XPost: comp.theory, sci.logic, sci.math   
   From: jbb@notatt.com   
      
   On 12/31/2025 7:53 PM, Ross Finlayson wrote:   
   > On 12/30/2025 05:05 PM, Jeff Barnett wrote:   
   >> On 12/29/2025 4:17 PM, Richard Damon wrote:   
   >>> On 12/29/25 6:07 PM, olcott wrote:   
   >>>> A DAG (Directed Acyclic Graph) that is also a tree   
   >>>> is a specific type of DAG where each node (except   
   >>>> the single root) has exactly one parent, creating   
   >>>> a hierarchy with no cycles.   
   >>>>   
   >>>> When building an inheritance hierarchy knowledge   
   >>>> ontology There may be a single root node such as   
   >>>> {Thing} yet DAG Trees would exclude multiple   
   >>>> inheritance.   
   >>>>   
   >>>> You can still have a DAG with a single root node   
   >>>> and have multiple inheritance yet you cannot   
   >>>> call it a tree.   
   >>>>   
   >>>   
   >>> So, what "fact" of knowledge needs nothing to base itself on?   
   >>>   
   >>> "Thing" as a word, doesn't have a meaning by itself.   
   >>>   
   >>> This is your problem, you NEED to embed your "system" into something   
   >>> with givens to establish your "roots".   
   >>>   
   >>> And, the problem is "Natural Language", your favorite source, is just   
   >>> too inconsistant of a source.   
   >>   
   >> If you are going to criticize that absurd idiot, at least comment on a   
   >> Freshmen stupidity. Think before you type. The circle jerk continues.   
   >> You both flunk.   
   >>   
   >> While a tree is a DAG, not all DAG are trees.   
   >   
   > Actually a DAG has at least one node with no edges-in,   
   > so it would be a root node in a tree.   
   >   
   > Otherwise it would have cycles and not be a-cyclic.   
   A non-DAG may have zero or more nodes with no in-edges and so might a   
   DAG. There is no requirement that every node in a graph must be in a   
   cycle in order to loose DAG status. The only requirements that G be a   
   DAG are 1) it be constructed from only directed edges and zero or more   
   nodes and 2) there are no cyclic paths formed by following edges in   
   their declared directions.   
   --   
   Jeff Barnett   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)