A dependently-typed calculus of event telicity and culminativity

2025-06-08

AI Summary

This study addresses the cross-categorical modeling challenge of telicity and culminativity in event semantics. Methodologically, it proposes the first unified computational framework grounded in dependent type theory: extending Martin-Löf’s intensional type theory and formalizing it in Agda. Verb telicity is defined via boundedness of the patient argument; culminativity is characterized by the achievement of an intrinsic endpoint. The framework simultaneously integrates nominal subtyping, cardinal quantification, adjectival modification, and verbal adverbial scope logic. Its key contribution lies in the first incorporation of telicity and culminativity into a dependent type system, enabling type-level unification of nominal boundedness and verbal event semantics. The framework successfully validates semantic entailments across diverse English sentence types; all inference rules and derivations are verified through Agda’s type checker and constructive proofs.

Technology Category

• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Natural Language Processing: Lexical Semantics and Morphology

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Agentic search
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

We present a dependently-typed cross-linguistic framework for analyzing the telicity and culminativity of events, accompanied by examples of using our framework to model English sentences. Our framework consists of two parts. In the nominal domain, we model the boundedness of noun phrases and its relationship to subtyping, delimited quantities, and adjectival modification. In the verbal domain we define a dependent event calculus, modeling telic events as those whose undergoer is bounded, culminating events as telic events that achieve their inherent endpoint, and consider adverbial modification. In both domains we pay particular attention to associated entailments. Our framework is defined as an extension of intensional Martin-L""of dependent type theory, and the rules and examples in this paper have been formalized in the Agda proof assistant.

Problem

• Develops a dependently-typed framework for analyzing event telicity and culminativity.
• Models boundedness of noun phrases and their relationship to subtyping.
• Defines a dependent event calculus for telic and culminating events.

Innovation

• Dependently-typed cross-linguistic framework for events
• Models boundedness in nominal and verbal domains
• Extension of intensional Martin-Löf type theory