∀**u, v** ∈ V
′
, ∃J(u,v) ∈ J ∗
G . Then G *is said connected if it is itself* a connected component (V
′ = V ).

Since all nodes in V
′
are defined by an objective truth value T and a degree of confidence (perceived truth value) dg it is obvious that the resistence to an opinion to change is denoted by these values in all the nodes in V
′
.

## 5 Conclusions

In this preliminary work we tried to sketch a cognitively grounded dynamic model of opinions, in which we defined these mental representations as carachterized by the presence of three specific features.

Differently than psychological theories of opinions that usually provide rich definitions that are too complex to be reduced to measurable variables, we isolated three main constitutive elements that characterize this kind of mental representations. On the other hand, we tried to overcome the reductionist approach of opinion dynamic models, in which the richness of human cognitive processes is substituted by easy-to-compute factors poorly related to actual human behaviors.

For this reason, we proposed to apply time-varying-graph to develop a formal model able to account for the way in which opinions are generated and change as a function of the presence and opinions of other agents in the network.

We are perfectly aware of the complexity of this issue and this work represents a preliminary attempt to merge the cognitive complexity of opinions with a rigorous formal approach, but there are many problems that we need to address. First, the cognitive model should be refined and specific hypotheses about opinion revision and diffusion should be put forward. Moreover, the robustness of the formal model will be tested and such a model will be implemented in cognitive multi-agent system in order to explore the parameter space upon which our model has been defined. Our ultimate aim is to build up a simulation environment in which agents endowed with heterogeneous representations of the external world interact and this leads to the creation of new opinions, the disappearing of some of the previous ones and, in general, to different distributions of representations in the population.

## 6 Acknowledgments

We thank two anonymous referees for their useful comments and participants of the Workshop on Gossip and Opinions (Rome, June 2010, ISTC CNR). A particular thanks goes to Isabella Poggi and Cristiano Castelfranchi for their comments.

## References

[1] E. Smith A. Mason, F.Conrey. Situating social influence processes:
Dynamic, multidirectional flows of influence within social networks. Personality and Social Psychology Review, 11(279-300), 2007.

[2] B. Latan´e A. Nowak, J. Szamrej. From private attitude to public opinion: A dynamic theory of social impact. *Psychological Review*, 97:362–
376, 1990.

[3] G.W. Allport. *Readings in attitude theory and measurement*, chapter Attitude, pages 1–13. Wiley, 1967.

[4] S. Brunetti, E. Lodi, and W. Quattrociocchi. Multicolored dynamos on toroidal meshes. *CoRR*, abs/1012.4404, 2010.

[5] S. Brunetti, E. Lodi, and W. Quattrociocchi. Dynamic monopolies in colored tori. *APDCM - Alaska*, 2011.

[6] I. Poggi C. Castelfranchi C. *Bugie, finzioni e sotterfugi. Per una scienza* dell'inganno. Carocci Editore, 1998.

[7] V. Loreto C. Castellano, S. Fortunato. Statistical physics of social dynamics. *Reviews of Modern Physics*, 81(2):591+, June 2009.

[8] A. Casteigts, P. Flocchini, W. Quattrociocchi, and N. Santoro. Timevarying graphs and dynamic networks. *Arxiv arXiv:1012.0009*, 2010.

[9] I. Crespi. *The public opinion process. How the people speak*. Lawrence Erlbaum Associates, 1997.

[10] G. Deffuant, D. Neau, F. Amblard, and G. Weisbuch. Mixing beliefs among interacting agents. *Advances in Complex Systems*, 3:87–98, 2001.

[11] L. Festinger, S. Schachter, and K. Back. Social Pressures in Informal Groups: A Study of Human Factors in Housing. Harper, New York, NY, USA, 1950.

[12] D. Fleming. Attitude: The history of a concept. *Perspectives in American History*, 1:287–365, 1967.

[13] B. Latan´e H. Lavine. A cognitive-social theory of public opinion:
Dynamic impact and cognitive structure. *Journal of Communication*,
46:48–56, 1996.

[14] H. Hu and X. Wang. Discrete opinion dynamics on networks based on social influence. *Journal of Physics A: Mathematical and Theoretical*, 42(22):225005+, June 2009.

[15] M.P. Zanna J.M. Olson. Attitudes and attitude change. Annual Review of Psychology, 44:117–154, 1993.

[16] B. Latan´e. The psychology of social impact. *American Psychologist*,
36:343–356, 1981.

[17] W. Lippmann. *Public opinion*. Penguin Books, 1946.

[18] J. Lorenz. Continuous opinion dynamics of multidimensional allocation problems under bounded confidence: More dimensions lead to better chances for consensus. Aug 2007.

[19] W. McGuire. The vicissitudes of attitudes and similar representational constructs in twentieth century psychology. European Journal of Social Psychology, 16:89–139, 1986.

[20] I. Ajzen M.Fishbein. *Belief, Attitude, Intention, and Behavior: An Introduction to Theory and Research*. Reading, MA: Addison-Wesley, 1975.

[21] V. Price. *Communication concepts 4: Public opinion*. Sage, 1992.

[22] W. Quattrociocchi and F. Amblard. Emergence through selection: The evolution of a scientific challenge. *Arxiv arXiv:1102.0257*, Dec 2010.

[23] W. Quattrociocchi and F. Amblard. Selection in scientific networks.

Arxiv arXiv:1012.4396v1, Dec 2010.

[24] W. Quattrociocchi, R. Conte, and E. Lodi. Simulating opinion dynamics in heterogeneous communication systems. *ECCS 2010 - Lisbon* Portugal, 2010.

[25] L.R. Fabrigar R.E. Petty, D.T. Wegener. Attitudes and attitude change.

Annual Review of Psychology, 48:609–647, 1997.

[26] N. Santoro, W. Quattrociocchi, P. Flocchini, A. Casteigts, and F. Amblard. Time varying graphs and social network analysis: Temporal indicators and metrics. *Arxiv arXiv:1102.0629*, 2010.