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Solving Epistemic Logic Programs using Generate-and-Test with Propagation

Jorge Fandinno, Lute Lillo

TL;DR

This work advances epistemic logic programming (ELP) by proposing a general generate-and-test solver framework and proving correctness conditions for instantiated generators and testers. A novel generator with epistemic propagation (G1) dramatically reduces candidate worldviews with only linear overhead, enabling strong empirical gains. The authors implement a practical solver atop clingo and demonstrate a ~3.3x speed-up and 91% more instances solved compared to state-of-the-art solvers on standard benchmarks. The results suggest broad applicability of the framework and point to future enhancements via worldview splitting and domain-specific heuristics to further boost performance.

Abstract

This paper introduces a general framework for generate-and-test-based solvers for epistemic logic programs that can be instantiated with different generator and tester programs, and we prove sufficient conditions on those programs for the correctness of the solvers built using this framework. It also introduces a new generator program that incorporates the propagation of epistemic consequences and shows that this can exponentially reduce the number of candidates that need to be tested while only incurring a linear overhead. We implement a new solver based on these theoretical findings and experimentally show that it outperforms existing solvers by achieving a ~3.3x speed-up and solving 91% more instances on well-known benchmarks.

Solving Epistemic Logic Programs using Generate-and-Test with Propagation

TL;DR

This work advances epistemic logic programming (ELP) by proposing a general generate-and-test solver framework and proving correctness conditions for instantiated generators and testers. A novel generator with epistemic propagation (G1) dramatically reduces candidate worldviews with only linear overhead, enabling strong empirical gains. The authors implement a practical solver atop clingo and demonstrate a ~3.3x speed-up and 91% more instances solved compared to state-of-the-art solvers on standard benchmarks. The results suggest broad applicability of the framework and point to future enhancements via worldview splitting and domain-specific heuristics to further boost performance.

Abstract

This paper introduces a general framework for generate-and-test-based solvers for epistemic logic programs that can be instantiated with different generator and tester programs, and we prove sufficient conditions on those programs for the correctness of the solvers built using this framework. It also introduces a new generator program that incorporates the propagation of epistemic consequences and shows that this can exponentially reduce the number of candidates that need to be tested while only incurring a linear overhead. We implement a new solver based on these theoretical findings and experimentally show that it outperforms existing solvers by achieving a ~3.3x speed-up and solving 91% more instances on well-known benchmarks.

Paper Structure

This paper contains 11 sections, 9 theorems, 33 equations, 3 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Normal Form
  4. Worldviews by Generate-and-Testing
  5. Basic Generator Programs
  6. Tester program as a generator.
  7. Generator with consistency constraints.
  8. Generator with Epistemic Propagation
  9. Implementation and Experimental Evaluation
  10. Results.
  11. Conclusions

Key Result

Theorem 1

There is a one-to-one correspondence between the worldviews of $\Pi$ and $\mathit{NF}(\Pi)$ s.t. $\mathbb{W}$ is a worldview of $\mathit{NF}(\Pi)$ if and only if ${\mathbb{W}}_{\!|\!\mathit{At}(\Pi)}$ is a worldview of $\Pi$.

Figures (3)

  • Figure 1: Comparison of our implementation of Algorithm \ref{['alg:guess-and-check']} with two different versions of the generator program.
  • Figure 2: Comparison of all Epistemic Solvers Eligible, Yale and Bomb Problems.
  • Figure : Instances for each benchmark solved by the different versions of the generator program.

Theorems & Definitions (24)

  • Definition 1: Subjective reduct; fafage22a
  • Definition 2
  • Theorem 1
  • Definition 3: Generator Program
  • Proposition 1
  • Definition 4: Tester Program
  • Definition 5: Generate and test worldviews
  • Theorem 2
  • Proposition 2
  • Proposition 3
  • ...and 14 more