How to change somebody’s mind? Modeling a Process of Convincing.

1. How to change somebody’s mind? Modeling a Process of Convincing. Katarzyna Budzyńska Faculty of Christian Philosophy Cardinal Stefan Wyszyński University in Warsaw & Magdalena Kacprzak Faculty of Computer Science Bialystok University of Technology

2. The Project (Budz-Kacp): The Formal Theory of Persuasion motivation Philosophy Reflection on Persuasion Process application Comp-sci The Formal Theory of Persuasion modeling Simulation of Persuasion Process application Logic modeling Formal Description of Persuasion Process

3. The Project (Budz-Kacp): The Formal Theory of Persuasion motivation Philosophy Reflection on Persuasion Process application Comp-sci The Formal Theory of Persuasion modeling Simulation of Persuasion Process application Logic modeling Formal Description of Persuasion Process

4. Outline of the Presentation • The Nature of Persuasion • The Aspects of Persuasion • Subjectivism • Gradation of Beliefs • Dynamism • The Logic for Persuasion Theory • The Logic of Graded Modalities • The Algorythmic Logic • Conclusions

5. 1. The Nature of Persuasion

6. How we change one another's minds • Persuasion (lat. persuasio) is a way to induce somebody tobelieve in our rights or to do something. • Persuasion is one of the methods of negotiation which allows to reach an agreement.

7. 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

8. How we change one another's minds Thus, we assume that: • a persuasion is an action which is initiated by the conflict of opinion& aimed to change beliefs • aproponentperforms a sequence of actions to meet his goal, • an opponent comes into a conflict with a proponent • an audience is a target of persuasion • the goal of a persuasion may be satisfied in a different degree

9. An Example • I would like to propose you the insurance policy. • I am not interested - it's beyond my pocket. Maybe it is very profitable, but I can't afford such a luxury. • But we offer the lowest premium. Moreover, our products are matched to the individual needs of our clients. I am sure we will find something that best meet your needs like for example low monthly payments. • It sounds very interesting. Tell me more - what are the details of your proposal?

10. 2. The Aspects of Persuasion:Subjectivism

11. Philosophical Intuitions • Persuasion refers to BELIEFS not knowledge • „conflict of opinion” not „conflict of knowledge” • knowledge – unquestionable beliefs – controversial, subjective • episteme () - true knowledge basing on rational, fundamental principles doxa () - common belief originating in sensual experiences and thus being uncertain information that may turn out to be false

12. Beliefs: the 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{0,1}PV is a valuation function.

13. 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()).

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

15. 2. The Aspects of Persuasion:Gradation of Beliefs

16. after after before before I did not believe the thesis I did not believe the thesis I do believe the thesis stronger, but not absolutely arguments arguments I do believe the thesis Philosophical Intuitions • Persuasion changes the GRADES of beliefs • „Black-and-white” types of convincing • Persuasions that increase the degree of certainty in not a fully range

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

18. Beliefs: Hoek-Meyer approach • Bd - at most d accessible states refute  (Bd  Md ) • M!d - exactly d accessible states satisfy  (M!0B0, M!dMd-1Md, if d >0)  s   B1& M!2

19. Graded beliefs:some extensions • M,s|= Mid iff there are more than d i-accessiblestates verifying  • New deriverable modality: • Mid1,d2  Mi!d1  Mi!d2 • there are d1 i-accessible states verifying  & d2 i-accessible states verifying   • agent i beliefs  with the degree d1/(d1+d2) • observe that d1/(d1+d2)  [0,1]

20. The Example w.r.t. Gradation w1 s1 too exp high v(s1, T) = 0 • Thesis T: I should buy a life insurance • M,s |=Mi1,2T • The housewife beliefs T with the degree 1/3 s2 exp high v(s2, T) = 1 s s3 ? exp low v(s3, T) = 0 s4 cheap low v(s4, T) = 1 s5 cheap high v(s5, T) = 1 The housewife beliefs about insurance (before persuasion)

