The formalized content of He Xin’s Pan-Evolutionary Logic (PEPC) system is mainly reflected in the following specific aspects:

1. Formal Language and Axiomatic System

The system has constructed a custom formal language ℒ_PEPC, which includes:

• Basic symbols: strategic concept variables (Cₖ), military attribute parameters (pₙ).

• Core operators: including dialectical inclusion (⊂), dialectical compatibility (∘), evolutionary sub-coherent implication (→ₙ꜀), and dialectical truth value (⊤^∘), among other specialized operators.

• Axiom system: an axiomatic framework from A1 (dialectical construction) to A7 (non-explosive reinforcement) has been established, providing a formal foundation for system reasoning.

2. Semantic Model and Mathematical Definitions

The system defines a clear semantic model Nℯvℴ, structured as ⟨T, <,C, ℐ, Vₙ꜀⟩, covering time order, concept domain, interpretation function, and sub-coherent valuation. Key operators have precise mathematical definitions, for example:

• Dialectical compatibility operator (∘) is defined as: the intersection of the intensions of two opposing concepts forms the core contradiction, while their extension intersection is non-empty.

• Evolutionary sub-coherent implication (⇒_ₙ꜀) is defined as the logical relationship of a concept evolving to the next stage under conditions of dialectical truth, coexistence of contradictions, and absence of external interference.

3. Computable Algorithm Modules

The system has implemented the transformation from theory to computation by designing four executable algorithm modules:

T1 (Contradiction Extraction Module): identifies and extracts core contradiction pairs driving evolution from multi-dimensional dynamic parameters.

T2 (Concept Construction Module): constructs formalized instances of strategic concepts based on parameter data.

T3 (Evolutionary Deduction Module): calculates the evolutionary path of concepts according to core contradictions.

T4 (Opposition Determination Module): determines whether there is a dialectical opposition relationship between concepts.

4. Empirical Application and Verification

The formalized system has been preliminarily applied to specific strategic analysis scenarios (e.g., simulation of the U.S.–Iran military standoff in 2026):

• Parametric modeling: transforms strategic situations into 17 quantifiable military parameters (such as base availability, missile stockpile, interception rate, etc.) and builds an observation data matrix.

• Dynamic deduction: the system can input real-time or simulated parameters, run the algorithm modules, and output different evolutionary paths and probabilities such as “strategic restraint” or “limited conflict.”

• Validity verification: comparison with key indicators from traditional wargaming simulations (e.g., RAND, CSIS) shows less than 5% error, initially verifying its effectiveness as a computable analytical tool.

5. Deepening of Theoretical Framework

The formalization work is built upon a solid theoretical framework and implements it concretely:

• Concretization of the “He Xin Tree” model: transforms the philosophical model of “historical concept sets” and the “He Xin Tree” into a three-dimensional dynamic formal model describing the processes of concept generation, differentiation, and sublation by introducing a time axis and topological structure.

• Implementation of multi-valued logic: beyond true/false binary values, introduces states such as “undefined” or “contradictory,” and uses sub-coherent logic (e.g., non-explosive axioms) to handle contradictions, enabling the system to accommodate and characterize transitional and contradictory states in evolution.

Summary: The PEPC system shifts from abstract philosophy to formal logic and computable models, integrating language, semantics, axioms, algorithms, and early validation to enable operational, testable computational systems.