Re: logic

Hi Yuk,

thanks for that pointer to the short history. I should read that up. I did not realise and would like to know more
about the relation between DL and Modal logic. If it is true that work has been done there, then that could
invalidate my claim that DL does not deal with intentional contexts. I was just going of what I had seen of
OWL, which seems very Object Oriented. 

What is missing from OWL at present ( though I suppose one could claim correctly that it is
there hidden in the form of literals ) is the relation to a graph. So something like 

:mary :believes { :Jane loves :Joe } .

Of course this could be expressed in RDF/OWL with

:mary :believes "@prefix : <http://ex.example>. :Jane :loves :Joe . "^^lang:Turtle .



On 25 Sep 2013, at 09:47, Yuk Hui <huiyuk@gmail.com> wrote:

> hi Delfi, 
> 
> Thank you for the quick reply.
> I understand logic no matter it is Frege's or Tarski's, truth is always at center of their inquiries, and of course this comes to the condition of truth.
> What i am interested here is the evolution of DL and its use in industry, I refer to the following passages from a chapter[1] on DL, but i don't think the historical background and its development in related to other logic is clear, so it will be great if anyone can comment or give some other resources. Thanks.
> 
> best,Yuk
> 
> [1]Franz Baader, Ian Horrocks, Ulrike Sattler, in Handbook of Knowledge Representation 135 Edited by F. van Harmelen, V. Lifschitz and B. Porter © 2008 Elsevier B.V. All rights reserved DOI: 10.1016/S1574-6526(07)03003-9, Chapter 3 Description Logics. 
> 
> Phase 1 (1980–1990) was mainly concerned with implementation of systems, such as KL-ONE, K-REP, KRYPTON, BACK, and LOOM [41, 119, 38, 137, 118]. These systems employed so-called structural subsumption algorithms, which first normalize the concept descriptions, and then recursively compare the syntactic structure of the normalized descriptions [126]. These algorithms are usually relatively efficient (poly- nomial), but they have the disadvantage that they are complete only for very inexpressive DLs, i.e., for more expressive DLs they cannot detect all subsumption/instance relationships. During this phase, the first logic-based accounts of the semantics of the underlying representation formalisms were given [38, 39], which made formal inves- tigations into the complexity of reasoning in DLs possible. For example, in [39] it was shown that seemingly small additions to the expressive power of the representation formalism can cause intractability of the subsumption problem. In [148] it was shown that subsumption in the representation language underlying KL-ONE is even unde- cidable, and in [127] it was shown that the use of a TBox formalism that allows the introduction of abbreviations for complex descriptions makes subsumption intractable if the underlying DL has the constructors conjunction and value restriction (these con- structors were supported by all the DL systems available at that time). As a reaction to these negative complexity results, the implementors of the CLASSIC system (the first industrial-strength DL system) carefully restricted the expressive power of their DL [135, 37].
> 
> Phase 2 (1990–1995) started with the introduction of a new algorithmic paradigm into DLs, so-called tableau based algorithms [149, 63, 89]. They work on propositionally closed DLs (i.e., DLs with all Boolean operators), and are complete also for expressive DLs. To decide the consistency of a knowledge base, a tableau based algorithm tries to construct a model of it by structurally decomposing the concepts in the knowledge base, thus inferring new constraints on the elements of this model. The algorithm either stops because all attempts to build a model failed with obvious contradictions, or it stops with a “canonical” model. Since, in propositionally closed DLs, the subsumption and the instance problem can be reduced to consistency, a consistency algorithm can solve all the inference problems mentioned above. The first systems employing such algorithms (KRIS and CRACK) demonstrated that optimized implementations of these algorithms led to an acceptable behavior of the system, even though the worst-case complexity of the corresponding reasoning problems is no longer in polynomial time [18, 44]. This phase also saw a thorough analysis of the complexity of reasoning in various DLs [63, 64, 62], and the important observation that DLs are very closely related to modal logics [144].
