Logics of Allies and Enemies: A Formal Approach to the Dynamics of Social Balance Theory

We combine social balance theory with temporal logic to obtain a Logic of Allies and Enemies (LAE), which formally describes the likely changes to a social network due to social pressure. We demonstrate how the rich language of LAE can be used to describe various interesting concepts, and show that both model checking and validity checking are PSPACE-complete.

[1]  Daniel Dajun Zeng,et al.  Social balance in signed networks , 2014, Information Systems Frontiers.

[2]  Krzysztof Kulakowski.  Some Recent Attempts to Simulate the Heider Balance Problem , 2007, Computing in Science & Engineering.

[3]  R. Kapuściński,et al.  A brief history of balance through time , 1996 .

[4]  F. Heider.  Attitudes and cognitive organization. , 1946, The Journal of psychology.

[5]  Fritz Heider,et al.  Social perception and phenomenal causality. , 1944 .

[6]  F. Heider.  The psychology of interpersonal relations , 1958 .

[7]  Zoé Christoff,et al.  A logic for diffusion in social networks , 2015, J. Appl. Log..

[8]  Patrick Doreian,et al.  Some dynamics of social balance processes: bringing Heider back into balance theory , 2003, Soc. Networks.

[9]  F. Harary.  On the notion of balance of a signed graph. , 1953 .

[10]  Hildegard Meyer-Ortmanns,et al.  Social balance as a satisfiability problem of computer science. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Peter Abell,et al.  Structural Balance: A Dynamic Perspective , 2009 .

[12]  Edmund M. Clarke,et al.  Design and Synthesis of Synchronization Skeletons Using Branching Time Temporal Logic , 2008, 25 Years of Model Checking.

[13]  Thomas Ågotnes,et al.  On the Logic of Balance in Social Networks , 2019, Journal of Logic, Language and Information.

[14]  Alexandru Baltag,et al.  Dynamic Epistemic Logics of Diffusion and Prediction in Social Networks , 2018, Stud Logica.

[15]  Albert R. Meyer,et al.  Word problems requiring exponential time(Preliminary Report) , 1973, STOC.

[16]  Edmund M. Clarke,et al.  Using Branching Time Temporal Logic to Synthesize Synchronization Skeletons , 1982, Sci. Comput. Program..

[17]  Mina Young Pedersen,et al.  Analyzing Echo Chambers: A Logic of Strong and Weak Ties , 2019, LORI.

[18]  B. A. Farbey,et al.  Structural Models: An Introduction to the Theory of Directed Graphs , 1966 .

[19]  Zhigang Wang,et al.  Sentiment and social mitosis: Implications of Heider's Balance Theory , 2003, J. Artif. Soc. Soc. Simul..

[20]  Wiebe van der Hoek,et al.  Who Should Be My Friends? Social Balance from the Perspective of Game Theory , 2019, Journal of Logic, Language and Information.

[21]  F. Harary,et al.  STRUCTURAL BALANCE: A GENERALIZATION OF HEIDER'S THEORY1 , 1977 .

[22]  P. L. Krapivsky,et al.  Social balance on networks : The dynamics of friendship and enmity , 2006 .