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.
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.
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.
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.
On 12/30/2025 7:05 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.
I am just now beginning to properly formalize things
A Turing-machine decider is a Turing machine D that
computes a total function D :-a +ureu raA {Accept,Reject},
where +ureu is the set of all finite strings over the
input alphabet. That is:
1. Totality: For every finite string input w ree +ureu,
D halts and outputs either Accept or Reject.
*This is my less formal essence of the above*
All deciders essentially: Transform finite string
inputs by finite string transformation rules into
{Accept, Reject} values.
On 12/30/2025 7:05 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.
*Maybe you can be the first human to understand this*
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
What is actually means is that Prolog detected
a cycle in the directed graph of the evaluation
sequence of LP.
I created Minimal Type Theory for this exact same purpose.
LP := ~True(LP)
All that MTT ever did was detect cycles in the
evaluation sequence of expressions by first
translating these expressions into direct graphs.
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.
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.
On 12/30/2025 05:05 PM, Jeff Barnett wrote:A non-DAG may have zero or more nodes with no in-edges and so might a
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.
On 12/31/2025 8:53 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.
I just examining this the structure of the body
of general knowledge seems to be a tree.
My initial design for a universal type hierarchy
knowledge ontology has two most basic types
{things} and {relations between things}
On 12/31/25 11:59 PM, olcott wrote:
On 12/31/2025 8:53 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.
I just examining this the structure of the body
of general knowledge seems to be a tree.
My initial design for a universal type hierarchy
knowledge ontology has two most basic types
{things} and {relations between things}
And what is the "root" node of knowledge that has meaning without any
other node?
Note, a "type hierarchy" doesn't contain all knowledge, so doesn't
qualify for you goal.
On 12/31/2025 7:53 PM, Ross Finlayson wrote:
On 12/30/2025 05:05 PM, Jeff Barnett wrote:A non-DAG may have zero or more nodes with no in-edges and so might a
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.
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.
On 01/01/2026 12:15 AM, Jeff Barnett wrote:
On 12/31/2025 7:53 PM, Ross Finlayson wrote:
On 12/30/2025 05:05 PM, Jeff Barnett wrote:A non-DAG may have zero or more nodes with no in-edges and so might a
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.
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.
That thusly there's a tree-traversal of it may be as after
a recursive necessarily traversal, of a finite directed acyclic graph,
about that the existence of a tree-traversal results thusly a tree
structure.
Then about that in the infinite is also its own thing,
about when infinite induction completes.
One may aver that for unbounded-induction to complete,
it's independent whether it's infinite-induction,
further independent whether it's continuum-induction,
of the (unbounded) inductive-limit and infinite-limit
and continuum-limit, here as about why and whether
it's independent ordinary induction whether all DAGs are trees.
On 1/1/2026 10:37 AM, Richard Damon wrote:
On 12/31/25 11:59 PM, olcott wrote:
On 12/31/2025 8:53 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.
I just examining this the structure of the body
of general knowledge seems to be a tree.
My initial design for a universal type hierarchy
knowledge ontology has two most basic types
{things} and {relations between things}
And what is the "root" node of knowledge that has meaning without any
other node?
Objects of thought.
Note, a "type hierarchy" doesn't contain all knowledge, so doesn't
qualify for you goal.
It can contain every expression:
"true on the basis of meaning expressed in language"
So that it can be better understood it is limited
to the finite set of general knowledge.
On 01/01/2026 10:35 AM, Ross Finlayson wrote:
On 01/01/2026 12:15 AM, Jeff Barnett wrote:
On 12/31/2025 7:53 PM, Ross Finlayson wrote:
On 12/30/2025 05:05 PM, Jeff Barnett wrote:A non-DAG may have zero or more nodes with no in-edges and so might a
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.
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.
That thusly there's a tree-traversal of it may be as after
a recursive necessarily traversal, of a finite directed acyclic graph,
about that the existence of a tree-traversal results thusly a tree
structure.
Then about that in the infinite is also its own thing,
about when infinite induction completes.
One may aver that for unbounded-induction to complete,
it's independent whether it's infinite-induction,
further independent whether it's continuum-induction,
of the (unbounded) inductive-limit and infinite-limit
and continuum-limit, here as about why and whether
it's independent ordinary induction whether all DAGs are trees.
Agreeably that's in a roundabout way, and in
a thoroughly roundabout sort of way,
and furthermore it's necessarily abstract,
then as with regards to uniqueness of order and origin,
or which sibling and which root, it's arbitrary,
then though the point is about that it's so.
I.e., it involves concepts like "ubiquitous ordinals"
and "traversals of the infinite tree", and the lattice
vis-a-vis the taxicab distance, while it arrives
as available the general notion, then that all sorts
of tree-theoretic theorems result about graph-theoretic
theorems, besides as for the usual sub-class of graph-theoretic
and dag-theoretic theorems about trees.
It gets involved usual notions of non-standard computability
and orderings like 1, 3, 5, ..., 2, 4, 6, ....
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