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Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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From Possibility to Responsibility. A Deduction in Homotopy Type Theory from a Single Axiom to the Coherence Conditions of Adequate Self-Reference

Authors: Killius, Markus;

From Possibility to Responsibility. A Deduction in Homotopy Type Theory from a Single Axiom to the Coherence Conditions of Adequate Self-Reference

Abstract

This paper presents a deduction within Homotopy Type Theory (HoTT) that proceeds from a single axiom – there is possibility – through fourteen steps to a formally derived coher- ence condition: any structurally adequate self-referential type in the presence of irreducible alterity has exactly one non-defective mode of operation – relation without reduction. This result is philosophically interpreted as the formal structure of responsibility. The deduc- tion runs in two parallel layers: a formal layer consisting of type-theoretic constructions, definitions, and derivations, and a philosophical layer providing interpretation of each for- mal structure. These layers are strictly separated. The point at which formal structure necessitates interpretive supplementation – the transition from ontology to epistemology – is explicitly marked. Schematic notation is identified as such. No additional axiom beyond the foundational one (and the standard framework of HoTT including the Univalence Axiom) is introduced. The strength of the concluding result depends on a definitional choice – the adequacy condition for self-reference – whose justification via Univalence is given and whose status as a definitional choice is made transparent.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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