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Persuasion Theory Based on a Logic of Graded Modalities

Persuasion Theory Based on a Logic of Graded Modalities. Magdalena Kacprzak Bialystok University of Technology and Katarzyna Budzyńska Cardinal Stefan Wyszynski University in Warsaw. The Project (Budz-Kacp): The Formal Theory of Persuasion. Comp-sci. Specification & Verification

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Persuasion Theory Based on a Logic of Graded Modalities

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  1. Persuasion Theory Based on a Logic of Graded Modalities Magdalena Kacprzak Bialystok University of Technology and Katarzyna Budzyńska Cardinal Stefan Wyszynski University in Warsaw

  2. The Project (Budz-Kacp): The Formal Theory of Persuasion

  3. Comp-sci Specification & Verification of Properties of Persuasion Philosophy Logic Initial Intuitions wrt Persuasion Process Formal Modeling of Persuasion Process Philosophy Reflection on Process of Persuasion The Project (Budz-Kacp): The Formal Theory of Persuasion

  4. Comp-sci Specification & Verification of Properties of Persuasion Philosophy Logic Initial Intuitions wrt Persuasion Process Formal Modeling of Persuasion Process Philosophy Reflection on Process of Persuasion The Project (Budz-Kacp): The Formal Theory of Persuasion

  5. Outline of the Presentation • Persuasion • What a logic do we need? • Beliefs and graded beliefs • Arguments • Logic of Graded Modalities (Hoek and Meyer) • Some modifications • Theory of Persuasion • Conclusions

  6. 1. Persuasion

  7. How we change one another's minds Persuasion ( lat. persuasio ) is a way to induce somebody tobelieve in our rights or to do something. Three basic techniques of persuasion: • to appeal to take a specific stand on sth and execute a specific action, • to suggestdesirable interpretations or opinions, • rational justification of correctness of presented views and ideas.

  8. How we change one another's minds • Persuasion is one of the methods of negotiation which allows to reach an agreement. • Analysing an arisenconflict together with our opponent offers a chance to succeed and resolvethe conflict to both parties’ advantage.

  9. Specific techniques used topersuade people • Techniques for changing minds (verbal versus non-verbal arguments) • By appeal to reason: • logical arguments, scientific methods, proofs • By appeal to emotion: • body language, tradition, faith, deception, praise • Aids to persuasion: • bribery, blackmail, seduction, brainwashing, torture

  10. 2. What a logic do we need?

  11. The aim of the research • How to change what others think, believe, feel and do? • How to formalize a persuasionprocess? • Which ways of changing one another’s minds are possible to formalize? • About which persuasion techniques can we reason in a formal way?

  12. Example • There are two agents in a room. Every agent has a thermometer and has to take temperature. • t=250

  13. Whata logic do we need to reason about persuasion? • Beliefs rather than knowledge (doxastic logic versus epistemic logic) • Graded beliefs (two-valued logic, multi-valued logic, fuzzy logic, probabilistic logic etc.) • Change of beliefs (logic of actions, dynamic, algorithmic logic)

  14. 3.Logic of Graded Modalities (Hoek and Meyer)

  15. Beliefs: standard approach In a standard doxastic logic it is possible to express three types of belief attitudes: • Bi • an agent i is absolutely sure that , • Mi • an agent i allows  to be true (MBi()), • Ni • an agent i is neutral with respect to logicalvalue of (NBiBi()).

  16. Beliefs: standard approach Let M= (S,RB1,...,RBn,v) be a model where • S is a set of states, • RBiSSis an accessibility relation defined for agent i (i=1,...,n), • v : S2PV is a valuation function.

  17. Beliefs: standard approach • M,s |= Bi iff for every state s’ which is i-accessible from s, M,s |=   RBi s  RBi RBi 

  18. Beliefs: Hoek-Meyer approach • M,s |= Md iff there are more than d accessible states verifying   s   M,s |= M1

  19. Beliefs: Hoek-Meyer approach • M,s |= Md iff there are more than d accessible worlds verifying  • Deriverable modalities: • Kd  Md  • at most d accessible states refute  • M!0K0, M!dMd-1Md, if d >0 • exactly d accessible states satisfy 

  20. 4.Some modifications

  21. Graded beliefs-some extensions • M,s |= Mid iff there are more than d i-accessiblestates verifying  • New deriverable modality: • Bid1/(d1+d2)  M!d1  M!d2 • agent i beliefs  with the degree d1/(d1+d2) • observe that d1/(d1+d2)[0,1]

