Paraconsistent Foundations for Probabilistic Reasoning, Programming and Concept Formation
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Ben Goertzel
Jan 2, 2021, 2:45:39 PM1/2/21
to opencog
To kick off the new year ... here is Part 2 of a trilogy of papers I'm
working on ...
https://arxiv.org/abs/2012.14474
this one grounds (key aspects of) PLN in paraconsistent logic, and
thus makes clearer the programming-language Curry-Howard cognate of
PLN (via the known prog-lang cognate of relevant sorts of
paraconsistent logic). Also some other related stuff like
paraconsistent Formal Concept Analysis...
Part 3 (another paper) will sketchily represent the core OpenCog
cognitive algorithms as Galois connections involving
continuation-passing-style metagraph chronomorphisms , where the
metagraph targets are labeled w/ probabilistic/paraconsistent
dependent types as outlined in Part 2 ...
But I will defer starting on that till I finish some work on the SNet
roadmap and related issues ...
--
Ben Goertzel, PhD
http://goertzel.org
“Words exist because of meaning; once you've got the meaning you can
forget the words. How can we build an AGI who will forget words so I
can have a word with him?” -- Zhuangzhi++
working on ...
https://arxiv.org/abs/2012.14474
this one grounds (key aspects of) PLN in paraconsistent logic, and
thus makes clearer the programming-language Curry-Howard cognate of
PLN (via the known prog-lang cognate of relevant sorts of
paraconsistent logic). Also some other related stuff like
paraconsistent Formal Concept Analysis...
Part 3 (another paper) will sketchily represent the core OpenCog
cognitive algorithms as Galois connections involving
continuation-passing-style metagraph chronomorphisms , where the
metagraph targets are labeled w/ probabilistic/paraconsistent
dependent types as outlined in Part 2 ...
But I will defer starting on that till I finish some work on the SNet
roadmap and related issues ...
--
Ben Goertzel, PhD
http://goertzel.org
“Words exist because of meaning; once you've got the meaning you can
forget the words. How can we build an AGI who will forget words so I
can have a word with him?” -- Zhuangzhi++
Jacques Basaldúa
Jan 3, 2021, 8:20:58 AM1/3/21
to ope...@googlegroups.com
Thanks for the great reading, Ben. It is amazing how much work and thought you are putting into the foundations of opencog. I confess that I wasn't familiarized with the idea of paraconsistent logic and it helps understanding the brittleness of something too logic based. Carry on with the great work.
Jacques.
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Ben Goertzel
Jan 3, 2021, 1:34:09 PM1/3/21
to opencog
thanks! as you know a group of us are working on a radical redesign
(and reimplementation of large parts of) of the OpenCog system
(Hyperon) , which is currently at the prototype phase.. we are guided
in large part by pragmatic lessons in working w. the current OpenCog
version, but we also want to clarify the theoretical foundations
insofar as possible to maximize the odds that Hyperon is the OC
version that gets us all the way to human-level AGI ...
In particular, the design of the Hyperon Atomese interpreter -- which
needs to work effectively in conjunction w/ large distributed &
decentralized Atomspaces -- presents a lot of tricky design choices
and having a clear idea of the CS foundations of the cognitive
algorithms we need seems like it will be helpful for guiding those
choices...
Of course another challenge is that we want to wrap all this
mathematical subtlety in a system that is significantly more usable
and approachable than the current OpenCog version, which is another
sort of challenge ;) ... But AGI is not for the faint-hearted, right?
ben
> To view this discussion on the web visit https://groups.google.com/d/msgid/opencog/CA%2B_pmb5JZ9qOn6du6K2XJpRNmY6hSOJ_34npfgUgLgmyh_Uxkg%40mail.gmail.com.
(and reimplementation of large parts of) of the OpenCog system
(Hyperon) , which is currently at the prototype phase.. we are guided
in large part by pragmatic lessons in working w. the current OpenCog
version, but we also want to clarify the theoretical foundations
insofar as possible to maximize the odds that Hyperon is the OC
version that gets us all the way to human-level AGI ...
In particular, the design of the Hyperon Atomese interpreter -- which
needs to work effectively in conjunction w/ large distributed &
decentralized Atomspaces -- presents a lot of tricky design choices
and having a clear idea of the CS foundations of the cognitive
algorithms we need seems like it will be helpful for guiding those
choices...
Of course another challenge is that we want to wrap all this
mathematical subtlety in a system that is significantly more usable
and approachable than the current OpenCog version, which is another
sort of challenge ;) ... But AGI is not for the faint-hearted, right?
ben
Jacques Basaldúa
Jan 4, 2021, 5:14:57 PM1/4/21
to ope...@googlegroups.com
" But AGI is not for the faint-hearted, right?"
So true.
To view this discussion on the web visit https://groups.google.com/d/msgid/opencog/CACYTDBf18iAytJywmni-1LUMB9tRdXMSx0fkc898mKVkRi-iDA%40mail.gmail.com.
Ben Goertzel
Jan 13, 2021, 3:59:49 PM1/13/21
to opencog
As it seems someone is actually looking at this stuff a bit -- here's
the current revision of the Paraconsistent Foundations paper --- I
simplified the mapping from Constructible Duality logic to PLN, which
allowed me to also figure out what seems a pretty cool mapping from
p-bits (paraconsistent bits) into qubits ...
