hmm for ontological inferences mechanism, I think I am designing new things now whilst studying the group theoretic book. 

e.g. there is a homomorphims from W to 1 element group 

e.g. W does  (Y)  where Y is only a Identity element having group conceptually a definition of verb. 

then there is 'has a' relation between R to W. e.g. R has a W.

has a means there is a global W group and R is contained under some groups w1, w2 or wn's intersection of containing R.  that W of R concept is closure of W covering R.

then this closure is of course a subset of entire W

then---> how to deduce R then has same homomorphism to Y?  even more constrained then isomorphism meaning I mean. 

I mean how to deduce R does (Y) then?

its because of ->  if  beta is the homomorphism of  W to Y 

so Wbeta = Y (which is identity element)

then Rbeta = Y also because R is closure of some sets inside W and subset of W. so concept of R by W also does Y. 

so hmm so this yet only one type ontological inference mechanism I decided. 

hmm of has a relation definitions. 

and of course its multi dimensional actually. e.g. 

W is somethign multi dimensional like (A, B, C, D)

R also has those dimensions. 

hmm this has a concept's inference mechanism is only one part. 

Then there is also is a mechanism. 

for that. 

e.g. R is a Q 

then

if Q does Y   does R do Y also?   its similar to has a 

e.g. R has a W is similar to   R is a W in this sense in the set theoretic closure wise definition. then the same logic there could be applied similarly.

but then of course if R does Y does Q do Y? of course not knowable.

Since

if we defined Q instances like Q1 Q2 instantiation alike

then 

there is an isa homomorphism from R1, R2 to Q1 Q2 Q3  then like  R  to Q homomorphism,,

then unless hmm without set theoretic how to explain this hmm could be some how defined free groups logic wise (but of course set theoretic inference in this is much easier I just wanted to check the whether any other  correspondent other inference method is possible)

e.g. unless R1 to Q1 is always one to one and surjective,  we can not guarantee 

e.g. R1theta = Q1 alike 

then 

Q1 inv_theta  = R1 

so Q1 inv_theta  does Y 

so unless Q1 is free group and also surjective for Rto Q then we can not know Q1 entire set would have
"does Y" homomorphism

so only if Q is isomorphic to R with soem function, we cant know dynamics of Q / Y and plus even if it were isomorphic, then it could still had meant either Q does Y or Q does not Y.  so isomorphism can only guarantee synonymity antonymy in terms of does verb. 

hmm so I think I am going to finish these ontological inference systems also on saturday possibly. 

seems as multidimensionality could be also reduced possibly in set theoretic logic side. hmm would check those later after saturday. 

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hmm i dont need to define a very advanced system in these, cause its not intending to be a very excelled nlp capabilities since its for algebra creation /inference mechanisms and basical nlp skills that is capable of reading some science books. so advanced nlp is not necessary.  algebraic inference systems is more important e.g. it should be possible to easily define lie groups for differential eqs based systems. or alike. this algebraic side is more important then nlp skill set for this ai since its intended to write code and read some science book and investigate theoretical physics frameworks autonomously as much as it can without experimental physics either. but to generate a set of theories.  e.g. for multiverse equation investigation for instance etc.  and also things like writing a simulator code to then also investigate quantum computer/algebra designs. then later after quantum computer is built, learning medical tehcnology etc to create simulations to build medicine based on particle physics simulators based on possible theoretical frameworks with defined on existing known experimental data results of theoretical physics experiment side. I mean, it would try to create medicine with particle physics based simulators on quantum computers or remodel how systems in our body work to heal tissues etc with quantum computers managed particle physics systems etc. 

hmm need to first build as an important milestone (after this ai is ready) is the building of quantum computer /algebra design etc. then the reverse engineering how our body works is from with simulations on quantum computers then creating medicine with quantum computer tech and particle physics based intervention e.g. to heal tissues etc etc.  yayy then we have infinite time having lives after such quantum computers are devised :D yayyy :D  

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I am very wondering the manifolds and geometry section of these group theoretic topics and its possible intersection with topology topics. had not learnt any yet these topics but very curious to learn soon and its necessary to learn. like as in this stage its currently necessary to strudy to this group theoretic study book. some months later  I need to study to manifolds/geometry discussions of algebra and then its relation to topology concepts. then we can use methods in topology from to here. yepp. as usual applicance of group theoretic topics is isomorphisms oeg. using one group instead of another one. e.g. were the some polynomials group were used in some specific spd energy levels what were after d i forgot :D that not being specifically isomorphism area but rather finding a suitable group definition I guess so but  i mean most basical application area of group theoretic topics as far as I infer such topics  but we could extend that to utilize methods from topology to this algebra side either possibly. after I learn manifolds/geometry concepts based on group theory concepts. but these for later first i currently need to finish this group theory book first. and code the ai with basic group theoretic inference systems. 

not something slow like Apache Jena either projects ontology definitions is targeting to be. I dont know how that apache project's ontological inference is exactly. but I wish to define this ontology inferences  via pure maths structures based inferences. with rigorous probability theory /set theory and group theoretic definitions set. in initial version of ai i mean. then generative isomorphisms features to try to define things with alternative underlying groups. e.g. a physical system might have some experimental data and there might have been some theories of its group structure (mathematical group structure) but ai needs to investigate alternative group structures alternative formulations if ever exists if there is no constraint of only possbile unique group structure definition. to auto generate alternative theories of formulations /group definitions to match with the experimental physics results at the same time.  it needs to be group theoretic wise very generative ai/ml project. and should have pure maths based inference systems also. hmm these be first specs of initial design imho. 

yeppp now rest time. 

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