Computational Semantics Tools for Glue Semantics (2025)

Abstract: This paper introduces a suite of computational semantic tools for Glue Semantics, an approach to compositionality developed in the context of Lexical Functional Grammar (LFG), but applicable to a variety of syntactic representations, including Universal Dependencies (UD). The three tools are: 1) a Glue Semantics prover, 2) an interface between this prover and a platform for implementing LFG grammars, and 3) a system to rewrite and add semantic annotations to LFG and UD syntactic analyses, with a native support for the prover. The main use of these tools is computational verification of theoretical linguistic analyses, but they have also been used for teaching formal semantic concepts.

## introduction this paper introduces a suite of tools related to glue semantics @xcite @xcite , an approach to compositionality based on the idea of resource sensitivity, for a wider computational semantic audience. 1 on this approach, the compositional process is not necessarily determined directly by phrasal constituency (as in, for example, @xcite , but is rather guided by pairing (partial) semantic representations with linear logic formulas referring to parts of syntactic representations. while glue semantics has been most extensively applied in the context of lexical functional grammar (lfg; @xcite @xcite , it has also been successfully combined with other syntactic formalisms, including universal dependencies (e.g., @xcite , lexicalized tree adjoining grammar @xcite , head-driven phrase structure grammar (asudeh and crouch 1 early versions of two of these tools have been presented lfg-internally, the third is presented here for the first time. within lfg, computational research evolves around the xerox linguistics environment (xle; @xcite , a platform that has been primarily tailored towards the modeling of syntax. although xle grammars are being developed all across the world, the investigation of semantic issues in lfg from a computational perspective received impetus with the introduction of an early version of the glue semantics workbench (gswb; @xcite . 2 this paper presents new contributions to gswb and two recently developed resources that make use of it. 3 the central resource presented in this paper is the glue semantics workbench (gswb), a modular system for calculating glue semantics (henceforth, glue) proofs. it provides three different glue provers and is designed to permit the implementation of additional provers based on varying linear logic fragments and meaning languages (e.g., predicate logic with lambdas, drt, etc.). the second tool, xle+glue, implements an interface between gswb and xle. 4 this tool allows users to specify semantic contributions of lexical items and syntactic rules in xle grammars, which can then be fed into gswb for semantic calculation. the system has been mainly developed to explore what is called a "co-descriptive approach" to glue (explained in §2.2). xle+glue also illustrates the possibility of gswb to work with different meaning languages. the third tool presented in this paper is a system for linguistic graph expansion and rewriting (liger). it is inspired by the original xle transfer system, which was initially used for machine translation @xcite ) and later mainly for semantic parsing @xcite , but also as a full-fledged reasoning engine @xcite , indicating its versatility. liger has been developed because the original transfer component of xle is no longer supported by xle. like the original transfer system, liger can be used to enrich xle analyses with information from other linguistic resources. with respect to semantic analysis, it provides the possibility of exploring the second major approach to deriving glue representations, "description-by-analysis" (see §2.2), and thus complements xle+glue. overall, the tools presented here allow researchers to experiment with different settings within the glue framework, including the choice of a suitable linear logic fragment, the choice of meaning language, and the choice of co-description vs. description-by-analysis approaches to deriving meaning representations. the goal of this paper is to illustrate the capabilities of these tools and how they can be used for verifying theoretical analyses and for exploring formal semantic concepts. section 2 explains the lfg architecture, focusing on two aspects: the projection structure and glue. section 3 describes the three tools in more detail, while §4 mentions some use cases. section 5 concludes. ## background within the lfg community, the development of xle grammars, as well as associated resources such as treebanks, is carried out mainly in the scope of the parallel grammar (pargram) project @xcite . such grammars have been developed for a wide variety of typologically diverse languages, demonstrating the cross-linguistic and formal validity of lfg's (morpho)syntactic component. 5 the work presented in this paper aims to facilitate extending such syntac- ## the tools the pargram project provided a crosslinguistically informed approach to syntactic and semantic parsing, though the latter was mostly worked out for english, while concrete implementations for other languages were of limited scope. this is largely due to the fact that the semantics relied heavily on various external resources that were not available cross-linguistically. semantic parsing relied on ordered rewriting rules implemented as part of a transfer system in xle @xcite . another important issue addressed with the present tools is that the existing transfer system is neither publicly available nor compatible with the currently available xle releases provided by every monkey likes a banana. a. λx.λy.like(x, y) : mσ ⊸ (bσ ⊸ fσ) b. λp.∀x[monkey(x) → p (x)] : (mσ ⊸ fσ) ⊸ fσ c. λq.∃y[banana(y) ∧ q(y)] : (bσ ⊸ fσ) ⊸ fσ λp.∀x[monkey(x) → p (x)] : (me ⊸ ft) ⊸ ft [x : me] 1 λx.λy.like(x, y) : me ⊸ (be ⊸ ft) ⊸e λy.like(x, y) : be ⊸ ft λq.∃y[banana(y) ∧ q(y)] : (be ⊸ ft) ⊸ ft ⊸e ∃y[banana(y)∧ like(x, y)] : ft ⊸i,1 λx.∃y[banana(y)∧ like(x, y)] : me ⊸ ft ⊸e ∀x[monkey(x) → ∃y[banana(y)∧ like(x, y)]] : ft the university of konstanz. 10 the tools described below are open source and compatible with various systems, including xle, and they are designed to be useful in theoretical linguistic work as well as in investigation of general issues of integrating semantics into the lfg projection architecture. ## use cases at this stage of development, xle+glue and liger have not been widely used for broad coverage semantic parsing (but see @xcite for a broad coverage use of the gswb). however, they have already been employed for verification of theoretical lfg+glue analyses (see §4.1), for a teaching grammar (see §4.2), and for research on ambiguity management (see §4.3). ## summary this paper has presented a suite of computational tools for glue semantics. it has established their relevance for exploring various important concepts, particularly how to embed a semantic component in the lfg projection architecture as implemented within xle. in this regard, both a co-descriptive and a description-by-analysis approach have been presented, covering the two major proposals for semantic analysis in lfg. the tools presented in this paper contribute to a growing ecosystem of lfg-based cl tools which are actively developed on multiple fronts. they receive regular updates and new features. however, it is not only the lfg community that may benefit from these tools. glue semantics is compatible with various kinds of syntactic and semantic analyses. from the perspective of nlp, one of the most interesting prospects may be its compatibility with universal dependencies (haug and findlay 2023), but even beyond that, the tools presented in this paper provide an exciting avenue for research on formal semantics in computational linguistics.