While somewhat off to the side of current OpenCog considerations, it
is interesting to note that Skilling and Knuth's 2019 paper
https://onlinelibrary.wiley.com/doi/full/10.1002/andp.201800057
implies that the only way to extend Kauffmann/Varela's Waveform
Algebra from crisp to uncertain truth values is to move to the complex
number algebra, which brings you of course to quantum mechanics right
away.
I'll give this draft another read/bugfix before posting on Arxiv though...
> To view this discussion on the web visit https://groups.google.com/d/msgid/opencog/CA%2B_pmb5JZ9qOn6du6K2XJpRNmY6hSOJ_34npfgUgLgmyh_Uxkg%40mail.gmail.com.
the current revision of the Paraconsistent Foundations paper --- I
simplified the mapping from Constructible Duality logic to PLN, which
allowed me to also figure out what seems a pretty cool mapping from
p-bits (paraconsistent bits) into qubits ...
While somewhat off to the side of current OpenCog considerations, it
is interesting to note that Skilling and Knuth's 2019 paper
https://onlinelibrary.wiley.com/doi/full/10.1002/andp.201800057
implies that the only way to extend Kauffmann/Varela's Waveform
Algebra from crisp to uncertain truth values is to move to the complex
number algebra, which brings you of course to quantum mechanics right
away.
I'll give this draft another read/bugfix before posting on Arxiv though...
Ben Goertzel
Feb 21, 2021, 5:47:42 AM2/21/21
to opencog
Ba-Da-Boom !! (see draft attached)
Patterns of Cognition:
Cognitive Algorithms as Galois Connections Fulfilled by Chronomorphisms
On Probabilistically Typed Metagraphs
"
It is argued that a broad class of AGI-relevant algorithms can be
expressed in a common formal framework, via specifying Galois
connections linking search and optimization processes on directed
metagraphs whose edge targets are labeled with probabilistic dependent
types, and then showing these connections are fulfilled by processes
involving metagraph chronomorphisms. Examples are drawn from the core
cognitive algorithms used in the OpenCog AGI framework: Probabilistic
logical inference, evolutionary program learning, pattern mining,
agglomerative clustering, pattern mining and nonlinear-dynamical
attention allocation.
The analysis presented involves representing these cognitive
algorithms as re- cursive discrete decision processes involving
optimizing functions defined over metagraphs, in which the key
decisions involve sampling from probability distri- butions over
metagraphs and enacting sets of combinatory operations on selected
sub-metagraphs. The mutual associativity of the combinatory operations
involved in a cognitive process is shown to often play a key role in
enabling the decomposi- tion of the process into folding and unfolding
operations; a conclusion that has some practical implications for the
particulars of cognitive processes, e.g. militating to- ward use of
reversible logic and reversible program execution. It is also observed
that where this mutual associativity holds, there is an alignment
between the hier- archy of subgoals used in recursive decision process
execution and a hierarchy of subpatterns definable in terms of formal
pattern theory.
"
This is in the same vein as good old OpenCoggy Probabilistic
Programming --- sorta OpenCoggy PP on dynamic programming, Galois
connections and chronomorphisms...
There is plenty that's still heuristic and slippery here, as is
inevitable w AGI under realistic resources, but I think this makes
non-trivial progress toward understanding how to implement the various
OpenCog cognitive algorithms in a common practical prog-language as
well as common theoretical framework...
Builds on the prior documents on metagraph folds and
paraconsistent/probabilistic logic, though not relying so much on the
details of the latter
Will post on Arxiv also
“He not busy being born is busy dying" -- Bob Dylan
Patterns of Cognition:
Cognitive Algorithms as Galois Connections Fulfilled by Chronomorphisms
On Probabilistically Typed Metagraphs
"
It is argued that a broad class of AGI-relevant algorithms can be
expressed in a common formal framework, via specifying Galois
connections linking search and optimization processes on directed
metagraphs whose edge targets are labeled with probabilistic dependent
types, and then showing these connections are fulfilled by processes
involving metagraph chronomorphisms. Examples are drawn from the core
cognitive algorithms used in the OpenCog AGI framework: Probabilistic
logical inference, evolutionary program learning, pattern mining,
agglomerative clustering, pattern mining and nonlinear-dynamical
attention allocation.
The analysis presented involves representing these cognitive
algorithms as re- cursive discrete decision processes involving
optimizing functions defined over metagraphs, in which the key
decisions involve sampling from probability distri- butions over
metagraphs and enacting sets of combinatory operations on selected
sub-metagraphs. The mutual associativity of the combinatory operations
involved in a cognitive process is shown to often play a key role in
enabling the decomposi- tion of the process into folding and unfolding
operations; a conclusion that has some practical implications for the
particulars of cognitive processes, e.g. militating to- ward use of
reversible logic and reversible program execution. It is also observed
that where this mutual associativity holds, there is an alignment
between the hier- archy of subgoals used in recursive decision process
execution and a hierarchy of subpatterns definable in terms of formal
pattern theory.
"
This is in the same vein as good old OpenCoggy Probabilistic
Programming --- sorta OpenCoggy PP on dynamic programming, Galois
connections and chronomorphisms...
There is plenty that's still heuristic and slippery here, as is
inevitable w AGI under realistic resources, but I think this makes
non-trivial progress toward understanding how to implement the various
OpenCog cognitive algorithms in a common practical prog-language as
well as common theoretical framework...
Builds on the prior documents on metagraph folds and
paraconsistent/probabilistic logic, though not relying so much on the
details of the latter
Will post on Arxiv also
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