[Paper Review] Bound Your Models! How to Make OWL an ASP Modeling Language

Sarah Alice Gaggl, Sebastian Rudolph+1 more|arXiv (Cornell University)|Nov 3, 2015

Multi-Agent Systems and Negotiation3 citations

TL;DR

This paper introduces bounded model semantics for OWL, enabling it to function as an answer set programming (ASP) language by restricting models to finite domains defined by named individuals. The authors propose a translation of SROIQ knowledge bases into ASP programs, allowing efficient solving of bounded-model reasoning tasks—such as satisfiability, entailment, model extraction, and enumeration—via existing ASP solvers, with empirical results showing significant performance gains over traditional OWL reasoners.

ABSTRACT

To exploit the Web Ontology Language OWL as an answer set programming (ASP) language, we introduce the notion of bounded model semantics, as an intuitive and computationally advantageous alternative to its classical semantics. We show that a translation into ASP allows for solving a wide range of bounded-model reasoning tasks, including satisfiability and axiom entailment but also novel ones such as model extraction and enumeration. Ultimately, our work facilitates harnessing advanced semantic web modeling environments for the logic programming community through an "off-label use" of OWL.

Motivation & Objective

• To address the lack of user-friendly, scalable modeling environments for answer set programming (ASP), which hinders its adoption despite its power in solving combinatorial problems.
• To overcome the mismatch between OWL’s classical semantics—allowing infinite models—and the needs of constraint-satisfaction problems, which require finite, bounded reasoning.
• To enable OWL, with its rich tooling and intuitive syntax (e.g., Manchester Syntax), to be used as a high-level modeling language for ASP tasks.
• To provide a translation from SROIQ knowledge bases to ASP programs such that bounded models correspond exactly to answer sets, enabling use of advanced ASP solvers.
• To demonstrate that bounded-model reasoning under this framework is NP-complete, making it computationally more tractable than classical OWL reasoning, which is N2ExpTime-complete.

Proposed method

• Introduce bounded model semantics by restricting the domain of interpretation to only the named individuals present in the ontology, thereby ensuring finite models.
• Axiomatize the bounded model condition within the latest version of OWL to preserve compatibility with existing OWL reasoners, though these struggle due to combinatorial explosion.
• Develop a direct translation from SROIQ knowledge bases into answer set programs (ASP), such that the answer sets of the ASP program correspond exactly to the bounded models of the original ontology.
• Leverage the built-in capabilities of ASP solvers (e.g., clasp, dlv) for efficient model enumeration, extraction, and minimization, which are not natively supported in standard OWL reasoners.
• Implement the translation pipeline in a system called Wolpertinger, which integrates with OWL tooling via an OWL API reasoner interface for seamless use in environments like Protégé.
• Optimize the translation to exploit ASP-specific features such as constraints, aggregates, and optimization statements, improving performance on complex reasoning tasks.

Experimental results

Research questions

• RQ1 Can OWL be effectively repurposed as a high-level modeling language for answer set programming through a non-classical semantics?
• RQ2 What is the computational complexity of bounded-model reasoning in OWL, and how does it compare to classical OWL reasoning?
• RQ3 Can a translation from SROIQ knowledge bases to ASP programs preserve the semantics of bounded models while enabling efficient reasoning?
• RQ4 To what extent can existing ASP solvers outperform traditional OWL reasoners on bounded-model reasoning tasks such as model enumeration and extraction?
• RQ5 Can the framework support non-standard reasoning tasks like axiom pinpointing, justification, and abduction using ASP’s native capabilities?

Key findings

• Bounded-model reasoning in OWL is NP-complete, a significant improvement over the N2ExpTime-completeness of classical OWL reasoning, making it more tractable for practical applications.
• The Wolpertinger system, using the ASP translation, solved a Sudoku knowledge base in under 6 seconds on average, with over 90% of time spent on grounding and less than 0.1 seconds on actual solving.
• For model enumeration of 1 million Sudoku instances, Wolpertinger required approximately 279 seconds, with 273 seconds spent on solving, demonstrating scalability for large-scale enumeration tasks.
• In unsatisfiability testing, Wolpertinger outperformed HermiT on larger knowledge bases: while HermiT timed out after 15 minutes on the largest instance, Wolpertinger solved it in 85 seconds.
• Model extraction and partial enumeration were infeasible with HermiT (timeout after 15 minutes), but Wolpertinger successfully retrieved 100,000 models in under 35 seconds.
• The framework enables advanced reasoning tasks such as model enumeration and extraction—tasks not natively supported by standard OWL reasoners—by leveraging ASP’s native capabilities.