📄 Extracting First Order Logic formulas from graphical semantic representations

Summary

Graph-based meaning representations such as amr are easy to annotate and parse, but they leave out logically important information like quantifier scope. Logic-based formalisms capture that information but are costly to produce. Yarn, a layered formalism, tries to combine the strengths of both. This paper asks how expressive Yarn really is by giving its structures a formal logical interpretation.

The authors define a translation in three steps:

• A Yarn structure becomes an intermediate pair (F, R). F is a labelled forest recording scope dependencies, and R holds flat predicate-argument relations.
• A constraint system C(F, R) is built. Its solutions are the admissible scope trees, so Yarn's underspecification is spelled out explicitly.
• A compositional function turns each admissible tree into a formula of modal first-order logic with temporality.

Because scope can stay underspecified, one Yarn graph maps to a set of formulas rather than a single one. Worked examples show that the approach handles interacting scopes and dynamic quantification. This grounds Yarn in formal semantics and positions it alongside constraint-based frameworks such as MRS and Predicate Logic Unplugged.

Key points

• Formally, Yarn (Pavlova et al., 2024; Pavlova, 2025) is defined as a tuple with nine components, which group by role as follows (with I as the ninth):
  • V and E form an amr-like predicate graph built on PropBank frames.
  • F, L and H encode features and their scope chains.
  • S, D and C carry discourse structure.
• The study restricts features to four layers: tense, modality, negation and quantification. I edges, which express set membership, are simply treated as E edges.
• The running example is "In the future, politicians won't like researchers who signed a petition." It shows that ordering future, necessity and negation differently gives distinct readings, either an impossible event or one that might not happen.
• The pipeline is Yarn → (F, R) → constraint system C(F, R) → admissible trees → modal temporal FOL formulas.
• The work is purely theoretical, with no corpus or parser evaluation. It continues earlier efforts to give logical semantics to amr (Bos, 2016; Lai et al., 2020), and its scope-constraint layer resembles Bos (1996).