Goldman (1971) analyzed interrelations between act-statements by inducing a structure by means of the relationship by, e.g.: "He turned on the light by flipping the switch." Generally, the structure is represented by act-diagrams, e.g. act-trees. In the present article the mathematical theory of directed graphs (digraphs), specifically the concepts of partially or strictly ordered sets, graph-theoretical trees, semi-lattices etc. are shown to be applicable and conducive to the formal and a more general description of networks of act statements generated by (...) a (relative) basic actionstatement and by the relation by. The well-known problem of identity of acts described by corresponding statements connected by by is differentiated by introducing the graph-theoretical equivalence relation of belonging to the same-graph {graph-sameness or graph-identity) admitting of a more refined classification and logical description of the interdependence of actions, acttypes, act-properties etc. (shrink)

Goldman (1971) analyzed interrelations between act-statements by inducing a structure by means of the relationship by, e.g.: "He turned on the light by flipping the switch." Generally, the structure is represented by act-diagrams, e.g. act-trees. In the present article the mathematical theory of directed graphs (digraphs), specifically the concepts of partially or strictly ordered sets, graph-theoretical trees, semi-lattices etc. are shown to be applicable and conducive to the formal and a more general description of networks of act statements generated by (...) a (relative) basic actionstatement and by the relation by. The well-known problem of identity of acts described by corresponding statements connected by by is differentiated by introducing the graph-theoretical equivalence relation of belonging to the same-graph {graph-sameness or graph-identity) admitting of a more refined classification and logical description of the interdependence of actions, acttypes, act-properties etc. (shrink)