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Sigma KEE - Graph
Graph(graph)Cartesian_coordinate_system, bus, bus_topology, coordinate_system, exponential_curve, frame_of_reference, inertial_frame, inertial_reference_frame, logical_topology, loop, loop_topology, mesh, mesh_topology, physical_topology, profile, reference_frame, reference_system, star, star_topology

appearance as argument number 1
-------------------------


(subclass Graph Proposition) Merge.kif 5742-5742 Graph is a subclass of proposition
(documentation Graph EnglishLanguage "The Class of graphs, where a graph is understood to be a set of GraphNodes connected by GraphArcs. Note that this Class includes only connected graphs, i.e. graphs in which there is a GraphPath between any two GraphNodes. Note too that every Graph is required to contain at least two GraphArcs and three GraphNodes.") Merge.kif 5744-5748 Graph is a subclass of proposition

appearance as argument number 2
-------------------------


(subclass DirectedGraph Graph) Merge.kif 5788-5788 Directed graph is a subclass of graph
(subclass MultiGraph Graph) Merge.kif 5891-5891 Multi graph is a subclass of graph
(subclass PseudoGraph Graph) Merge.kif 5921-5921 Pseudo graph is a subclass of graph
(termFormat EnglishLanguage Graph "graph") english_format.kif 1077-1077 Pseudo graph is a subclass of graph

appearance as argument number 3
-------------------------


(domain graphPart 2 Graph) Merge.kif 6008-6008 The number 2 argument of graph part is an instance of graph
(domain subGraph 1 Graph) Merge.kif 6017-6017 The number 1 argument of sub graph is an instance of graph
(domain subGraph 2 Graph) Merge.kif 6018-6018 The number 2 argument of sub graph is an instance of graph
(domain CutSetFn 1 Graph) Merge.kif 6190-6190 The number 1 argument of cut set is an instance of graph
(domain MinimalCutSetFn 1 Graph) Merge.kif 6198-6198 The number 1 argument of minimal cut set is an instance of graph
(domain graphMeasure 1 Graph) Merge.kif 6268-6268 The number 1 argument of graph measure is an instance of graph

antecedent
-------------------------


(=>
    (and
        (instance ?GRAPH Graph)
        (instance ?NODE1 GraphNode)
        (instance ?NODE2 GraphNode)
        (graphPart ?NODE1 ?GRAPH)
        (graphPart ?NODE2 ?GRAPH)
        (not
            (equal ?NODE1 ?NODE2)))
    (exists (?ARC ?PATH)
        (or
            (links ?NODE1 ?NODE2 ?ARC)
            (and
                (subGraph ?PATH ?GRAPH)
                (instance ?PATH GraphPath)
                (or
                    (and
                        (equal
                            (BeginNodeFn ?PATH) ?NODE1)
                        (equal
                            (EndNodeFn ?PATH) ?NODE2))
                    (and
                        (equal
                            (BeginNodeFn ?PATH) ?NODE2)
                        (equal
                            (EndNodeFn ?PATH) ?NODE1)))))))		 Merge.kif 5750-5770 If All of the following hold: (1) X is an instance of graph (2) Y is an instance of graph node (3) Z is an instance of graph node (4) Y is a part of X (5) Z is a part of X (6) equal Y and Z, then All of the following hold: (1) there exist W (2) V such that W links Y (3) Z, V is a subgraph of X (4) V is an instance of graph path (5) equal the beginning of V (6) Y (7) equal the end of V (8) Z, or equal the beginning of V (9) Z (10) equal the end of V (11) Y
(=>
    (instance ?GRAPH Graph)
    (exists (?NODE1 ?NODE2 ?NODE3 ?ARC1 ?ARC2)
        (and
            (graphPart ?NODE1 ?GRAPH)
            (graphPart ?NODE2 ?GRAPH)
            (graphPart ?NODE3 ?GRAPH)
            (graphPart ?ARC1 ?GRAPH)
            (graphPart ?ARC2 ?GRAPH)
            (links ?NODE1 ?NODE2 ?ARC1)
            (links ?NODE2 ?NODE3 ?ARC2)
            (not
                (equal ?NODE1 ?NODE2))
            (not
                (equal ?NODE2 ?NODE3))
            (not
                (equal ?NODE1 ?NODE3))
            (not
                (equal ?ARC1 ?ARC2)))))		 Merge.kif 5772-5786 If X is an instance of graph, then All of the following hold: (1) there exist Y, Z,, , W,, , V (2) U such that Y is a part of X (3) Z is a part of X (4) W is a part of X (5) V is a part of X (6) U is a part of X (7) V links Y (8) Z (9) U links Z (10) W (11) equal Y (12) Z (13) equal Z (14) W (15) equal Y (16) W (17) equal V (18) U
(=>
    (instance ?GRAPH Graph)
    (subclass
        (MinimalCutSetFn ?GRAPH)
        (CutSetFn ?GRAPH)))		 Merge.kif 6206-6208 If X is an instance of graph, then the set of minimal paths that partition X into two separate graphs is a subclass of the set of paths that partition X into two separate graphs

consequent
-------------------------


(=>
    (instance ?PART GraphElement)
    (exists (?GRAPH)
        (and
            (instance ?GRAPH Graph)
            (graphPart ?PART ?GRAPH))))		 Merge.kif 5945-5950 If X is an instance of graph element, then there exists Y such that Y is an instance of graph and X is a part of Y
(=>
    (instance ?TS TransitSystem)
    (exists (?G)
        (and
            (instance ?G Graph)
            (abstractCounterpart ?G ?TS))))		 Transportation.kif 3980-3985 If X is an instance of transit system, then there exists Y such that Y is an instance of graph and the abstract counterpart of X is Y


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