> 
> Phase 3 (1995–2000) is characterized by the development of inference procedures for very expressive DLs, either based on the tableau approach [100, 92], or on a translation into modal logics [57, 58, 56, 59]. Highly optimized systems (FaCT, RACE, and DLP [95, 80, 133]) showed that tableau-based algorithms for expressive DLs led to a good practical behavior of the system even on (some) large knowledge bases. In this phase, the relationship to modal logics [57, 146] and to decidable fragments of first- order logic [33, 129, 79, 77, 78] was also studied in more detail, and applications in databases (like schema reasoning, query optimization, and integration of databases) were investigated [45, 47, 51].
> 
> We are now in Phase 4, where the results from the previous phases are being used to develop industrial strength DL systems employing very expressive DLs, with applications like the Semantic Web or knowledge representation and integration in medical- and bio-informatics in mind. On the academic side, the interest in less expressive DLs has been revived, with the goal of developing tools that can deal with very large terminological and/or assertional knowledge bases [6, 23, 53, 1]. 
> 
> 
> 
> 2013/9/25 Delfi Ramirez <delfin@delfiramirez.info>
> Dear all:
> 
> I post this mail to the common field. My apologies it was send only to destinators.
> 
> Best Regards
> 
> On 2013-09-25 01:00, Delfi Ramirez wrote:
> 
>> Hi Yuik:
>> 
>> Please might you concrete the fields of DL you need to meet. 
>> 
>> I mention : First and second order logic belongs to our field of knowledge  as a philosphers). For this reason,  as kindly Henry has appointed, we might provide some points of knowledge for you  before Ontologies come abroad. The main idea in Tarky's model is the concept of Truth: "Tarski's theory of truth is for formalized languages so giving examples in natural language has no validity according to Tarski's theory of truth"
>> 
>> Here, one of my professors approach to the question : http://plato.stanford.edu/entries/consequence-algebraic/
>> 
>> Even he is nearly reatired, I can always mail to him for any questions 
>> 
>> Waiting for your needs
>> 
>> Best Regards
>> 
>> On 2013-09-25 00:41, Henry Story wrote:
>> 
>> On 25 Sep 2013, at 00:09, Yuk Hui <huiyuk@gmail.com> wrote:
>> 
>> hi henry,
>> hope this finds you well. i need a bit of your help with logic, since you are the expert! what is the relation between description logic and Tarski's model logic? SW is based on description logic, how far does it go away from the FOL? i am interested in the question of systems, and the evolution of these systems... millions of thanks.
>> all the best,
>> yuk 
>> Hi Yuk,
>>    Dean Allemang who wrote "Semantic Web for the Working Ontologist" will be much 
>> better placed to guide you with regard to your question above.
>>   As I understand from our philosophy of the Web Conferences the Semantic Web is
>> a variation on  Common Logic which Christopher Menzel presented in the Philosophy
>> of the Web seminars in Paris in 2012:
>>    http://web-and-philosophy.org/seminaire-philosophie-du-web/slides/
>> And Common Logic is just first order logic where you start with names as
>> the invariants, allowing one to change syntax as one wishes. But that maps
>> down to first order logic I think. So RDF and first order logic seem really close
>> to each other when you look at documents such as RDF Semantics.
>> Now OWL is a subset of this. It defines particular set theoretic relations it
>> seems to me, and establishes the consequences one can draw from them. 
>> It seems to be missing thoughts on indirect contexts which we now know to
>> be named graphs. 
>> But really the answer is that I don't know - I can just make educated guesses.
>> There are people on the Web Philosophy  mailing list who will be able to guide 
>> you much better.
>> Henry
>> 
>> Social Web Architect
>> http://bblfish.net/
>> -- 
>> Delfi Ramirez
>> http://segonquart.net
>> http://delfiramirez.info
>> 
>> skype:segonquart 
>> twitter:delfinramirez
> 

Social Web Architect
http://bblfish.net/