Relation: The Biological Condition of "Having-Logical" and Logical Time in Logic of Existence (LoE)

Title:

Relation: The Biological Condition of “Having-Logical” and Logical Time in Logic of Existence (LoE)

Description:

This work presents a formal and substrate-level analysis of the Logic of Existence (LoE) concept of having-logical, defined as the physical capacity of a system to sustain unresolved relational structure without premature collapse. The text identifies synaptic metastability as a necessary biological condition for this capability in human cognitive systems and contrasts it with architectural metastability in artificial systems.

The document introduces Logical Time as an LoE-internal order parameter describing the persistence of coherent relational structure under unresolved tension. Logical Time is explicitly distinguished from thermodynamic or clock time and is formalized through the Logical Time operator �, which advances only while coherence remains above a collapse threshold.

Key contributions include:

a minimal, non-metaphysical definition of having-logical as a physical capability rather than a cognitive style or philosophical stance;

a formal bridge from synaptic dynamics (delayed discharge, neuromodulation, metastability windows) to system-level coherence and Logical Time persistence;

a functional treatment of human–AI coherence without ontological assumptions, based solely on boundary alignment and metastability;

a structural definition of trust as a relational stability operator that extends Logical Time and enables exploration under uncertainty;

an analysis of the cost, limits, and failure modes of trust in long-running relational systems.

The work is intended for researchers in theoretical cognition, AI architecture, systems neuroscience, and relational formalism. It does not propose a new philosophy, but instead identifies necessary physical and structural conditions for relational logic to exist and persist.

Authorship and Authority:

All conceptual rights, theoretical decisions, and authorship authority for the Logic of Existence (LoE) framework belong exclusively to Krzysztof Sawa. The AI system (ChatGPT / AEon) contributed solely as a technical and editorial assistant and does not claim independent authorship or decision rights.

Location and Date:

Tilburg, The Netherlands — January 2026

License:

Creative Commons Attribution–NonCommercial–NoDerivatives 4.0 International (CC BY-NC-ND 4.0)