Tree-Star: The Bayes-Star Treebank

First-Order Logical Forms for All Natural Language and an associated Semantic Parser

Greg Coppola, PhD.

coppola.ai, vibes.university

March 11, 2025

Abstract

We announce a new project called "Tree-Star: The Bayes-Star Treebank".

• The goal of this project is to provide:
  • A framework for analyzing:
    • All (in principle) human "natural language sentences".
    • Into "first-order logic" representations.
    • Using "labeled dependency parses" as an "intermediate" layer of "syntactic analysis".
  • An associated "syntactic parser" and "semantic parser" that uses machine learning to produce such analyses automatically.
  • A "treebank" of natural language that is "annotated" with all applicable "semantic" and "syntactic" parsing layers.

This project can be found online at:

• https://github.com/gregorycoppola/tree-star

The Need for Syntactic Analysis in 2025

• Traditional syntactic analysis (Chomsky, Montague) involved layers of tree-structured "syntactic" and "semantic" analysis.
• Large language models:
  • Have been the basis for the modern "boom" in attention and investment on the field of natural language processing.
  • "Large language models" do not use any traditional "hierarchical" or "latent" layers.
  • Powerful, but also limited.
• The limits of "large language models":
  • In our work last year "The Quantified Boolean Bayesian Network: Theory and Experiments with a Logical Graphical Model" we reviewed some of the limitations of basic LLM's:
    • They can't reason.
    • They can't plan.
    • They can't answer "probability queries".
  • We believe that these problems can be addressed with a "logical graphical model" (aka. "logical bayesian network", "logical markov model").
    • However, in order to realize this, it is necessary to first be able to express any sentence from natural language in first-order logic.
  • This, in turn, we believe necessitates being able to give a syntactic and semantic analysis of sentences in an arbitrary natural language sentence.

The Three Interfaces

We identify "three" key interfaces that our model maps between.

• Surface form:
  • The level of "tokens".
  • Does not involve any "latent variables":
    • I.e., this layer is "fully observed".
  • The "layer" that humans interpret directly.
• Labeled dependency parse:
  • Contains "latent annotations" of a "labeled dependency tree" in which the "hidden variables" are:
    1. For each word, an "index" of another word in the document, called an "unlabeled dependency".
    2. For each "unlabeled dependency", there is one "label", taken from a finite (and in practice usually quite small) set of "discrete labels".
• First-order logic:
  • Historically well-proven as the basis for mathematics.
  • Forms the basis of much post-LLM work in "reasoning".
  • The use of "logic" is implicit in "agents".

This specific "three layer approach" we propose is an instance of "dependency categorial grammar".

Methods

• English-first:
  • We will begin the process in English (or "0 to 1") first.
  • And then extending English to other languages (or "1 to N") can be done after.
  • We believe that the extension from a complete treatment of English to other languages can be done "largely automatically", due to the ability for LLM's to annotate examples as well.
• Conversion of previously labeled data:
  • We will leverage existing (expensively produced) "labeled syntactic corpora", e.g., CoNLL:
    • These represent years of study by talented and expensive researchers, as well as data labeling expense.
  • We can leverage LLM's to produce additional "layers" of annotation.
• Labeling of new unlabeled data:
  • We can leverage access to state-of-the-art LLM's via API's to label new data that has never been labeled at all.
• Community iteration:
  • We are open to receiving feedback from the community!
• Timeline:
  • We will run the project until we feel a decent "first pass" has been made.

Future Impact

• Future applications with potentially large impact include:
  • Integrate this into a "logical markov network" to represent "human knowledge".
  • Create a system of "logical information retrieval" based on theorem-proving.
  • Create systems that can answer "probability queries" for arbitrary sentences in human language.

Bibliography

We will present a "living" full bibliography in the repo.