CS6905 Advanced Technologies for e-Business May 1

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CS6905 Advanced Technologies for e-Business May
1 July 31 2003

• Segment 1
• Bruce Spencer
• May 1 May 29 2003

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Course Overview
INTRO

• NRC e-Business Application Groups
• e-Health (Saint John)
• e-Government (Fredericton)
• e-Learning (Moncton)
• Technology Groups
• Human Web (Fredericton)
• Internet Logic (Fredericton)
• reasoning systems for e-business (on the web)

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Internet logic meeting needs of e-business
applications
INTRO

• privacy, security, trust
• Does this transaction meet with users
  intentions, espressed as rules
• semantic processing of web data
• natural language, data bases, web logs
• market modelling
• maximizing utilities for buying and selling
• diagnosis
• fixing faults, comparing to models of what should
  happen
• qualitative reasoning
• models of what should happen are described
  abstractly
• collaborative filtering, data mining
• information from data

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Specific Project NBON
INTRO

• online tendering for purchasing by govts,
  schools, hospitials universities
• purchasing agent assigns GSIN codes to items to
  be purchased, from among 16K codes in hierarchy
• each vendor (private business) codes self
  according to what is for sale
• NBON system if two items on the same branch of
  hierarchy, send an email notification to vendor
• NB is only place this is done in Canada (world?)
• Problem too much email
• coding too high (not precise enough)
• inaccurate coding

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INTRO
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Technologies that can help
INTRO

• Natural Language Processing
• mapping NL descriptions of items to the codes is
  hard for most people to do experts hired by NBON
• Bayes network of conditional probabilities P(code
  word).
• For a given code, combine all of the probties
  over words
• Report codes with highest probties
• Uses years of previous codes assigned to tenders
• OLAP
• How many furniture purchases by municipalities in
  southeast NB municipalities cost in range 50-100
  in 2002?
• In constant time?

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Diagnostics
INTRO

• a machine that takes tender description and
  vendor description and generates a yes/no to the
  question should this tender be sent to this
  vendor?
• False positives
• too much email, system becomes ineffective
• False negative
• missed tendering opportunity, company dies
• Fix the machine so that neither fault occurs

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Logic, Policies and eBusiness
INTRO

• Policies govern any eBusiness transaction
• privacy policies
• pricing policies
• eligibilities
• access control
• Logic and proofs
• logic for expressing policies
• exact correspondence with desired states of the
  world
• convincing proofs that policies were adopted

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Policies and Rules
INTRO

 
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Interactive system for negotiating policy
INTRO
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Lectures for Segment 1
Overview

• 1 Intro to logic
• Syntax
• Semantics
• Web-ized Logic
• 2 More logic
• Logical Consequences
• Inference Rules
• Proofs
• Soundness and Completeness
• 3 Logic for the Web
• Well Founded Semantics
• Description Logic
• Efficiency vs. Expressiveness

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Lectures for Segment 1 (contd)
Overview

• 4 Ontologies and the Semantic Web
• 5 Rules for e-Commerce
• 6 Rules for Privacy
• 7 Discrimination Trees and Indexing
• 8 Inference Queue

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Example

• Suppose Prof Phil teaches at the university and
  has two students, a boy Bob and girl Gail. Bob
  likes Gail but we are not sure whether Gail likes
  Bob. We know that each person has one best
  friend, and always likes that friend. Also if
  one person likes another, then it is always
  mutual.

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Intro to Logic Syntax
Intro to Logic

• Given V, CS, FS, PS, connectives, quantifiers
• Variables x, y, z, u, v, w, x1, y1,
• Constant Symbols a, b, c, d, e, a1, b1,
• Function Symbols f, g, h, f1, g1,
• Predicate Symbols P, Q, R, P1, Q1,
• ?, ?,?,?
• ?, ?
• Function Symbols and Predicate Symbols have
  arities
• FSi is the set of functions symbols with arity i
• PSi is the set of functions symbols with arity i
• FS is the union of all FSi
• PS is the union of all PSi

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Exercise
Intro to Logic

• Think of reasonable constant symbols, function
  symbols and predicate symbols for the example.

