19123},
  eprint = {2310.19123},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2310.19123}
}

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