User:Dcresti

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Diana Cresti
Born Yes
Nationality Earth

Hello. I am a formal semanticist by training, but I'm not doing much of that these days (see my current home page).

So I decided to sign up to Wikipedia to put this knowledge to use again, and contribute to some relevant pages.

I also hope to add information on what my group is doing in Grid computing.

It remains to be seen whether I will actually find the time to do any of this.


Contents

[edit] Notes for EGI wiki

Proposed EGI Functions: Early 2007 Survey
Coordination of infrastructure operations
       
Testing, certification and validation service including middleware
       
Managed resource centers to provide initial resources for new user communities
         
Coordination of user and application support
         
Coordination of dissemination and training efforts
         
Representation of European Grid efforts on standards bodies
         
Representation of European Grid efforts with similar bodies from other continents
     
Image:v1.gif Very Important;  Image:v2.gif Quite Important;  Image:v3.gif No Opinion;  Image:v4.gif Not Important;  Image:v5.gif Unhelpful.

[edit] NGI example

Italy
NGI Full Name: Italian Grid Infrastructure
Acronym: IGI
URL: http://www.italiangrid.org

Italy's National Grid Initiative takes the form of an association of institutions under the name Italian Grid Infrastructure (IGI). As of July 2007, the IGI constituting document does not bear official signatures; operationally, however, the institutions at the core of IGI jointly manage one of the largest national production grid infrastructures in Europe: INFN Grid and grid.it.



[edit] Notes for Logic page

Logic is formal in the sense that it analyzes the ‘form’ of statements, as opposed to how such statements relate to facts about the world. In a basic logic, we assume that a statement can be True or False (1 or 0) in a given context of use, but we are not concerned with how this truth or falsity comes about. There are, however, logics that admit more than two truth values; these multi-valued logics reflect a common intuition that there are systematic cases where a statement (in a given context of use) cannot be evaluated as either True or False.

At the sentence level, a basic logic typically has truthfunctional operators such as \lnot for not or it-it-not-the-case-that, \land for and, \lor for what we call 'inclusive' or, and \rightarrow for statements of the form if...then. These are defined in terms of their truth tables:

Basic operators
p q \lnotp p \land q p \lor q p \rightarrow q
T T F T T T
T F F F T F
F T T F T T
F F T F F T

This type of abstraction entails a loss of some complexities and ambiguities of natural language. At the same time, it provides a systematic way of describing many different kinds of procedures, and a variety of forms of human reasoning. The tension and interplay between the expressiveness and subtlety of natural language, and the functionality of formal languages such as the logic we are describing here, is at the core of several areas of philosophy, linguistics, computer science etc. See Partee et. al. (1990) for an introduction to this area of inquiry.

[edit] Example (I)

How do we know that the statement It is raining and it is not raining is always False, independently of whether or not it is actually raining in a given context? Let’s “tease out” the sentence It is raining and call it p; rephrase the sentence It is not raining as It is not the case that p. Our example can then be written as:

p and it-is-not-the-case-that p

Or, in symbols:

p \land \lnotp

where '\land' substitutes for natural language ‘and’, and '\lnot' substitutes for ‘it-is-not-the-case-that’.
We define \land and \lnot in terms of truth tables, from which we can compute p \land \lnotp as follows:
p \lnot p p \land \lnotp
T F F
F T F
From the last column in this table, we see that no matter whether p is True or False, a statement of the form p-and-not-p is always interpreted as False in this system. A statement of this kind (one that is always False) is called a contradiction. Conversely, a statement that is always True, such as It is raining or it is not raining, is called a tautology.

[edit] Example (II)

If we know that (a) all cats are mammals, and (b) all mammals have a heart, how do we deduce that all cats have a heart?
Intuitively, we can think in terms of relations between sets of entities in the universe (U - the universe of discourse):
Image:cat-mammal-heart.png
If CAT is a subset of MAMMAL, and MAMMAL is a subset of HAS-HEART, then CAT is a subset of HAS-HEART. Note that it is merely a coincidence that these sets are realistic—i.e., that they reflect what we agree are facts about the world. We easily take our premises (a) and (b) as true because of this, but the deduction itself does not rely on truth in the actual world. Suppose we hear of the discovery of a new species called fwox, and we are told that (d) all fwoxes are mammals. If we believe (d) and thus take it as a premise ("fact"), we are entitled to deduce from (d) and (b) that all fwoxes have a heart.
The sets in the picture above have isomorphic predicates via their characteristic functions. Let's call C the predicate for CAT, M the one for MAMMAL, and H the one for HAS-HEART. Following a tradition that goes back to Aristotle, we could paraphrase our statement (a) as All C are M. In addition to the predicates C and M, we introduce the universal quantifier \forall, generally paraphrased as for-all.
We are now "inside" our sentences; this is an extension of our statement logic commonly known as predicate logic. In this system, we interpret (a) as follows:
(a) All cats are mammals. \forall x (Cx \rightarrow Mx) For all x: if x is-a-cat then x is-a-mammal


Example of a formal proof
1 \forall x (Cx \rightarrow Mx) Premise
2 \forall x (Mx \rightarrow Hx) Premise
3 \forall x (Cx \rightarrow Mx) \land \forall x (Mx \rightarrow Hx) 1, 2, Conjunction
4 (Ca \rightarrow Ma) \land (Ma \rightarrow Ha) 3, Universal Instantiation (twice)
5 Ca \rightarrow Ha 4, Hypothetical Syllogism
6 \forall x (Cx \rightarrow Hx) 5, Universal Generalization
Let's now add to our knowledge the premise ("fact") that some mammals are erbivores; can we deduce from this, plus our pre-existing statements, that some cats are erbivores? Can we deduce that some cows are erbivores?

[edit] References