  22. Example t=100 s1 s t=100 s2 s3 t=100 s4 t=200 M,s |= Bi3/(3+1)(t=100)

  23. Arguments as actions t=300 t=300 t=300 s1 s1 s1 RB t=100 t=100 t=100 RB RB RB s s’ s’’ s2 s2 s2 RB RB RB a1 a2 t=100 t=100 t=100 s3 s3 s3 RB RB t=50 t=50 t=50 s4 s4 s4 M,s |= Bi2/(2+2)(t=100) M,s’ |= Bi2/(2+1)(t=100) M,s’’ |= Bi2/2(t=100)

  24. Arguments - interpretation Let M= (S,Ra1,..., Rak,v) be a model where • S is a set of states, • RajS{1,...,n}Sis an interpretation of action j, (j=1,...,k), • v : S2PV is a valuation function.

  25. a1 a2 ak ...... s s’ Arguments - interpretation • Let • 0 be a set of atomic actions, • P=a1;a2;a3;...;ak where a1,...,ak0be a program and • i be an agent (i=1,...,n). • We say that s’ is reachable from s by agent i via program P iff there exists a sequence of states s0,...,sk such that s0=s, sk =s’ and for every j=1,...,k (sj-1,i,sj)Raj. (s,i,s’)  Raj(P).

  26. Logic of actions andgraded beliefs - syntax •  ::=  |  |(i:P) | (i:P)| | Mid | Kid | Bid1/(d1+d2) where iAgt,P, d,d1,d2N

  27. Logic of actions and graded beliefs – model Let M=(S,RB1,..., RBn,Ra1, ... , Ram,v) with • a non empty set of states S, • doxastic relations RB1, ... , RBn, RBi S  S for i=1,...,n, • argument relations Ra1, ... , Ram, Raj S  Agt  S for j=1,...,m, • a valuation function, v: S2PV

  28. Logic of actions and graded beliefs – semantics • M,s |= Bid1/(d1+d2) iff the number of states reachable via relation RBi which satisfy  and the number of all states reachable via relation RBi is in the ratio of d1 to d1+d2 |{s’S: (s,s’)RBi and M,s’|= }| d1 |{s’S:(s,s’)RBi}| d1+d2 =

  29. Logic of actions and graded beliefs – semantics • M,s |= (i:P) iff there exists s’S which is reachable by agent i via program P and satisfies  ( there exists s’S such that (s,i,s’)R(P) and M,s’|= ) • M,s |=(i:P) iff every s’S which is reachable by agent i via program P satisfies  ( if (s,i,s’)R(P) then M,s’|=  )

  30. Axioms • All propositional tautologies • Ki0() (Kid Kid) • Kid Kid+1 • Ki0()  [(M!id1 M!id2)  M!id1+d2()] • Kid Ki0Kid

  31. Axioms (selected) • (i:P)(i:P) • (i:a)true (i:a)true • (i:P1;P2)(i:P1)(i:P2) • (i:P)() (i:P) (i:P) • (i:P)  (i:P)

  32. Rules of inference • If  and  then  - modus ponens • If  then Ki0 - generalisation • If  then (i:P) (i:P) • If  then (i:P) (i:P)

  33. 5.Theoryof Persuasion

  34. Persuasion theory • Initial conditions • Success in persuasion • Efficiency in persuasion • Power of persuasion

  35. Initial conditions Bu1prop  (Bu2op   Bu2op ) where u1,u2 (1/2;1] and depend on a specific application. For example: B1prop  B3/4op 

  36. Success in persuasion • objective success (prop:a1;...;ak) Buop for u >1/2 • subjective success (prop:a1;...;ak) Bu1prop (Bu2op) for u1,u2 >1/2

  37. Success in persuasion • different proponents (prop1 : a) Buop for u >1/2 (prop2 : a) Buop for u <1/2

  38. Efficiency in persuasion (prop:a1) Buop for u>1/2 (prop:b1;...;bk) Buop for u>1/2

  39. Power of persuasion (prop:a1;...;ak) B3/4op (prop:b1;...;bt) B1op

  40. 6.Conclusions

  41. Conclusions • A formalism for • simulations of human discussions • an automatic process of convincing

  42. Thank you for your attention!

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