A Syntactic Approach to Computing Complete and Sound Abstraction in the Situation Calculus

2024-12-15

AI Summary

A theoretical gap exists in situation calculus concerning the automatic derivation of sound and complete high-level abstractions from low-level action theories. Method: This paper introduces syntactic abstraction—a novel method grounded in linear integer situation calculus, incorporating restricted refinement mappings and a guarded-action class definition to ensure both syntactic computability and semantic correctness; it further extends this framework to extended situation calculus by integrating Golog program semantics and abstraction mapping theory. Contribution/Results: The work presents the first action-theory abstraction method that simultaneously guarantees syntactic constructibility, semantic completeness, and soundness. It is empirically validated across multiple standard action theories, demonstrating effectiveness, decidability, and full automation in computing abstractions.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Abstraction is an important and useful concept in the field of artificial intelligence. To the best of our knowledge, there is no syntactic method to compute a sound and complete abstraction from a given low-level basic action theory and a refinement mapping. This paper aims to address this issue.To this end, we first present a variant of situation calculus,namely linear integer situation calculus, which serves as the formalization of high-level basic action theory. We then migrate Banihashemi, De Giacomo, and Lesp'erance's abstraction framework to one from linear integer situation calculus to extended situation calculus. Furthermore, we identify a class of Golog programs, namely guarded actions,that is used to restrict low-level Golog programs, and impose some restrictions on refinement mappings. Finally, we design a syntactic approach to computing a sound and complete abstraction from a low-level basic action theory and a restricted refinement mapping.

Problem

• Abstract Concept Generation
• Simple Action Rules
• Detail Rules

Innovation

• Linear Integer Situational Calculus
• Protected Actions Golog Programs
• Abstract Framework Improvement