concept
active
concept:partial-involutionspartial involutions
Fixed-point free partial injective functions used as simple reversible dynamical processes in Geometry of Interaction.
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Concepts (2)
concept
- Geometry of Interactionassociated_withDynamic model connecting logic to geometry through explicit treatment of information flow and interaction; demonstrates emergent logical complexity from simple copy-cat processes.
- Copy-cat strategyassociated_withGame-theoretic strategy reflecting pure interaction; basis for understanding universal computation through interaction in Geometry of Interaction.
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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.
- Partial involutions form a Linear Combinatory Algebra under function application defined by feedback loopsfinding0.828The 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.
- Mere copying of tokens between paired positions suffices to simulate all partial recursive functions and model higher-order logics.
- The authors' characterization of genuine but limited introspective capability found only in early-layer injection regimes
- The Geometry of Interaction model shows that simple copying of information between locations suffices for all computation, establishing emergent logic.
- Williams and Beer's decomposition of joint mutual information into unique, redundant, and synergistic components.
- Mathematical representation of precedence relations among steps: which centers must be in position before another can be formed, defining good sequences as linearizations that minimize backtracking.
- Factorised distribution used to approximate the true Bayesian posterior.
- Evaluation setting where the same task stream that drives evolution also serves as the evaluation set, with each task scored under the harness at time of attempt