I think it have to be a probabilistic logic or a fuzzy logic.

Some kind of systems logic, though as Gustavo points out it'd have to allow for normative value ranges...

@Saleem Gul

Thank you for your perfect answers.

I have tried formal method Backus-Naur Form (BNF) to express how the logic among project breakdown packages. Actually, to your view, it’s truly complex to describe. UML is a good language but it’s not fit the problem well.

My problem can be described as follows:

1. project package nodes set include some attributes as ES[Early start], EF[early finish], node slack, node resource requirement, sub-set etc. so as to the relationships are so complicated to elaborate.

2. the similarity of multi-project nodes was hard to set mathematic model[do you have some ideas? as the similarity analysis].

you have referred a ontology as common description using ‘there is’ or other types, but I have never seen any unified language standard. I am so puzzled.

My email is [email protected] , welcome to discuss more deeply.

HANG ON HANG ON HANG ON

As I specified in the "sticky" thread, 'ontology' has a very different sense in philosophy and in information science.

Fang (or should it be Shonvon - I misremember the convention - please forgive me!): you're taking for granted that 'ontologies' are representations of conceptual domains. This is the information science use, and is due to Tom Gruber, who was generally influenced by Husserlian formal ontology. In analytic philsophy, an ontology is determined by an *interpretation*, which is - loosely speaking - a function that projects an element of a language onto an element of the world, however widely-set or limited ‘the world’ might be. In more formal semantics, an interpretation determines a model by assigning values to the variables of a theory; if the theory is of first or higher order, then its domain will be those individuals over which the quantifiers range and the properties and relations which obtain between and among them.

So, in analytic metaphysics, an ontology is usually determined by an interpretation of a first-order theory; and a first-order theory is (evidently) expressed in first-order logic. This, I think, provides a "unified language standard" that is sufficient to anyone's requirement ;-)

Of course, this is entirely irrelevant to your particular practical interrogations. But I surmise that your puzzlement is due to the divergence between:

1.*extensional ontology*, which is the ontology of first-order theories, and is derived from the Frege-Russell school through Carnap, the Polish logicians, and Quine. Such ontologies are concerned with the *extension* of concepts

2. *formal ontology*, which is derived from Brentano and Husserl; Barry Smith is a typical theorist in this field and any top-level ontology (BFO, DOLCE, GFO...) gives an example. Such ontologies are concerned with *concepts* and the relations between concepts

3. *applied ontologies*, which derive from formal ontologies through Tom Gruber’s use of the term, are representations of a certain domain of knowledge. Vanrullen and Hirst (forthcoming) will show that "ontology" is, in fact, a misnomer here: as such ontologies concern concepts and the representation of knowledge, they range over *semantic* and *epistemic* domains, rather than *ontic* domains in sense (1) above; they would perhaps be better described as "applied epistemologies".

Applied ontologies in sense (3) range over domain-specific concepts and the relations obtaining between such concepts: thus, the ‘objects’ of such ontologies are not ‘regions of the world’, but ‘concepts’. The ontologies I describe (in sense (1)) range over the *extensions* of concepts - that is, things in the world that supposedly correspond to, exemplify, or satisfy concepts.

As far as ‘social systems’ are concerned:

Generally, the relation between a concept and the range or sequence of things in the world that might satisfy that concept is a matter of *determination* - of how well the concept picks out one specific thing or class of things in the world. Where an applied ontology models a well-defined taxonomy (as in ontologies applied to biological sciences) or a domain having a prescribed or semi-formalised language (as in air traffic control), the concepts which figure in the ontology have a clear, well-defined extension. Practical tools based on such ontologies (decision-making tools, diagnostic tools) function efficiently because there’s not much room for concept-based indetermination.

However, when the ontology ranges over concepts with a less well-defined extension (as in most social interactions), the content of the concepts is not fixed and objectively-determinable in every situation, but is normative and context-sensitive. In everyday interaction, the precise sense of a concept depends on a context-sensitive and speaker-sensitive *interpretation* - and here, there’s a strong risk of underdetermination of any concept with respect to the range of things and situations ‘in the world’ to which it might apply. Such indetermination can touch terms with an apparently technical definition – and here we can take the different understandings of the term “ontology” as an example. It follows that indetermination is common where terms have social and cultural connotations that will be understood differently by different actors (this is a common problem in employer-employee relations, where notions of the nature and finalities of collective action can be understood very differently by operational agents, management, and direction); such distinctions are often determined by the sociolect of the interlocutors. The possibilities of indetermination are already large in exchanges between sociolects in one language and within a common general culture; they’re evidently far greater in exchanges between interlocutors having different native languages and no shared general culture.

All this being the case (and this rejoins Gustavo’s interrogations), any ‘tools’ which might apply to ‘social situations’ (sociometric tools, tools for managing and planning the disposition of human resources, tools for skills management, training tools etc.) need to integrate norm-based rather than rule-based conceptual domains (domains in which a term takes a range of possible values or sets of values that are further determined by context, rather than domains in which a concept takes one, fixed value or set of values).

A particular problem in the use of such devices as is to decision or consulting is that the user (and, for that matter, the technician) can confuse ‘concepts’ with the putative ‘extension of concepts’ – for example, that he or she can take for granted not only that “everyone knows what a family is”, but also that “everyone knows that a family is a system”. The first is perhaps pragmatically the case for all competent speakers of English, but the second depends on the speaker having a reasonably sophisticated understanding of what a ‘system’ is... that is, on the speaker possessing a ‘theory of systems’. Indeed, this is precisely the ‘weakness’ of most systems thinking – systems theory originated with biologists, and biological entities (living organisms, organs, cells...) are probably the most “self-evident” class of systems in the natural world. However, while it might be evident to a biologist that some thing is a system, this is a product of the biologist’s particular epistemic context – it doesn’t follow that it is *universally* evident that that thing is a system. The biological systems theorist is confusing a concept – “organism”, “organ” – with the extension of that concept: a liver is a system *with respect to a system of theories* - but with respect to the man on the Clapham omnibus, it’s a piece of offal that he’s going to fry with onions for his tea.

