The Quantum Like Revolution : A Festschrift for Andrei Khrennikov Over the last ten years elements of the formalism of quantum mechanics have been successfully applied beyond physics in areas such as psychology (especially cognition) economics and finance (especially in the formalization of so called ‘decision making’) political science and molecular biology. An important stream of work along these lines commonly under the heading of quantum like modeling has been published in well regarded scientific journals and major publishers have devoted entire books to the topic. This Festschrift honors a key figure in this field of research: Andrei Khrennikov who made momentous contributions to it and to quantum foundations themselves. While honoring these contributions and in order to do so this Festschrift orients its reader toward the future rather than focusing on the past: it addresses future challenges and establishes the way forward in both domains quantum like modeling and quantum foundations. A while ago in response to the developments of using the quantum formalism outside of quantum mechanics the eminent quantum physicist Anton Zeilinger said ‘Why should it be precisely the quantum mechanics formalism Maybe its generalization would be more adequate…’ This volume responds to this statement by both showing the reasons for the continuing importance of quantum formalism and yet also considering pathways to such generalizations. Khrennikov’s work has been indispensable in establishing the great promise of quantum and quantum like thinking in shaping the future of scientific research across the disciplines. ‘Quantum like’ and the quantum revolution outside of physics Arkady Plotnitsky (Purdue University USA) Andrei Khrennikov: a look back on past research successes Arkady Plotnitsky (Purdue University USA); M. A. Man’ko (Lebedev Physical Institute Russia); Philippe Grangier (CNRS France); Emmanuel Haven (Memorial University Canada) The Vaxjo Conference Series: the longest conference series in the world on the foundations of quantum mechanics Theo Niewenhuizen (Universiteit van Amsterdam The Netherlands) When John Wheeler said: ‘all things physical are information theoretic in origin’ Gregg Jaeger (Boston University USA) More on information: categorical quantum mechanics Samson Abramsky (Oxford University UK) Improving the applicability of ‘quantum like’: first generalization: the informational axioms Mauro d’Ariano (University of Pavia Italy); G. Chiribella (University of Hong Kong China); P. Perinotti (University of Pavia Italy) Applying information axioms in social science Sandro Sozzo; Polina Khrennikova (University of Leicester UK); Emmanuel Haven (Memorial University Canada) Improving the applicability of ‘quantum like’: a second generalization: positive operator valued measures (POVM) and more general operator formalisms Irina Basieva (City University UK) POVM and the advanced modelling of cognition and other areas of decision making Jerome Busemeyer (Indiana University USA); Emmanuel Pothos (City University UK); Joyce Wang (Ohio State University USA) Improving the applicability of ‘quantum like’: a third generalization: contextuality Dzhafarov E.N. (Purdue University USA); de Barros A. (San Francisco State University USA); Adan Cabello (University of Seville Spain); J.A. Larsson (Linkoping University Sweden); P. Kurzzinsky (Poznan University Poland) A fourth generalization: probability theories beyond quantum probability R. D. Sorkin (Perimeter Institute Canada) Heterodoxy: non Hermiticity and other issues Carl Bender (Washington University USA) and Irina Basieva (City University UK) Epilogue.