[Paper Review] ASP Essentials: Modelling and Efficient Solving (Invited Paper)

Mark Law, Alessandra Russo|arXiv (Cornell University)|May 2, 2020

Logic, Reasoning, and Knowledge27 references22 citations

TL;DR

This paper presents ILASP, a system for inductive learning of Answer Set Programs (ASPs) that extends traditional Inductive Logic Programming (ILP) by supporting normal rules, choice rules, and hard and weak constraints. It introduces a conflict-driven learning framework that improves scalability through iterative constraint generation, enabling efficient learning of complex, non-monotonic logic programs from positive, negative, and ordering examples—particularly effective for preference learning and real-world knowledge acquisition.

ABSTRACT

Answer Set Programming (ASP) is a logic-based Knowledge Representation and Reasoning (KRR) paradigm that facilitates rapid prototyping of solutions for complex problems. It is particularly effective for tackling Deep Reasoning tasks involving exponentially large search spaces, such as combinatorial search and optimization. While getting started with ASP is relatively easy, mastering its advanced constructs and scaling solutions to real-world problem sizes can be challenging. This paper provides an introduction to ASP, guiding the reader from the fundamentals of the language to the application of programming methodologies and the computation of answer sets. Beyond the core framework, the paper also examines selected extensions of ASP that enable the modeling of complex problems, as well as compilation techniques designed to enhance solving efficiency. Furthermore, it mentions some recent tools that combine ASP with LLMs.

Motivation & Objective

• To develop a scalable, general-purpose system for learning Answer Set Programs (ASPs) from examples, extending beyond traditional Prolog-based ILP.
• To address the limitations of existing ILP frameworks by supporting expressive ASP constructs such as choice rules and weak constraints.
• To enable preference learning by incorporating ordering examples that specify preferred answer sets.
• To improve scalability and efficiency in handling noisy data, large example sets, and large search spaces through iterative constraint-based learning.

Proposed method

• The ILASP system uses a learning framework that combines brave and cautious reasoning to learn the full class of ASP programs, including those not learnable by prior systems.
• It models learning tasks using background knowledge, mode bias (defining the rule space), and three types of examples: positive, negative, and ordering examples for weak constraints.
• The system employs a conflict-driven approach where each iteration generates constraints based on relevant examples, refining the solution space iteratively.
• ILASP3 introduces an Example Translator that converts relevant examples into coverage constraints, approximating program scores to guide efficient search.
• The program search uses these approximations to find optimal hypotheses, with validation via relevant example search within the set of examples predicted to be covered.
• ILASP4 further optimizes this by generating only necessary (not sufficient) constraints, reducing computational cost per iteration despite potential for more iterations.

Experimental results

Research questions

• RQ1 Can a general-purpose ILP system learn the full class of Answer Set Programs, including those with choice rules and weak constraints, which are not learnable by traditional brave or cautious ILP frameworks?
• RQ2 How can ILP systems be made scalable to handle large example sets, noisy data, and large search spaces while maintaining correctness and optimality?
• RQ3 What is the impact of using constraint-based, conflict-driven search on the efficiency and convergence of inductive logic programming for ASP?
• RQ4 Can the rule space be pruned effectively to avoid full enumeration, and how does this improve scalability in practice?
• RQ5 How can preference learning be formalized and supported in ILP through ordering examples that specify preferred answer sets?

Key findings

• ILASP is capable of learning the full class of Answer Set Programs, including those requiring both brave and cautious reasoning, which previous systems could not handle.
• The integration of weak constraints enables preference learning, allowing the system to infer user preferences from examples of preferred solutions.
• ILASP3 significantly improves scalability by approximating program scores using coverage constraints, reducing the number of iterations needed compared to ILASP2i.
• The conflict-driven approach in ILASP3 and ILASP4 reduces the search space by generating constraints that are necessary for example coverage, improving efficiency despite larger constraint sizes.
• FastLAS, a new algorithm derived from ILASP, computes an OPT-sufficient subset of the rule space, reducing it by orders of magnitude and enabling single-shot solving with Clingo.
• ILASP4's relaxation of constraint generation to only necessary conditions leads to smaller, faster constraints per iteration, improving performance even if more iterations are required.