Re: logic

Hi All,

I'm also very interested in these issues and supposed to deliver a talk on  
that very same topic next year.Yuk, let's also discuss this off-list :)

To begin with the modal aspect, I'd recommend a book by Michael Genesereth  
: Logical foundations of artificial intelligence   
(http://dl.acm.org/citation.cfm?id=31838)

Regarding the models behind OWL, these papers might help :
- Three Theses of Representation in the Semantic Web,  
http://www2003.org/cdrom/papers/refereed/p050/p50-horrocks.html
- From SHIQ and RDF to OWL: The Making of a Web Ontology Language,  
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.7039

Then you can look at
- Lbase: Semantics for Languages of the Semantic Web,  
http://www.w3.org/TR/2003/NOTE-lbase-20030123/

Also, Common Logic is an inspiration  behind the semantics of RDF as Henry  
mentioned, look at Chris Menzel's work here.

Hope that helps.

Cheers,
A.

P.S. : As an aside, I'd never put together Frege and Tarski... :)


Le Wed, 25 Sep 2013 10:19:37 +0200, Henry Story <henry.story@bblfish.net>  
a écrit:

> 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/
>


-- 


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Received on Thursday, 26 September 2013 02:22:08 UTC