Modelling Imprecise Arguments in a Weighted Argument System

1
Modelling Imprecise Argumentsin a Weighted
Argument System

• Adrian Groza
• Technical University of Cluj-Napoca,
• Department of Computer Science,
• Adrian.Groza_at_cs.utcluj.ro

5th International Conference on
Intelligent Computer Communication and Processing
2
Outline

• Motivation and Research Hyphothesis
• Weighted Argument Systems
• Running Scenario
• Conclusion

3
Research Hyphotesis

• Real arguments are a mixture of fuzzy and
  ontological knowledge

Human arguments
Logic-based agents
p?q
Fuzzy logic
4
The semantic web
Argumentation
5
Plenty of Arguments on the Web
Vision create an infrastructure for
mass-collaborative editing of structured
arguments in the style of Semantic Wikipedia.

• WWAW World Wide Argument Web1
• based on the Argument Interchange Format Ontology

Definition large scale network of
inter-connected arguments created by human agents
in a structured manner.
1I. Rahwan, F. Zablith, and C. Reed. Laying the
foundations for a World Wide Argument Web. Artif.
Intell.,171(10-15)897921, 2007.
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Mix of fuzzy and ontological knowledge

• It may be very hard to reverse the trend of
  eating junk food.
• (B) It is cheap and easy for people to eat junk
  food,
• opposite to the nutrition food.
• (C) At the store where I shop, a candy bar costs
  less than a dollar
• and is ready to eat.
• (D) Candy bar can be classified as junk food.
• (E) Fresh fruits and vegetables tend to be
  inconveniently packaged and cost more.
• (F) Fresh fruits and vegetables can be classified
  as nutritious foods.
• (G) It is also highly profitable for
  manufacturers because
• (H) junk food has a long shelf life in the retail
  outlet.

Food JunkFood ? NutritionalFood
CandyBar ? JunkFood
FreshFruits ? NutritionalFood Vegetables ?
NutritionalFood
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Fuzzy concepts
JunkFood Food ? (?NutritionalValue.Little ?
?hasIngredients.Unhealthy)
Pizza ? JunkFood?0.7? Pizza ?
NutritionalFood?0.3?
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Fuzzy Logic and Argumentation

• Godel semantics
• maps the weakest link principle in argumentation
  an argument supported by a conjunction of
  arguments is as good as the weakest premise -
  min?,?
• when several reasons to support a consequent are
  available, the strongest justification is chosen
  to be conveyed in an argumentation protocol -
  max?,?

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Fuzzy Logic and Argumentation

• Lukasiewicz semantics
• fits the concept of accrual of arguments
  independent reasons supporting the same
  consequent provide stronger arguments (i.e law)
  - min??,1
• difficulty to identify independent reasons an
  argument presented in different forms contributes
  with all its avatars to the alteration of the
  current degree of truth
• An argument subsumed by a more general concept
• Pizza ? NutritionalFood ? AcceptableFood

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Fuzzy Logic and Argumentation

• Negation
• The subject of a debate cannot be easily
  categorised as true or false the degree of truth
  for an issue and its negation are continuously
  changing during the dispute
• Argument bases are characterised by a degree of
  inconsistency
• Rules supporting both a consequent and its
  negation co-exist in the KB
• The inconsistency is naturally accomodated in
  fuzzy logic

A ? neg A ? 0
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Outline

• Motivation and Research Hyphothesis
• Weighted Argument Systems
• Running Scenario
• Conclusion

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Weighted Argument Systems (WAS)
2

• extend the Dung abstract argument systems by
  adding numeric weights to every edge in the
  argument graph.
• the weights correspond to the relative strengths
  of attacks between arguments.

Definition A Dung abstract argument system is a
pair D ltX, Agt where X ?1,..., ?k, is a
finite set of arguments, and A in X X is a
binary attack relation.

• given the attack relation (?1, ?2) ? A if one
  accepts ?1, it would be inconsistent to accept
  ?2.
• it happens that the only consistent set of
  arguments to be the empty set.

Definition A WAS is a triple W ltX, A, wgt,
where ltX,Agt is a Dung abstract argument system,
and w A ? R is a function assigning positive
real valued weights to attacks.

• Inconsistency budget ? ? 0,1
• characterises how much inconsistency one is
  willing to tolerate within the argument base.
• the attacks up to a total weight of ? cannot be
  taken into consideration

2P. Dunne, A. Hunter, P. McBurney, S. Parsons,
and M. Wooldridge. Inconsistency tolerance in
weighted argument systems. In AAMAS, pages
851858, 2009.
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Outline

• Motivation and Research Hyphothesis
• Weighted Argument Systems
• Running Scenario
• Conclusion

14
Running scenario

• ?1 The house is in good location, it is large
  enough for our family and it is affordable we
  should buy it.
• ?2 The house suffers from subsidence, which is
  expensive to fix we shouldnt buy it.

?
?

• A (?1, ?2), (?2, ?1)
• estimate the relative weights of the attack
  relations (use fuzzy description logic)
• the set of arguments which require the smallest
  inconsistency budget is preferred in order to
  take the decision of buying the house or not.

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Computing the strength of the arguments

• Specify the house selling domain

3
GoodLocation
?
0 1 2 4 5 10 km
Affordable
?
50000 70000 100000
Large
79
?
70 80 150 m2

• Lukasiewicz

• Godel

3F. Bobillo and U. Straccia. fuzzyDL An
expressive fuzzy description logic reasoner. In
FUZZ-08, pages 923930.2008.
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Computing the strength of the arguments

• Specify the house selling domain

Affordable
Subsidence
?0.667
1 4 10 years
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Computing the ß-solutions

• The strengths of the arguments a1 and a2

?
?

• Inconsistency budget principle
• The argument that requires the smallest
  inconsistency budget is preferred
• ß ?0, 0.65) no attack relation can be
  disregarded
• ß ?0.65,0.667) the relation (?1, ?2)0.65 can
  be eliminated
• ß ?0.667, 1 the attack relation becomes the
  empty set
• ß 0.65 the smallest inconsistency budget
• The solution is given under the Lukasiewicz
  semantics

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Conclusions

• We advocated the use of fuzzy reasoning and DL in
  argumentation systems, aiming to fill the gap
  between human arguments and software agents
  arguments.
• We identified links between fuzzy reasoning and
  some issues in the argumentation theory
• the weakest link principle, the accrual of
  arguments, inconsistency
• We applied the newly proposed WASs and the notion
  of inconsistency budget.

Thank you !
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• Argument Interchange Format Ontology (AIF)
• Aiming to unify the majority of conceptual work
  in argumentation theory under one umbrella
• Extendable ontology

Information nodes
Scheme nodes
PA-node
Passive information claim, premise, data,
locution, etc.
Preference application node legis posterior,
legis specialis, legis superior, etc.
Conflict application schemes negation, rebuttal,
undercutting defeater, etc.
Rule of inference schemes modus ponens, modus
tolens, defeasibile modus ponens, etc.
Form-node
This presentation
PIA-node
Protocol Interaction Application node (Modgil
2007)
Extensions
Context application node social, intentional,
dialectical (Letia, 2008)
Argumentation schemes argument from expert
opinion (Rahwan, 2007)