Definite Descriptions in KR Languages

Half-day Tutorial at KR-2026

Overview

Definite descriptions are expressions having the logical form of "the x such that \(\varphi\)". In classical first-order logic, since singular terms are assumed to be always denoting, definite descriptions are typically paraphrased by sentences expressing existence and uniqueness conditions (a proposal that dates back to Russell). To treat definite descriptions as genuine terms of the language, other approaches rely instead on free logics, which depart from standard FOL by allowing for singular terms that may not designate. Over the years, several theories of definite descriptions have been investigated, from a semantical and a proof-theoretical perspective, in both standard and modal FOL.

Recently, definite descriptions have been studied also in the context of Knowledge Representation formalisms. In description logics, terms of the form \(\iota C\) ("the object that is \(C\)") have been added to standard languages, leading to extensions like \(\mathcal{ALC}\iota\), \(\mathcal{ALCO}^{\iota}_{u}\) and \(\mathcal{ELO}^{\iota}_{u}\), for which the complexity of reasoning matches that of their standard counterparts. Similarly, expressive power and complexity have been investigated for propositional modal logics enriched with formulas of the form \(@_{\varphi} \psi\), which hold whenever there exists a unique state satisfying \(\varphi\) that makes \(\psi\) true. As a mean to construct complex temporal references, definite descriptions have been also introduced as terms in first-order monadic logic of orders, as well as in first-order hybrid tense logic. Finally, names and definite descriptions that can act as non-rigid designators, referring to different objects across worlds or over time, have been studied also for their impact on the decidability boundaries of well-known monodic fragments of first-order modal and temporal logics.

The purpose of this tutorial is to give a comprehensive overview of the recent developments in the field, introducing a unifying framework and discussing the main results on definite descriptions that are relevant to KR applications. In addition, we intend to mention and compare alternative approaches, on the referring expression generation problem, and on the use of referring expressions for query answering in information systems.

Target Audience and Prerequisites

Target Audience

This tutorial is aimed at researchers, students, and practitioners in KR, with an interest in logic, semantics of formal and natural languages, ontology engineering, and commonsense reasoning.

Prerequisite Knowledge

Basic familiarity with FOL, modal logics, and DLs is expected. We will in any case briefly recap most of the necessary background notions.

Learning Goals

At the end of this tutorial, participants will:

• Understand the history and the philosophical motivations behind the development of free logic and the theory of definite descriptions
• Have an overview of the main syntactic and semantic choices in first-order languages regarding terms that do not denote, both in the classical and in the modal case
• Have a comprehensive picture on the use of definite descriptions in KR formalisms, in particular regarding their impact on semantics, proof-theory, expressive power and decidability

Outline

Part 1: Introduction and Motivation

Part 2: Definite Descriptions in First-Order Logic, Free Logics, and Description Logics

Part 3: Definite Descriptions in Modal, Temporal, and Hybrid Logics – Propositional and First-Order

Part 4: Conclusion and Discussion

Presenters

Resources