Ali,
I’m not sure this will help, but we’ll see.
I think sometimes this is called heterogeneous reasoning or sometimes hybrid knowledge representation and reasoning. There are a couple of strands, some from
AI or closely related cognitive science.
Johnson-Laird, P. N. 2006. Models and heterogeneous reasoning. Journal of Experimental & Theoretical Artificial Intelligence, Vol. 18, No. 2, June 2006, 121–148.
http://mentalmodels.princeton.edu/papers/2007hetreasoning.pdf.
An old friend of mine, Mark Graves, did a PhD back in 1993 under Bill Rounds at U Michigan on pre-ontology application-specific knowledge base development and
reasoning methods, perhaps superseded by subsequent research now:
Graves, Mark. 1993. Theories and Tools for Designing Application-Specific Knowledge Base Data Models. PhD, University of Michigan. http://www.healsci.org/people/mgraves/pubs/diss.pdf.
Also, I recall that Barwise and Etchemendy did some work that followed on from their Tarski’s World work in the 1990s, that focused on reasoning methods. But
I don’t remember the papers.
You can also perhaps think of your question as a kind of a factoring or global analyzing knowledge compiler, in which case you should look at the literature
on knowledge compilation. We had a local proposal to do some distributed reasoning and knowledge compilation research in 1999, but it never got funded. It was along the lines of subsequent research:
Eyal, Amir, and Sheila McIlraith. 2000a. Improving the Efficiency of Reasoning Through Structure-Based Reformulation. Proceedings of the Symposium on Abstraction,
Reformulation, and Approximation (SARA2000). Published by Springer-Verlag in Lecture Notes in Artificial Intelligence, vol. 1864. Lake LBJ, Texas. July 2000.
Eyal, Amir, and Sheila McIlraith. 2000b. Partition-Based Logical Reasoning. Proceedings of the Sthemath International Conference on Principles of Knowledge
Representation and Reasoning (KR2000). Breckenridge, Colorado, USA. April 12-15, 2000: 389-400. ftp://ftp.ksl.stanford.edu/pub/KSL_Reports/KSL-00-02.ps
Eyal, Amir, and Sheila McIlraith. 2005. Partition-based logical reasoning for first-order and propositional theories. Artificial Intelligence, Volume 162 ,
Issue 1-2 (February 2005). Special volume on reformulation, pp. 49 – 88. See the AI special issue on reformulation: http://www.sciencedirect.com/science?_ob=PublicationURL&_tockey=%23TOC%235617%232005%23998379998%23551202%23FLP%23&_cdi=5617&_pubType=J&_auth=y&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=195c8e553ef6dce8c9b911bfd40eca0a.
I’m not sure this will help, but I hope it does.
Thanks,
Leo
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx]
On Behalf Of Ali SH
Sent: Friday, November 30, 2012 9:21 PM
To: [ontolog-forum]
Subject: [ontolog-forum] Hybrid Reasoning Literature / Systems / Model Theory
Ok, this has been sitting in my drafts for a couple of weeks, and I'm really unsure how to frame the question in a coherent way. Anyway, here goes...
I have been working with what I consider hybrid reasoning systems for a couple of years now, but have had difficulty in finding good literature on the topic. Can anyone point me to literature on this front?
Particularly, I have been deploying relatively expressive ontologies using a variety of dbs, algorithms etc. For example, these ontologies may represent geo-spatial reasoning (i.e. generate path from A to B, or tell me what X is beside
what Y) or in another domain, relatively complex mathematical analyses (i.e. protein-gene pathway interactions, or relations between entities which involve solving differential equations etc.)
In my current approach, I capture all of these theories in the ontology, but when I have a query that requires "reasoning" in one of these specialized modules, if I can deconstruct the query, I pass off the subpart of the query to the tool
best suited for the task (i.e. for the geo-spatial ontology, I would compute path or adjacency using a 3D physics engine). At a very high level, it is similar in many ways to the blackboard approach used in earlier systems.
In terms of the model theory behind this - is there a name for this approach? I've found some literature touching vaguely similar things, but nothing really satisfying thus far. Moreover, I'm unclear what this entails for the model theory.
I currently try to have the implementing reasoning modules sign "semantic contracts" with the sub-theory of the ontology they perform reasoning services for, but in general I cannot guarantee that the axioms in the ontology are always satisfied by the results
of the computation in these services. In some cases, the mathematics which are implemented computationally and algorithmically may have theorems for the results, though it's still unclear to me how the implementing algorithm can be guaranteed to satisfy the
underlying theory. Unit testing, and competency questions re the expected output are the best I have for most classes of implementation algorithms. To some degree, literature on formal verification of algorithms come close to what i'm looking for, but they
rarely connect the results to integrating the algorithms with a broader reasoning system....
A simpler illustrative example might be to represent arithmetic in an ontology (say using Peano's axioms), but to use the built-in functionality provided your favourite programming language to actually perform arithmetic (as opposed to
trying to deduce that 1+1=2 based on the axioms in the theory). In cases where I can oversee the implementation of an algorithm, I can try to develop correctness proofs, and also cite literature, but these "semantic contracts" often end up being statistical
confidence intervals over a large set of inputs.
Any help or pointers would be greatly appreciated. Or any help in better formulating the problem at hand or which communities to approach.