Simulating dynamic systems using Linear Time Calculus theories

TL;DR

This work extends Linear Time Calculus (LTC) in the IDP^3 framework to support a broad family of dynamic-inference tasks on a single specification, enabling progression, interactive simulation, planning, and invariant verification within one knowledge-base-based formalism. It demonstrates that most dynamic inferences can be reduced to existing inference mechanisms, providing a unified approach to dynamic domains and highlighting knowledge reuse across tasks. The results indicate IDP^3's strength relative to domain-specific systems and outline pathways to integrate temporal model checking (CTL/LTL) in future work, enhancing verification while preserving a single-specification paradigm.

Abstract

To appear in Theory and Practice of Logic Programming (TPLP). Dynamic systems play a central role in fields such as planning, verification, and databases. Fragmented throughout these fields, we find a multitude of languages to formally specify dynamic systems and a multitude of systems to reason on such specifications. Often, such systems are bound to one specific language and one specific inference task. It is troublesome that performing several inference tasks on the same knowledge requires translations of your specification to other languages. In this paper we study whether it is possible to perform a broad set of well-studied inference tasks on one specification. More concretely, we extend IDP3 with several inferences from fields concerned with dynamic specifications.

Theorems & Definitions (11)

• Definition Appendix G.1
• Definition Appendix G.2
• Proposition Appendix G.3
• Proposition Appendix G.4
• Proposition Appendix G.5
• Definition Appendix G.6: Weakly $\mathcal{T}$-compatible, weak $\mathcal{T}$-successor
• Proposition Appendix G.7
• Example Appendix G.8
• Definition Appendix G.9: Deadlock
• Definition Appendix G.10: Weak Progression inference