initial node fn (InitialNodeFn)

A UnaryFunction that maps a GraphArc to the initial node of the GraphArc. Note that this is a partial function. In particular, the function is undefined for GraphArcs that are not part of a DirectedGraph.

Ontology

SUMO / GRAPH-THEORY

Class(es)

class

inheritable relation

unary function

initial node fn

Coordinate term(s)

absolute value fn abstraction fn arc cosine fn arc sine fn arc tangent fn back fn begin fn begin node fn cardinality fn ceiling fn complement fn cosine fn cut set fn denominator fn end fn end node fn extension fn floor fn front fn future fn generalized intersection fn generalized union fn giga fn imaginary part fn immediate future fn immediate past fn integer square root fn kilo fn list length fn magnitude fn mega fn micro fn milli fn minimal cut set fn nano fn numerator fn organization fn past fn path weight fn pico fn power set fn predecessor fn principal host fn probability fn property fn rational number fn real number fn reciprocal fn round fn signum fn sine fn skin fn square root fn successor fn tangent fn tera fn terminal node fn wealth fn when fn year fn

Type restrictions

graph node InitialNodeFn(graph arc)

Axioms (4)

If graph is an instance of directed graph and arc is an instance of graph arc and arc is a part of graph, then there exist node1,node2 so that "the starting node of arc" is equal to node1 and "the terminal node of arc" is equal to node2.

(=>
      (and
            (instance ?GRAPH DirectedGraph)
            (instance ?ARC GraphArc)
            (graphPart ?ARC ?GRAPH))
      (exists
            (?NODE1 ?NODE2)
            (and
                  (equal
                        (InitialNodeFn ?ARC)
                        ?NODE1)
                  (equal
                        (TerminalNodeFn ?ARC)
                        ?NODE2))))

if graph is an instance of graph path and arc is an instance of graph arc and arc is a part of graph,
then if "the starting node of arc" is equal to node, then there doesn't exist other so that "the starting node of other" is equal to node and other is not equal to arc

(=>
      (and
            (instance ?GRAPH GraphPath)
            (instance ?ARC GraphArc)
            (graphPart ?ARC ?GRAPH))
      (=>
            (equal
                  (InitialNodeFn ?ARC)
                  ?NODE)
            (not
                  (exists
                        (?OTHER)
                        (and
                              (equal
                                    (InitialNodeFn ?OTHER)
                                    ?NODE)
                              (not
                                    (equal ?OTHER ?ARC)))))))

If "the starting node of arc" is equal to node and "the terminal node of arc" is equal to node, then arc is an instance of graph loop.

(=>
      (and
            (equal
                  (InitialNodeFn ?ARC)
                  ?NODE)
            (equal
                  (TerminalNodeFn ?ARC)
                  ?NODE))
      (instance ?ARC GraphLoop))

begin node fn is internally related to initial node fn.

(relatedInternalConcept BeginNodeFn InitialNodeFn)