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Definitions Terms

• The set T of terms is defined inductively
• V ? T (variables are terms)
• CS ? T (constants are terms)
• If t1,,tn?T and f ?FSn then f(t1,,tn) ?T.
• Terms from (3) are called functional terms, ti
  are called the arguments.
• A term s occurs in t if st, or s occurs in an
  argument of t.
• V(t) denotes the set of variables occurring in a
  term t.
• If V(t) ? then t is ground.
• FS(t) is the set of all function symbols
  occurring in t. FSn(t) is the set of all
  function symbols of arity n occurring in t.PS(t)
  and PSn(t) are similarly defined.

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Exercise

• Think of reasonable constant symbols, function
  symbols and predicate symbols for the example.
  What are their arities?
• Write terms for the best friend of the Gail, for
  the best friend of the best friend of Phil. What
  other terms occur in your terms? Give some
  examples with non-empty sets of variables.

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Definitions Formulas
Intro to Logic

• If t1,,tn?T and P?PSn then P(t1,,tn) is an
  atom formula or atom. P is called the leading
  symbol and the ti are called the arguments.
• If A is an atom formula, A and ?A are called
  literals.
• AT is the set of all atoms. LIT is the set of
  all literals.
• The set of all predicate logic formulas PL is
  defined inductively
• LIT ? PL (literals are in PL)
• If A,B ? PL then (A?B), (A?B), (A?B) ? PL.
• If A? PL and x ? V and neither (?x) nor (?x)
  occurs in A then (?x) A and (? x) A ? PL.

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Exercise

• Write some atoms, some literals and some formulas
  using the symbols from the previous exercise.

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Interpretations
Intro to Logic

• An interpretation of a formula F in PL is a pair
  ? (D,?) with the following properties.
• D is a non-empty set called the domain.
• ? is a mapping on PS(F) ? FS(F) ? CS(F)
• For c ? CS(F) ? (c)? D
• For f ? FSn(F) ? (f) is a function of type Dn
  ? D
• For P ? FSn(F) ? (P) is a function of type Dn ?
  T,F. (That is, P is an n-ary predicate.)

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Exercise

• Give an explicit interpretation for this example.
  Can there be more than three people in the
  domain of your interpretation?

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Evaluation of a formula
Intro to Logic

• Let ? (D,?) be an interpretation of a formula F.
  
• We assume that F has no free variables.
• The evaluation function v? is a function of type
  PL(F) ? T,F defined inductively as follows
• If A P(t1,,tn) then v?(A) ?(P)(v?(t1),,v?(tn
  ))
• v?(A?B) and(v?(A),v?(B))
• v?(A?B) or(v?(A),v?(B))
• v?(A ? B) imp(v?(A),v?(B))
• v?(? A) not(v?(A))
• v?( (?x) A ) T iff v?( A ) T where A is A
  where the value chosen for x is d, for all values
  d ? D
• v?( (?x) A ) T iff v?( A ) T where A is A
  where the value chosen for x is d, for some value
  d ? D
• where and, or, imp and not have the usual
  meanings.

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Definitions Verifies, Falsifies, Model

• An interpretation ? of a formula A verifies A if
  v?(A) T. Then we say that ? is a model of A.
• ? falsifies A if v?(A) F.
• A formula A is satisfiable if it has a model. A
  is valid if every interpretation is a model.
• Two formulas are logically equivalent of they
  have the same models. They are satisfiably
  equivalent if one is satisfiable iff the other is.

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Exercises

• Give a formula that characterizes the situation
  described. Give a model of those formulas.
• Describe a situation that would be a non model
  for the formula you gave.
• Give a formula that is a conjunction of
  subformulas, for which the described situation is
  a model. Select each of these conjuncts in turn
  and give an interpretation that falsifies the
  selected conjunct but not any of the others.
• Give an example of a valid formula.
• Remember, the formula describes the situation,
  but the situation models (is a model of) the
  formula.

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Hint
Intro to Logic

• Male(bob) ? Male(phil) ? Female(gail) ?
  Teaches(phil, bob) ? Teaches(phil, gail) ?
  Likes(bob, gail) ? (?z) (Likes(z,
  bestFriendOf(z)) ? (?x) (?y) (Likes(x,y) ?
  Likes(y,x))

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Web-ized logic
Intro to Logic

• Consider a variant of PL in which all constant
  symbols are Uniform Resource Indexes, consisting
  of a host and domain name and path from the root
  of the web directory of the host. Thus it
  defines the current world-wide-web.
• Could function and relation symbols also be
  URIs?
• Could constant, function and relation symbols
  also refer to files, i.e. could they be URLs?
  What would they reasonably point to?

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Clausal formulas
Intro to Logic

• Definition A clause is defined inductively