# Discourse Algebra

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Related KMR-pages:

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Template for supra-, inter-, and intra-acts:

Possible- and Realized conversation threads 1:

Possible- and Realized conversation threads 2:

Negotiating agreement through coherence:

Combining Hom-o-sapiens 1:

Combining Hom-o-sapiens 2:

Agents A and B contribute to X –> Y –> Z:

… as part of a Conversational Cascade:

A Conversational Complex:

Homology of an Odd-Party Conversational Complex:

Template for Recursive Conversations
:

Combination of arrows in HumConV:

SECI-based conversation between two agents:

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$\, \{ ABC \, , \, AB \, , \, BC \, , \, AC \, , \, A \, , \, B \, , \, C \, , \, \emptyset \, \} \,$.

Preorder:

$\, ABC \, \leq \, AB \, \leq \, A \,$ $\, ABC \, \leq \, AB \, \leq \, B \,$ $\, ABC \, \leq \, BC \, \leq \, B \,$ $\, ABC \, \leq \, BC \, \leq \, C \,$ $\, ABC \, \leq \, AC \, \leq \, A \,$ $\, ABC \, \leq \, AC \, \leq \, C \,$

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Hasse diagram
Hasse Diagrams of integer Divisors (at demonstrations.wolfram.com)

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Representation: $\, [ \, p_{resentant} \, ]_{B_{ackground}} \, \mapsto \, \left< \, r_{epresentant} \, \right>_{B_{ackground}}$

Reconstruction: $\, \left( \, \left< \, r_{epresentant} \, \right>_{B_{ackground}} \, \right)_{B_{ackground}} \mapsto \,\, p_{resentant}$

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$\, [ \, s_{ubject} \, ]_{ABC} \, \leq \, [ \, s_{ubject} \, ]_{AB} \, \leq \, [ \, s_{ubject} \, ]_{A} \,$ $\, [ \, s_{ubject} \, ]_{ABC} \, \leq \, [ \, s_{ubject} \, ]_{AB} \, \leq \, [ \, s_{ubject} \, ]_{B} \,$ $\, [ \, s_{ubject} \, ]_{ABC} \, \leq \, [ \, s_{ubject} \, ]_{BC} \, \leq \, [ \, s_{ubject} \, ]_{B} \,$ $\, [ \, s_{ubject} \, ]_{ABC} \, \leq \, [ \, s_{ubject} \, ]_{BC} \, \leq \, [ \, s_{ubject} \, ]_{C} \,$ $\, [ \, s_{ubject} \, ]_{ABC} \, \leq \, [ \, s_{ubject} \, ]_{AC} \, \leq \, [ \, s_{ubject} \, ]_{A} \,$ $\, [ \, s_{ubject} \, ]_{ABC} \, \leq \, [ \, s_{ubject} \, ]_{AC} \, \leq \, [ \, s_{ubject} \, ]_{C} \,$

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$\, [ \, s_{ubject} \, ]_{[ \, ABC \, ]_{{c_{ontext}}_{1}} } \, \leq \, [ \, s_{ubject} \, ]_{[ \, AB \, ]_{{c_{ontext}}_{2}} } \, \leq \, [ \, s_{ubject} \, ]_{[ \, A \, ]_{{c_{ontext}}_{3}} } \,$

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Interpretation of semantic events:

Template for Recursive Conversations: