{
  "content": {
    "icon": "bi-signpost-split",
    "id": "the-representations",
    "intro": "A result can be encoded in any of these representation layers.",
    "subsections": [
      {
        "blocks": [
          {
            "kind": "text",
            "text": "equations, formulas, notation"
          },
          {
            "kind": "text",
            "text": "How it is checked"
          },
          {
            "entries": [
              {
                "description": "the ontology resolution gate over the nodes and structured-document constructs that name the representation",
                "term": "Checked by"
              },
              {
                "description": "Every node and document construct that names the representation",
                "term": "Population"
              },
              {
                "description": "A verdict stands until the representations or a record that names one changes",
                "term": "Freshness"
              },
              {
                "description": "The gate fails on a node or construct that names a representation that does not exist",
                "term": "Refusal"
              },
              {
                "description": "None, because a representation is a form of encoding, and nothing observes it while a run executes",
                "term": "Observation"
              },
              {
                "description": "Watched to fire and to accept: a suite plants a node that names a missing representation, and the bundled references resolve",
                "term": "Evidence"
              },
              {
                "description": "The representation list, which every node and construct that names a representation cites",
                "term": "Authoritative side"
              },
              {
                "description": "Not answered",
                "term": "Depends on"
              },
              {
                "description": "Not answered",
                "term": "Shape it refuses"
              }
            ],
            "kind": "glossary"
          }
        ],
        "id": "reasoning-representation-symbolic",
        "title": "symbolic"
      },
      {
        "blocks": [
          {
            "kind": "text",
            "text": "statements, predicates, proofs"
          },
          {
            "kind": "text",
            "text": "How it is checked"
          },
          {
            "entries": [
              {
                "description": "the ontology resolution gate over the nodes and structured-document constructs that name the representation",
                "term": "Checked by"
              },
              {
                "description": "Every node and document construct that names the representation",
                "term": "Population"
              },
              {
                "description": "A verdict stands until the representations or a record that names one changes",
                "term": "Freshness"
              },
              {
                "description": "The gate fails on a node or construct that names a representation that does not exist",
                "term": "Refusal"
              },
              {
                "description": "None, because a representation is a form of encoding, and nothing observes it while a run executes",
                "term": "Observation"
              },
              {
                "description": "Watched to fire and to accept: a suite plants a node that names a missing representation, and the bundled references resolve",
                "term": "Evidence"
              },
              {
                "description": "The representation list, which every node and construct that names a representation cites",
                "term": "Authoritative side"
              },
              {
                "description": "Not answered",
                "term": "Depends on"
              },
              {
                "description": "Not answered",
                "term": "Shape it refuses"
              }
            ],
            "kind": "glossary"
          }
        ],
        "id": "reasoning-representation-logic",
        "title": "logical"
      },
      {
        "blocks": [
          {
            "kind": "text",
            "text": "numbers, quantities, measurements"
          },
          {
            "kind": "text",
            "text": "How it is checked"
          },
          {
            "entries": [
              {
                "description": "the ontology resolution gate over the nodes and structured-document constructs that name the representation",
                "term": "Checked by"
              },
              {
                "description": "Every node and document construct that names the representation",
                "term": "Population"
              },
              {
                "description": "A verdict stands until the representations or a record that names one changes",
                "term": "Freshness"
              },
              {
                "description": "The gate fails on a node or construct that names a representation that does not exist",
                "term": "Refusal"
              },
              {
                "description": "None, because a representation is a form of encoding, and nothing observes it while a run executes",
                "term": "Observation"
              },
              {
                "description": "Watched to fire and to accept: a suite plants a node that names a missing representation, and the bundled references resolve",
                "term": "Evidence"
              },
              {
                "description": "The representation list, which every node and construct that names a representation cites",
                "term": "Authoritative side"
              },
              {
                "description": "Not answered",
                "term": "Depends on"
              },
              {
                "description": "Not answered",
                "term": "Shape it refuses"
              }
            ],
            "kind": "glossary"
          }
        ],
        "id": "reasoning-representation-number",
        "title": "numerical"
      },
      {
        "blocks": [
          {
            "kind": "text",
            "text": "operations, groups, fields"
          },
          {
            "kind": "text",
            "text": "How it is checked"
          },
          {
            "entries": [
              {
                "description": "the ontology resolution gate over the nodes and structured-document constructs that name the representation",
                "term": "Checked by"
              },
              {
                "description": "Every node and document construct that names the representation",
                "term": "Population"
              },
              {
                "description": "A verdict stands until the representations or a record that names one changes",
                "term": "Freshness"
              },
              {
                "description": "The gate fails on a node or construct that names a representation that does not exist",
                "term": "Refusal"
              },
              {
                "description": "None, because a representation is a form of encoding, and nothing observes it while a run executes",
                "term": "Observation"
              },
              {
                "description": "Watched to fire and to accept: a suite plants a node that names a missing representation, and the bundled references resolve",
                "term": "Evidence"
              },
              {
                "description": "The representation list, which every node and construct that names a representation cites",
                "term": "Authoritative side"
              },
              {
                "description": "Not answered",
                "term": "Depends on"
              },
              {
                "description": "Not answered",
                "term": "Shape it refuses"
              }
            ],
            "kind": "glossary"
          }
        ],
        "id": "reasoning-representation-algebra",
        "title": "algebraic"
      },
      {
        "blocks": [
          {
            "kind": "text",
            "text": "shapes, coordinates, spaces"
          },
          {
            "kind": "text",
            "text": "How it is checked"
          },
          {
            "entries": [
              {
                "description": "the ontology resolution gate over the nodes and structured-document constructs that name the representation",
                "term": "Checked by"
              },
              {
                "description": "Every node and document construct that names the representation",
                "term": "Population"
              },
              {
                "description": "A verdict stands until the representations or a record that names one changes",
                "term": "Freshness"
              },
              {
                "description": "The gate fails on a node or construct that names a representation that does not exist",
                "term": "Refusal"
              },
              {
                "description": "None, because a representation is a form of encoding, and nothing observes it while a run executes",
                "term": "Observation"
              },
              {
                "description": "Watched to fire and to accept: a suite plants a node that names a missing representation, and the bundled references resolve",
                "term": "Evidence"
              },
              {
                "description": "The representation list, which every node and construct that names a representation cites",
                "term": "Authoritative side"
              },
              {
                "description": "Not answered",
                "term": "Depends on"
              },
              {
                "description": "Not answered",
                "term": "Shape it refuses"
              }
            ],
            "kind": "glossary"
          }
        ],
        "id": "reasoning-representation-geometry",
        "title": "geometric"
      },
      {
        "blocks": [
          {
            "kind": "text",
            "text": "connectivity, continuity"
          },
          {
            "kind": "text",
            "text": "How it is checked"
          },
          {
            "entries": [
              {
                "description": "the ontology resolution gate over the nodes and structured-document constructs that name the representation",
                "term": "Checked by"
              },
              {
                "description": "Every node and document construct that names the representation",
                "term": "Population"
              },
              {
                "description": "A verdict stands until the representations or a record that names one changes",
                "term": "Freshness"
              },
              {
                "description": "The gate fails on a node or construct that names a representation that does not exist",
                "term": "Refusal"
              },
              {
                "description": "None, because a representation is a form of encoding, and nothing observes it while a run executes",
                "term": "Observation"
              },
              {
                "description": "Watched to fire and to accept: a suite plants a node that names a missing representation, and the bundled references resolve",
                "term": "Evidence"
              },
              {
                "description": "The representation list, which every node and construct that names a representation cites",
                "term": "Authoritative side"
              },
              {
                "description": "Not answered",
                "term": "Depends on"
              },
              {
                "description": "Not answered",
                "term": "Shape it refuses"
              }
            ],
            "kind": "glossary"
          }
        ],
        "id": "reasoning-representation-topology",
        "title": "topological"
      },
      {
        "blocks": [
          {
            "kind": "text",
            "text": "diagrams, graphs, networks"
          },
          {
            "kind": "text",
            "text": "How it is checked"
          },
          {
            "entries": [
              {
                "description": "the ontology resolution gate over the nodes and structured-document constructs that name the representation",
                "term": "Checked by"
              },
              {
                "description": "Every node and document construct that names the representation",
                "term": "Population"
              },
              {
                "description": "A verdict stands until the representations or a record that names one changes",
                "term": "Freshness"
              },
              {
                "description": "The gate fails on a node or construct that names a representation that does not exist",
                "term": "Refusal"
              },
              {
                "description": "None, because a representation is a form of encoding, and nothing observes it while a run executes",
                "term": "Observation"
              },
              {
                "description": "Watched to fire and to accept: a suite plants a node that names a missing representation, and the bundled references resolve",
                "term": "Evidence"
              },
              {
                "description": "The representation list, which every node and construct that names a representation cites",
                "term": "Authoritative side"
              },
              {
                "description": "Not answered",
                "term": "Depends on"
              },
              {
                "description": "Not answered",
                "term": "Shape it refuses"
              }
            ],
            "kind": "glossary"
          }
        ],
        "id": "reasoning-representation-graph",
        "title": "graphical"
      },
      {
        "blocks": [
          {
            "kind": "text",
            "text": "linear transformations"
          },
          {
            "kind": "text",
            "text": "How it is checked"
          },
          {
            "entries": [
              {
                "description": "the ontology resolution gate over the nodes and structured-document constructs that name the representation",
                "term": "Checked by"
              },
              {
                "description": "Every node and document construct that names the representation",
                "term": "Population"
              },
              {
                "description": "A verdict stands until the representations or a record that names one changes",
                "term": "Freshness"
              },
              {
                "description": "The gate fails on a node or construct that names a representation that does not exist",
                "term": "Refusal"
              },
              {
                "description": "None, because a representation is a form of encoding, and nothing observes it while a run executes",
                "term": "Observation"
              },
              {
                "description": "Watched to fire and to accept: a suite plants a node that names a missing representation, and the bundled references resolve",
                "term": "Evidence"
              },
              {
                "description": "The representation list, which every node and construct that names a representation cites",
                "term": "Authoritative side"
              },
              {
                "description": "Not answered",
                "term": "Depends on"
              },
              {
                "description": "Not answered",
                "term": "Shape it refuses"
              }
            ],
            "kind": "glossary"
          }
        ],
        "id": "reasoning-representation-matrix",
        "title": "matrix"
      },
      {
        "blocks": [
          {
            "kind": "text",
            "text": "mappings between spaces"
          },
          {
            "kind": "text",
            "text": "How it is checked"
          },
          {
            "entries": [
              {
                "description": "the ontology resolution gate over the nodes and structured-document constructs that name the representation",
                "term": "Checked by"
              },
              {
                "description": "Every node and document construct that names the representation",
                "term": "Population"
              },
              {
                "description": "A verdict stands until the representations or a record that names one changes",
                "term": "Freshness"
              },
              {
                "description": "The gate fails on a node or construct that names a representation that does not exist",
                "term": "Refusal"
              },
              {
                "description": "None, because a representation is a form of encoding, and nothing observes it while a run executes",
                "term": "Observation"
              },
              {
                "description": "Watched to fire and to accept: a suite plants a node that names a missing representation, and the bundled references resolve",
                "term": "Evidence"
              },
              {
                "description": "The representation list, which every node and construct that names a representation cites",
                "term": "Authoritative side"
              },
              {
                "description": "Not answered",
                "term": "Depends on"
              },
              {
                "description": "Not answered",
                "term": "Shape it refuses"
              }
            ],
            "kind": "glossary"
          }
        ],
        "id": "reasoning-representation-function",
        "title": "functional"
      },
      {
        "blocks": [
          {
            "kind": "text",
            "text": "entropy, encoding, compression"
          },
          {
            "kind": "text",
            "text": "How it is checked"
          },
          {
            "entries": [
              {
                "description": "the ontology resolution gate over the nodes and structured-document constructs that name the representation",
                "term": "Checked by"
              },
              {
                "description": "Every node and document construct that names the representation",
                "term": "Population"
              },
              {
                "description": "A verdict stands until the representations or a record that names one changes",
                "term": "Freshness"
              },
              {
                "description": "The gate fails on a node or construct that names a representation that does not exist",
                "term": "Refusal"
              },
              {
                "description": "None, because a representation is a form of encoding, and nothing observes it while a run executes",
                "term": "Observation"
              },
              {
                "description": "Watched to fire and to accept: a suite plants a node that names a missing representation, and the bundled references resolve",
                "term": "Evidence"
              },
              {
                "description": "The representation list, which every node and construct that names a representation cites",
                "term": "Authoritative side"
              },
              {
                "description": "Not answered",
                "term": "Depends on"
              },
              {
                "description": "Not answered",
                "term": "Shape it refuses"
              }
            ],
            "kind": "glossary"
          }
        ],
        "id": "reasoning-representation-information-theory",
        "title": "information-theoretic"
      },
      {
        "blocks": [
          {
            "kind": "text",
            "text": "distributions and likelihoods"
          },
          {
            "kind": "text",
            "text": "How it is checked"
          },
          {
            "entries": [
              {
                "description": "the ontology resolution gate over the nodes and structured-document constructs that name the representation",
                "term": "Checked by"
              },
              {
                "description": "Every node and document construct that names the representation",
                "term": "Population"
              },
              {
                "description": "A verdict stands until the representations or a record that names one changes",
                "term": "Freshness"
              },
              {
                "description": "The gate fails on a node or construct that names a representation that does not exist",
                "term": "Refusal"
              },
              {
                "description": "None, because a representation is a form of encoding, and nothing observes it while a run executes",
                "term": "Observation"
              },
              {
                "description": "Watched to fire and to accept: a suite plants a node that names a missing representation, and the bundled references resolve",
                "term": "Evidence"
              },
              {
                "description": "The representation list, which every node and construct that names a representation cites",
                "term": "Authoritative side"
              },
              {
                "description": "Not answered",
                "term": "Depends on"
              },
              {
                "description": "Not answered",
                "term": "Shape it refuses"
              }
            ],
            "kind": "glossary"
          }
        ],
        "id": "reasoning-representation-probability",
        "title": "probabilistic"
      },
      {
        "blocks": [
          {
            "kind": "text",
            "text": "state transitions"
          },
          {
            "kind": "text",
            "text": "How it is checked"
          },
          {
            "entries": [
              {
                "description": "the ontology resolution gate over the nodes and structured-document constructs that name the representation",
                "term": "Checked by"
              },
              {
                "description": "Every node and document construct that names the representation",
                "term": "Population"
              },
              {
                "description": "A verdict stands until the representations or a record that names one changes",
                "term": "Freshness"
              },
              {
                "description": "The gate fails on a node or construct that names a representation that does not exist",
                "term": "Refusal"
              },
              {
                "description": "None, because a representation is a form of encoding, and nothing observes it while a run executes",
                "term": "Observation"
              },
              {
                "description": "Watched to fire and to accept: a suite plants a node that names a missing representation, and the bundled references resolve",
                "term": "Evidence"
              },
              {
                "description": "The representation list, which every node and construct that names a representation cites",
                "term": "Authoritative side"
              },
              {
                "description": "Not answered",
                "term": "Depends on"
              },
              {
                "description": "Not answered",
                "term": "Shape it refuses"
              }
            ],
            "kind": "glossary"
          }
        ],
        "id": "reasoning-representation-dynamical-systems",
        "title": "dynamical"
      },
      {
        "blocks": [
          {
            "kind": "text",
            "text": "algorithms and programs"
          },
          {
            "kind": "text",
            "text": "How it is checked"
          },
          {
            "entries": [
              {
                "description": "the ontology resolution gate over the nodes and structured-document constructs that name the representation",
                "term": "Checked by"
              },
              {
                "description": "Every node and document construct that names the representation",
                "term": "Population"
              },
              {
                "description": "A verdict stands until the representations or a record that names one changes",
                "term": "Freshness"
              },
              {
                "description": "The gate fails on a node or construct that names a representation that does not exist",
                "term": "Refusal"
              },
              {
                "description": "None, because a representation is a form of encoding, and nothing observes it while a run executes",
                "term": "Observation"
              },
              {
                "description": "Watched to fire and to accept: a suite plants a node that names a missing representation, and the bundled references resolve",
                "term": "Evidence"
              },
              {
                "description": "The representation list, which every node and construct that names a representation cites",
                "term": "Authoritative side"
              },
              {
                "description": "Not answered",
                "term": "Depends on"
              },
              {
                "description": "Not answered",
                "term": "Shape it refuses"
              }
            ],
            "kind": "glossary"
          }
        ],
        "id": "reasoning-representation-computation",
        "title": "computational"
      },
      {
        "blocks": [
          {
            "kind": "text",
            "text": "objects and morphisms"
          },
          {
            "kind": "text",
            "text": "How it is checked"
          },
          {
            "entries": [
              {
                "description": "the ontology resolution gate over the nodes and structured-document constructs that name the representation",
                "term": "Checked by"
              },
              {
                "description": "Every node and document construct that names the representation",
                "term": "Population"
              },
              {
                "description": "A verdict stands until the representations or a record that names one changes",
                "term": "Freshness"
              },
              {
                "description": "The gate fails on a node or construct that names a representation that does not exist",
                "term": "Refusal"
              },
              {
                "description": "None, because a representation is a form of encoding, and nothing observes it while a run executes",
                "term": "Observation"
              },
              {
                "description": "Watched to fire and to accept: a suite plants a node that names a missing representation, and the bundled references resolve",
                "term": "Evidence"
              },
              {
                "description": "The representation list, which every node and construct that names a representation cites",
                "term": "Authoritative side"
              },
              {
                "description": "Not answered",
                "term": "Depends on"
              },
              {
                "description": "Not answered",
                "term": "Shape it refuses"
              }
            ],
            "kind": "glossary"
          }
        ],
        "id": "reasoning-representation-category-theory",
        "title": "categorical"
      }
    ],
    "title": "The representations"
  },
  "graph": {
    "narrative": true,
    "requires": [],
    "teaches": [],
    "traces": []
  },
  "href": "https://banes-lab.com/ontology/reasoning#the-representations",
  "number": "205",
  "page": "ontology",
  "ref": "chapter:/ontology/reasoning#the-representations",
  "relations": [],
  "route": null,
  "section": "the-representations",
  "summary": "A result can be encoded in any of these representation layers.",
  "tab": "reasoning",
  "title": "The representations",
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