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A Generalised Approach for Encoding and Reasoning with Qualitative Theories in Answer Set Programming

George Baryannis, Ilias Tachmazidis, Sotiris Batsakis, Grigoris Antoniou, Mario Alviano, Emmanuel Papadakis

TL;DR

This paper tackles the challenge of integrating qualitative reasoning with non-qualitative tasks by using Answer Set Programming as a unifying framework. It introduces a generalised encoding (GEN-0) for any binary qualitative calculus, along with optimised variants (GEN-1, GEN-2) that exploit algebraic properties, and a prototype converter to generate encodings from existing tool formats. Empirical evaluation on a real-world telecommunication case study shows that the optimised encodings significantly improve scalability and memory usage, though they do not outperform dedicated CSP solvers like GQR in raw speed. The work demonstrates that ASP can effectively handle mixed qualitative and non-qualitative reasoning, offering human-readability, configurability, and broad applicability, with future work to broaden case studies and tooling.

Abstract

Qualitative reasoning involves expressing and deriving knowledge based on qualitative terms such as natural language expressions, rather than strict mathematical quantities. Well over 40 qualitative calculi have been proposed so far, mostly in the spatial and temporal domains, with several practical applications such as naval traffic monitoring, warehouse process optimisation and robot manipulation. Even if a number of specialised qualitative reasoning tools have been developed so far, an important barrier to the wider adoption of these tools is that only qualitative reasoning is supported natively, when real-world problems most often require a combination of qualitative and other forms of reasoning. In this work, we propose to overcome this barrier by using ASP as a unifying formalism to tackle problems that require qualitative reasoning in addition to non-qualitative reasoning. A family of ASP encodings is proposed which can handle any qualitative calculus with binary relations. These encodings are experimentally evaluated using a real-world dataset based on a case study of determining optimal coverage of telecommunication antennas, and compared with the performance of two well-known dedicated reasoners. Experimental results show that the proposed encodings outperform one of the two reasoners, but fall behind the other, an acceptable trade-off given the added benefits of handling any type of reasoning as well as the interpretability of logic programs. This paper is under consideration for acceptance in TPLP.

A Generalised Approach for Encoding and Reasoning with Qualitative Theories in Answer Set Programming

TL;DR

This paper tackles the challenge of integrating qualitative reasoning with non-qualitative tasks by using Answer Set Programming as a unifying framework. It introduces a generalised encoding (GEN-0) for any binary qualitative calculus, along with optimised variants (GEN-1, GEN-2) that exploit algebraic properties, and a prototype converter to generate encodings from existing tool formats. Empirical evaluation on a real-world telecommunication case study shows that the optimised encodings significantly improve scalability and memory usage, though they do not outperform dedicated CSP solvers like GQR in raw speed. The work demonstrates that ASP can effectively handle mixed qualitative and non-qualitative reasoning, offering human-readability, configurability, and broad applicability, with future work to broaden case studies and tooling.

Abstract

Qualitative reasoning involves expressing and deriving knowledge based on qualitative terms such as natural language expressions, rather than strict mathematical quantities. Well over 40 qualitative calculi have been proposed so far, mostly in the spatial and temporal domains, with several practical applications such as naval traffic monitoring, warehouse process optimisation and robot manipulation. Even if a number of specialised qualitative reasoning tools have been developed so far, an important barrier to the wider adoption of these tools is that only qualitative reasoning is supported natively, when real-world problems most often require a combination of qualitative and other forms of reasoning. In this work, we propose to overcome this barrier by using ASP as a unifying formalism to tackle problems that require qualitative reasoning in addition to non-qualitative reasoning. A family of ASP encodings is proposed which can handle any qualitative calculus with binary relations. These encodings are experimentally evaluated using a real-world dataset based on a case study of determining optimal coverage of telecommunication antennas, and compared with the performance of two well-known dedicated reasoners. Experimental results show that the proposed encodings outperform one of the two reasoners, but fall behind the other, an acceptable trade-off given the added benefits of handling any type of reasoning as well as the interpretability of logic programs. This paper is under consideration for acceptance in TPLP.

Paper Structure

This paper contains 20 sections, 6 theorems, 3 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Motivation and Related Work
  3. Qualitative Calculi
  4. Systematic Approach for Encoding Qualitative Calculi in ASP
  5. Domain and Base Relations
  6. Composition Table and Search Space
  7. Input Constraints
  8. Correctness and Complexity
  9. Optimisations based on Algebraic Properties
  10. Antisymmetric optimisation
  11. Identity optimisation
  12. Implementation
  13. Custom Propagation
  14. Experiments
  15. Dataset and Processing
  16. ...and 5 more sections

Key Result

Theorem 4.1

Let $Q = \langle QC, C \rangle$ be an instance of the model existence problem according to Definition def:problem2. Let $\Pi_Q$ be the GEN-0 encoding of $Q$ and $S$ be an answer set of $\Pi_Q$. Then, there exists a model $M$ of $Q$ that corresponds to $S$.

Figures (3)

  • Figure 1: RCC-5 relations.
  • Figure 2: Performance results for finding consistent solutions when one relation per region is known.
  • Figure 3: Performance of the proposed ASP encoding compared to GQR and SparQ.

Theorems & Definitions (14)

  • Definition 3.1: Binary Partition Scheme
  • Definition 3.2: Binary Qualitative Calculus
  • Definition 3.3: Binary Qualitative Calculus Model Existence
  • Definition 3.4: Involution of converse
  • Definition 3.5: Identity Law
  • Theorem 4.1: Soundness
  • Theorem 4.2: Completeness
  • Corollary 4.1: QC Model Existence Complexity
  • Theorem A.1: Soundness
  • proof
  • ...and 4 more