(and after that, "Vanrullen and Hirst (forthcoming)" had better forthcome... come on, Mr Vanrullen!)

To David

call me Fang or Shonvon, either one is ok, Shonvon is better, but it doesn't matter.

Thank you for describing the ontology, I have almost got the meaning and the derivation of ‘ontology’. I have been shocked by your beautiful demonstration about ontology but I am not professional in philosophy and do you mind to help me understand some words or phrases as follows you mentioned in your answer :

1. first-order theory, or first-order logic. [answer 1]

2. *ontic* domains [answer 1]

After reading your answers, I am so shy about my misunderstanding and misinterpreting of ontology. well , the extension of the concepts will be clearly determined? In our natural world, I think that is merely impossible because uncertainty is exist and the new meaning are continually updated, as an open system.

What do you think? maybe philosophic talk is so complicated.

@ Saleem

Thank you, I have read the book online. That's a good book. Z is an available language to describe the complex relationships or concepts or logic.

Shonvon - I've got a meeting this morning but I'll deal with your remarks as soon as I get back.

It's a very good thing that you ask for clarifications - this will help us to create a common, collective understanding of the different defintions of ontology, and from there we'll have a good basis for collaboration.

Higher orders are problematic - richer expressive power, but require that we quantify over classes

(sorry, David's VERY busy at the moment...)

ok...

(and Saleem, correct me or give alternatives if you wouldn't agree ;-)

*Propositional* logic concerns the relations of entailment between 'sentences', as in the tautology ¬(p ˄ ¬q) → (¬p ˅ q). The 'sentence variables' p and q stand for any grammatically well-formed sentence; however, the theory itself doesn't specify what a "grammatically well-formed sentence" might be. We could say that propositional logic 'takes sentences for granted' and concentrates on the various relations on and between sentences (negation, conjunction, disjunction, coordination, implication...).

*First order logic* or *predicate logic* gives a theory of sentence structure: a well-formed sentence has an object-predicate structure, as in Fa where the predicate "F" is satisfied by some object a. In the simplest (set-theoretical) understanding, "F" can be seen as some set, and "a" names or designates particular, individual member of that set (so, "Fa" is a *propositional function*). Thus, if Fa is true, we're saying that the set F is non-empty.

If we can give 'objects' by names (constants such as a, b, c...), then the veracity of our theory is just a matter of the object named by "a" having "F": imagine that "a" 'names' Barack Obama, "b" names Nicolas Sarkozy and that "F" ranges over "tall people". Fa is thus true insofar as Barack Obama satisfies the predicate "is tall".

We can also give 'objects' not on a one-to-one naming, but as sequences of objects x1,x2...xn such that, for any xk, xk satisfies "F": this is an *abstraction* of the propositional function "F" in "Fa". "Fx" is thus "thing that is F" or, in set theoretic terms, "member of F".

Here, I used the expression "for any xk, xk satisfies F" - the entities over which F ranges are given as a conjunctive sequence "Fx1 ˄ Fx2 ˄ Fx3 ˄...˄ Fx-n ˄ Fxn". Thus (∀x) Fx is read as "all x such that x satisfies F". This is UNIVERSAL QUANTIFICATION

Thus, "(∀x) Fx → Gx" means "for any object x, if x is F, then x is G". This could be "all unicorns are one-horned horses" or "Sherlock Holmes lives at 221b Baker Street" - a universally quantified expression can be 'true' even though there are no 'real objects' that satisfy it.

If, however, we say that SOME thing satisfies F, we're saying that at least one xk in the sequence satisfies F. Here, "F" ranges over a *disjunctive* sequence "Fx1 ˅ Fx2 ˅ Fx3 ˅...˅ Fx-n ˅ Fxn". Thus (∃x) Fx is read as "some x such that x satisfies F". This is EXISTENTIAL QUANTIFICATION.

The distinction between universal and existential quantification is that existential quantification entails *commitment*: "(∃x) Fx" is equivalent to claiming that the 'set' "F" is non-empty. In philosophical logic, what we hold as "existing" are those variables that are bound under existential quantification.

Thus, our ontological domain is given by the range of the universal quantifier, and our ontology is an interpretation on this domain given by existential quantification.

I don't know how clear this is to you, Shonvon - or whether Saleem would agree - so I'll leave it here and wait for feedback ;-)

I agree with you. Dr. David

That’s a good explanation about universal quantification and existential quantification. There is no problem about *Propositional logic* and *predicate logic*. After reading carefully and my puzzles are clarified.

With the help of Discrete Mathematics basis, I could simply get the meaning of formal expression of logic problem.

existential quantification focuses on existence? to find an element is in/out the conceptual set. as ∃x∈Set A but universal quantification care if ∀x .∈Set A ?

Something I have try to simply the concept, I am so glad to find you to use these mathematical symbols. You told your related papers, well, do you mind to give me to read them? I also plan to write a paper of Metaphysics logic in ancient problem but short of English language expression. So would you like to help me about that article writing?

Shonvon - how do you post symbols?

aha, I wrote in MS Word.exe first, and copy(Ctrl+C), Paste(Ctrl+V) in the comment text area, that's ok..

Which font? (not that it matters now, I can copy the symbols from your message ;-)

AS A MATTER OF FACT, IT'S "CAMBRIA MATH" !!!

I am eternally grateful to you, Shonvon

And of course I'll help you with your paper - after all, metaphysics and English are my areas of specialisation ;-)