Re: logic

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 <https://twitter.com/delfinramirez>
>
>