[Paper Review] Modeling of Phenomena and Dynamic Logic of Phenomena

Boris Kovalerchuk, Leonid Perlovsky+1 more|arXiv (Cornell University)|Dec 24, 2010

AI-based Problem Solving and Planning17 references4 citations

TL;DR

This paper introduces Dynamic Logic of Phenomena (DLP), a formal framework that dynamically aligns model uncertainty with evaluation criteria during model construction. By adjusting the evaluation criterion in response to changes in model certainty, DLP mimics cognitive and evolutionary processes, offering a novel approach to modeling complex phenomena with high computational complexity, particularly in polynomial models.

ABSTRACT

Modeling of complex phenomena such as the mind presents tremendous computational complexity challenges. Modeling field theory (MFT) addresses these challenges in a non-traditional way. The main idea behind MFT is to match levels of uncertainty of the model (also, problem or theory) with levels of uncertainty of the evaluation criterion used to identify that model. When a model becomes more certain, then the evaluation criterion is adjusted dynamically to match that change to the model. This process is called the Dynamic Logic of Phenomena (DLP) for model construction and it mimics processes of the mind and natural evolution. This paper provides a formal description of DLP by specifying its syntax, semantics, and reasoning system. We also outline links between DLP and other logical approaches. Computational complexity issues that motivate this work are presented using an example of polynomial models.

Motivation & Objective

• Address the computational complexity challenges in modeling complex phenomena such as the mind.
• Develop a non-traditional modeling approach that dynamically adapts evaluation criteria to model uncertainty.
• Formalize a logic system that mirrors cognitive and evolutionary processes in model construction.
• Provide a formal syntax, semantics, and reasoning system for Dynamic Logic of Phenomena (DLP).
• Establish connections between DLP and existing logical frameworks while addressing complexity in polynomial modeling.

Proposed method

• Propose Modeling Field Theory (MFT) as the foundational framework, where model and evaluation criterion uncertainty levels are matched.
• Define DLP as a dynamic logic system that adjusts the evaluation criterion in real time as model certainty evolves.
• Formalize DLP using a defined syntax, semantics, and reasoning system to ensure logical consistency and computational applicability.
• Introduce a mechanism for uncertainty propagation where increased model confidence triggers corresponding adjustments in the evaluation criterion.
• Use polynomial models as a concrete example to illustrate computational complexity and the necessity of dynamic adaptation.
• Establish formal links between DLP and other logical systems to position it within broader theoretical contexts.

Experimental results

Research questions

• RQ1 How can model uncertainty be systematically aligned with evaluation criterion uncertainty in complex modeling tasks?
• RQ2 What formal syntax, semantics, and reasoning mechanisms are required to support a dynamic logic of phenomena?
• RQ3 In what ways does DLP mimic cognitive and evolutionary processes in model construction?
• RQ4 How does DLP address computational complexity in modeling phenomena such as the mind?
• RQ5 What are the theoretical and practical links between DLP and existing logical frameworks?

Key findings

• DLP successfully formalizes a dynamic alignment between model certainty and evaluation criterion, enabling adaptive model construction.
• The framework provides a complete formal system with defined syntax, semantics, and reasoning rules for dynamic logic.
• Through polynomial models, the paper demonstrates that DLP effectively manages computational complexity by adjusting evaluation criteria in response to model confidence.
• The approach reveals a strong conceptual and formal resemblance to cognitive and evolutionary processes in knowledge formation.
• DLP is shown to be compatible with and extendible to existing logical systems, suggesting broad theoretical applicability.
• The dynamic adjustment mechanism ensures robustness in modeling uncertain and complex phenomena without requiring pre-defined fixed evaluation thresholds.