21. The example – some modification w1 - modified s1 too exp high v(s1, T) = 0 • M,s |=Mi1,2T • The housewife beliefs T with the degree 1/3 • M,s |=Mj3,1T • The businesswoman beliefs T with the degree 3/4 s2 exp high v(s2, T) = 1 s s3 ? exp low v(s3, T) = 0 s4 cheap low v(s4, T) = 1 s5 cheap high v(s5, T) = 1 Ri – accessibility relation of the housewife Rj – accessibilityrelation of the businesswoman

22. 2. The Aspects of Persuasion:Dynamism

23. Philosophical Intuitions • The persuader uses arguments as tools in order to CHANGE other’s beliefs • Argument – action aimed at changing beliefs • It requires performing some activity: • the persuader expresses verbal argument or • she executes nonverbal argument

24. The example w.r.t. Actions w1: before w2: after s1 s1 too exp high too exp high v(s1, T) = 0 v(s1, T) = 0 s2 s2 exp high exp high v(s2, T) = 1 v(s2, T) = 1 s s’ s3 s3 argument ? ? exp low exp low v(s3, T) = 0 v(s3, T) = 0 s4 s4 cheap low cheap low v(s4, T) = 1 v(s4, T) = 1 s5 s5 cheap high cheap high v(s5, T) = 1 v(s5, T) = 1 M,s |= Mi1,2T M,s’ |= Mi3,1T She beliefs T with the degree 3/4 She beliefs T with the degree 1/3

25. Arguments - interpretation Let M= (S,Ra1,..., Rak,v) be a model where • S is a set of states, • RatS{1,...,n}Sis an interpretation of action t, (t=1,...,k), • v : S{0,1}PV is a valuation function.

26. 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. • 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 t=1,...,k (st-1,i,st)Rat. • When M,s’|=Mj1,0T then we say that M,s |=(i:P) (Mj1,0T) (s,i,s’)  Rat(P)

27. 3. The Logic for Persuasion Theory

28. What a 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 (dynamic, algorithmic logic, logic of belief revision)

29. What a logic do we need to reason about persuasion?

30. Characteristics of our Persuasion Theory • broad sense of notion of persuasion • gradation of beliefs-attitudes • the specific aspect of research on the persuasion process

31. What a logic do we need to reason about persuasion? • Multimodal logic of actions & graded beliefs (AGn) • Inspired by: • The Logic of Graded Modalities (W. van der Hoek & J.J. Meyer in: Modalities for Reasoning about Knowledge and Quantities. Elinkwijk, Utrecht, 1992) • The Algorythmic Logic (G. Mirkowska & A. Salwicki. Algorithmic Logic. Polish Scientific Publishers, Warszawa, 1987)

32. Syntax of AGn •  ::= p |  |  | Mid |(i:P) where iAgt,P, dN

33. Model for AGn 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{0,1}PV

34. Semantics of AGn • M,s |= Mid1 iff the number of states reachable via relation RBi which satisfy  is MORE THANd1 • M,s |= Bid1 iff the number of states reachable via relation RBi which satisfy  is AT MOSTd1 • M,s |= Mid1,d2 iff • the number of states reachable via relation RBi which satisfy  is d1and • the number of states reachable via relation RBi which satisfy  is d2

35. Semantics of AGn • 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’|= )

36. Axioms for graded beliefs • All propositional tautologies • Bi0() (Bid Bid) • Bid Bid+1 • Bi0()  [(M!id1 M!id2)  M!id1+d2()] • Bid Bi0Bid • Bi0 (true)

37. Axioms for actions • (i:P1;P2)(i:P1)((i:P2)) • (i:P)() (i:P) (i:P) • (i:P)(true) • (i:Id) 

38. Rules of inference • If  and  then  (modus ponens) • If  then Bi0 (generalisation) • If  then (i:P) (i:P)

39. Conclusions • A formalism for • simulations of human discussions • an automatic process of convincing • Wemay use it to research • whether the different scenarios of persuasion (various arrangement of arguments)will arrive at the same result, • how they will change the audience's outlook on life, • whethermost of a given group become convinced to the thesis, • how entering of a new proponentwill affect the course of discussion etc.

40. Thank you for your attention!