Dear Dr. Mohammad Reza Beik Zadeh (01)
Thank you very much for your post to the [ontolog-forum] mailing list.
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operating in an "open" collaborative work environment (CWE), which
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As such, I am writing to let you know that the
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members have found it easier to just subscribe with an alternate
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firewalls. You might consider that too. (04)
Thank you for your attention. (05)
Regards. =ppy (06)
Peter P. Yim (07)
On Sun, Aug 21, 2011 at 7:34 PM, Dr. Mohammad Reza Beik Zadeh
> Dear All
> I am looking for a good review paper, Book or presentation on challenges of
>current semantic technology languages and features of an ideal semantic
> May I have your guidance?
> A strategic agency under MOSTI
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> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
>[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F. Sowa
> Sent: Sunday, 21 August, 2011 2:45 AM
> To: [ontolog-forum]
> Cc: rick@xxxxxxxxxxxxxx
> Subject: [ontolog-forum] Type Systems for Common Logic
> In the recent discussions, I was responding to comments about the
> "type free" Common Logic, but I didn't bring up a very important
> point: Conceptual Graphs have had a very rich type system from
> Day 1 -- actually from the first published paper about CGs in 1976:
> Conceptual Graphs for a Database Interface
> In that paper, I called CGs a version of sorted logic. But for the
> book version in 1984, I used the term 'type' rather than 'sort'.
> Following is a brief summary of the CG type system, which evolved
> from the original sorted logic in the 1976 paper:
> 1. A partial ordering of types by generalization and specialization.
> Type T1 is a generalization of T2 (and T2 is a specialization of
> T1) iff for every model, every instance of T2 is an instance of T1.
> 2. The universal type, which is true of everything in every model,
> is a generalization of every type. The absurd type, which is
> true of nothing, is a specialization of every type.
> 3. Canonical graphs, which specify type constraints for well formed
> CGs, are a generalization of the signatures used for specifying
> the type constraints in logics and programming languages. A
> single relation with type constraints on its arguments, which
> is called a star graph, is the simplest kind of canonical graph.
> 4. Canonical formation rules are a graph grammar for generating
> all well formed CGs that preserve the type constraints, but they
> don't necessarily preserve truth. (For example, the negation
> of any statement would obey the same type constraints.)
> 5. Inference rules for CGs specify additional constraints
> that preserve truth.
> 6. The CG theory does not use the word 'polymorphism', but it
> supports a very general kind of polymorphism that is necessary
> for natural language semantics. The polymorphism used in
> programming languages is a subset of the CG polymorphism.
> For more detail about these topics, see the following paper:
> To support this type system in Common Logic, I adopted the
> following approach:
> 1. Define an untyped notation, called Core CGIF (Conceptual
> Graph Interchange Format), which maps directly to the
> Common Logic model theory. In effect, the absence of
> a type label designates the universal type, which imposes
> no restriction whatever on the domain of quantification.
> 2. Then define Extended CGIF by a translation to Core CGIF.
> Extended CGIF uses the Common Logic mechanism of restricted
> quantification. But it does not enforce the constraints
> of canonical graphs and the canonical formation rules.
> 3. The type labels in Extended CGIF, as in the CLIF dialect
> of Common Logic, can use any monadic relation to restrict
> the domain of quantification. There is no assumption of
> a type hierarchy or any constraints on type signatures.
> 4. Points #1, #2, and #3 are specified in the ISO 24707 standard.
> But the system of canonical graphs and formation rules add
> the constraints for a type hierarchy and the graph grammar.
> Those rules can support the derivation of CGs that preserve
> the type constraints and the static testing of CGs to verify
> whether the type constraints are satisfied.
> 5. The CG theory assumes a partial ordering of types, but it
> does not require any specific rules or method for determining
> that partial ordering. If desired, the techniques used for
> Description Logics or the techniques of intuitionistic logic
> could be used to specify the type hierarchy.
> This is the method that I used to add a type system to Common Logic,
> but there is no dependency on a graph grammar. A similar method
> could be adapted to any type system that anybody might prefer
> to add to Common Logic.
> Rick cited the Girard-Reynolds Isomorphism as a desirable feature
> for a type hierarchy. The proof of that isomorphism used something
> they called "second order logic". However, the only features they
> required to prove the theorem were the ability to quantify over
> types and relations. They did not require the hierarchy of
> infinities that are usually assumed in "true" second order logic.
> Common Logic is more than adequate to prove that theorem.
> Fundamental principle: The model theoretic semantics for a logic
> must be compatible with the logic used to derive a type hierarchy
> for a typed version of that logic. Since intuitionistic logic is
> a subset of FOL (in the sense that every theorem of intuitionistic
> logic is also a theorem of FOL), the use of intuitionistic logic
> for specifying the type hierarchy is compatible with Common Logic.
> Therefore, the method I outlined for building the CG type system
> on top of Common Logic can be adapted to the kinds of typed logics
> that Rick was asking for. In particular, intuitionistic logic,
> the Girard-Reynolds Isomorphism, the Description Logic constraints,
> or many other kinds of constraints can be used for a type system
> that is compatible with the semantics of Common Logic.
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