finding
active
finding:partial-involutions-form-a-linear-combinatory-algebra-under-function-application-defined-by-feedback-loopsPartial involutions form a Linear Combinatory Algebra under function application defined by feedback loops
The set of fixed-point free partial involutions on a countable set, with composition via interaction, yields a linear combinatory algebra, hence a universal model of computation.
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Claims (1)
claim
- The Geometry of Interaction model shows that simple copying of information between locations suffices for all computation, establishing emergent logic.
Related by similarity (8)
cosine ≥ 0.65 · no typed edgeEntities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.
- Fixed-point free partial injective functions used as simple reversible dynamical processes in Geometry of Interaction.
- Mere copying of tokens between paired positions suffices to simulate all partial recursive functions and model higher-order logics.
- Foundational hypothesis of Domain Theory: partial order structure (D, ⊑) captures information ordering without quantification.
- Mathematical formalization of what representation models converge to
- A resource-sensitive combinatory algebra with modalities for copying; provides a fine-grained model of computation.
- The interactive processes described are reversible in a very strong sense, linking logic and physicsclaim0.720Partial involutions are invertible; the same structures can axiomatize quantum mechanics and analyse entanglement.
- Neural plausibility argument for softmax policy selection.
- The idea that features are encoded as directions in activation space.