An Introduction to Abstract Argumentation Stefan Woltran Vienna University of Technology, Austria Jun 12, 2014
Prologue “Some people believe football is a matter of life and death, I am very disappointed with that attitude. I can assure you it is much, much more important than that.” (Bill Shankly) Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 2 / 36
Prologue Argumentation is the study of processes “concerned with how assertions are proposed, discussed, and resolved in the context of issues upon which several diverging opinions may be held”. [Bench-Capon and Dunne: Argumentation in AI. Artif. Intell., 171:619-641, 2007] Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 3 / 36
Prologue Argumentation is the study of processes “concerned with how assertions are proposed, discussed, and resolved in the context of issues upon which several diverging opinions may be held”. [Bench-Capon and Dunne: Argumentation in AI. Artif. Intell., 171:619-641, 2007] Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 3 / 36
Prologue Argumentation is the study of processes “concerned with how assertions are proposed, discussed, and resolved in the context of issues upon which several diverging opinions may be held”. [Bench-Capon and Dunne: Argumentation in AI. Artif. Intell., 171:619-641, 2007] Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 3 / 36
Prologue Seminal Paper by Phan Minh Dung: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artif. Intell., 77(2):321–358, 1995. Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 4 / 36
Prologue Seminal Paper by Phan Minh Dung: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artif. Intell., 77(2):321–358, 1995. “The purpose of this paper is to study the fundamental mechanism, humans use in argumentation, and to explore ways to implement this mechanism on computers.” Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 4 / 36
Prologue Seminal Paper by Phan Minh Dung: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artif. Intell., 77(2):321–358, 1995. “The purpose of this paper is to study the fundamental mechanism, humans use in argumentation, and to explore ways to implement this mechanism on computers.” “The idea of argumentational reasoning is that a statement is believable if it can be argued successfully against attacking arguments.” Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 4 / 36
Prologue Seminal Paper by Phan Minh Dung: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artif. Intell., 77(2):321–358, 1995. “The purpose of this paper is to study the fundamental mechanism, humans use in argumentation, and to explore ways to implement this mechanism on computers.” “The idea of argumentational reasoning is that a statement is believable if it can be argued successfully against attacking arguments.” “[...] a formal, abstract but simple theory of argumentation is developed to capture the notion of acceptability of arguments.” Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 4 / 36
Prologue Argumentation Frameworks . . . thus abstract away from everything but attacks (calculus of opposition) Example a c e f b d Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 5 / 36
Prologue Argumentation Frameworks . . . thus abstract away from everything but attacks (calculus of opposition) Example a a c e e f b d d � naive ( F ) = { a , d , e } , Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 5 / 36
Prologue Argumentation Frameworks . . . thus abstract away from everything but attacks (calculus of opposition) Example a c c e e f b b d � naive ( F ) = { a , d , e } , { b , c , e } , Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 5 / 36
Prologue Argumentation Frameworks . . . thus abstract away from everything but attacks (calculus of opposition) Example a a c e e f b b d � � naive ( F ) = { a , d , e } , { b , c , e } , { a , b , e } Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 5 / 36
Prologue Argumentation Frameworks . . . thus abstract away from everything but attacks (calculus of opposition) Example a a c e e f b d d � � naive ( F ) = { a , d , e } , { b , c , e } , { a , b , e } � stb ( F ) = { a , d , e } , Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 5 / 36
Prologue Argumentation Frameworks . . . thus abstract away from everything but attacks (calculus of opposition) Example a c c e e f b b d � � naive ( F ) = { a , d , e } , { b , c , e } , { a , b , e } � � stb ( F ) = { a , d , e } , { b , c , e } Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 5 / 36
Prologue Argumentation Frameworks . . . thus abstract away from everything but attacks (calculus of opposition) Example a a c e e f b d d � � naive ( F ) = { a , d , e } , { b , c , e } , { a , b , e } � � { a , d , e } , { b , c , e } stb ( F ) = � pref ( F ) = { a , d , e } , Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 5 / 36
Prologue Argumentation Frameworks . . . thus abstract away from everything but attacks (calculus of opposition) Example a c c e e f b b d � � naive ( F ) = { a , d , e } , { b , c , e } , { a , b , e } � � { a , d , e } , { b , c , e } stb ( F ) = � pref ( F ) = { a , d , e } , { b , c , e } , Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 5 / 36
Prologue Argumentation Frameworks . . . thus abstract away from everything but attacks (calculus of opposition) Example a a c e f b b d � � naive ( F ) = { a , d , e } , { b , c , e } , { a , b , e } � � { a , d , e } , { b , c , e } stb ( F ) = � � pref ( F ) = { a , d , e } , { b , c , e } , { a , b } Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 5 / 36
Prologue How to obtain such frameworks? . . . identify conflicting information Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 6 / 36
Prologue How to obtain such frameworks? . . . identify conflicting information (it is everywhere!) Domain Argument Attack Aim People person “dislike” coalition formation DSupport statement “conflict” conflict resolution BBS message reply identify opinion leaders ¬ α ∈ Cn (Φ ′ ) KB (Φ , α ) inconsistency handling LP derivation viol. assumption comparison LP semantics DL support chain viol. justification nonmonotonic logics Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 6 / 36
Outline Fundamentals of Argumentation Frameworks State of the Art: Semantics, Add-Ons, Systems Dynamics of Argumentation (and an open question) What Argu can learn from Provenance (and vice versa) Conclusion Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 7 / 36
Fundamentals Definition An argumentation framework ( A F) is a pair ( A , R ) where A ⊆ A is a finite set of arguments and R ⊆ A × A is the attack relation representing conflicts. Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 8 / 36
Fundamentals Definition An argumentation framework ( A F) is a pair ( A , R ) where A ⊆ A is a finite set of arguments and R ⊆ A × A is the attack relation representing conflicts. Example a c e f b d � F = { a , b , c , d , e , f } , � { ( a , c ) , ( c , a ) , ( c , d ) , ( d , c ) , ( d , b ) , ( b , d ) , ( c , f ) , ( d , f ) , ( f , f ) , ( f , e ) } Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 8 / 36
Fundamentals Conflict-free Sets Given an A F F = ( A , R ), a set E ⊆ A is conflict-free in F , if, for each a , b ∈ E , ( a , b ) / ∈ R . Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 9 / 36
Fundamentals Conflict-free Sets Given an A F F = ( A , R ), a set E ⊆ A is conflict-free in F , if, for each a , b ∈ E , ( a , b ) / ∈ R . Example a a c e e f b b d � cf ( F ) = { a , b , e } , Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 9 / 36
Fundamentals Conflict-free Sets Given an A F F = ( A , R ), a set E ⊆ A is conflict-free in F , if, for each a , b ∈ E , ( a , b ) / ∈ R . Example a a c e e f b d d � cf ( F ) = { a , b , e } , { a , d , e } , Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 9 / 36
Fundamentals Conflict-free Sets Given an A F F = ( A , R ), a set E ⊆ A is conflict-free in F , if, for each a , b ∈ E , ( a , b ) / ∈ R . Example a c c e e f b b d � cf ( F ) = { a , b , e } , { a , d , e } , { b , c , e } , Stefan Woltran (TU Wien) Introduction to Abstract Argumentation Jun 12, 2014 9 / 36
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