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A generalized quantum theoretical framework, not restricted to the validity domain of standard quantum physics, is used to model the dynamics of the bistable perception of ambiguous visual stimuli such as the Necker cube. The central idea is to treat the perception process in terms of the evolution of an unstable two-state system. This gives rise to a "Necker-Zeno" effect, in analogy to the quantum Zeno effect. A quantitative relation between the involved time scales is theoretically derived. This relation is found to be satisfied by empirically obtained cognitive time scales relevant for bistable perception.

Quantum cognition research applies abstract, mathematical principles of quantum theory to inquiries in cognitive science. It differs fundamentally from alternative speculations about quantum brain processes. This topic presents new developments within this research program. In the introduction to this topic, we try to answer three questions: Why apply quantum concepts to human cognition? How is quantum cognitive modeling different from traditional cognitive modeling? What cognitive processes have been modeled using a quantum account? In addition, a brief introduction to quantum probability theory and a concrete example is provided to illustrate how a quantum cognitive model can be developed to explain paradoxical empirical findings in psychological literature.Keywords: Quantum probability; Classical probability; Cognitive process; Compatibility; Entanglement; Non-Boolean logic With astonishing counterintuitive ramifications, quantum theory is the best empirically confirmed scientific theory in human history. It is "essential to every natural science" and its practical applications, such as the laser and the transistor, form the direct basis of at least one-third of our current economy (Rosenblum & Kuttner, 2006, p. 81). However, applying quantum theory to human cognition is not merely a simple extension of a most successful scientific theory. Rather, this endeavor is driven by a myriad of puzzling findings and stubborn challenges in psychological literature, by deep resonations between basic notions of quantum theory and psychological conceptions and intuitions, and by the Correspondence should be sent to Zheng Wang, School of Communication, The Ohio State University, 3045 Derby Hall, 154 N Oval Mall, Columbus OH 43210-1339 exhibited potential of the theory to provide coherent and mathematically principled explanations for the puzzles and challenges in human cognitive research (Busemeyer & Bruza, 2012).Given the still nascent status of quantum cognition research, it is important to note that it differs from the approaches which treat (parts of) the brain literally as material quantum systems or a quantum computer (e.g., Beck & Eccles, 1992;Hameroff & Penrose, 1996; Stapp, 1993;Vitiello, 1995). In contrast, our approach applies abstract, mathematical principles of quantum theory to inquiries in cognitive science. In fact, to convey the idea that researchers in this area are not doing quantum mechanics, various modifiers have been proposed to describe the approach, such as cognitive models based on quantum structure (Aerts, 2009), quantum-like models (Khrennikov, 2010), and generalized quantum models (Atmanspacher, R€ omer, & Walach, 2002).This topic presents new developments within the quantum cognition modeling research program. In the introduction to this special issue, we try to answer three questions: Why apply quantum concepts to human cognition? How is quantum cognitive modeling different from traditional cognitive modeling? What cognitive processes have been modeled using a quantum account? In addi...

Forthcoming in Foundations of PhysicsThe role of contingent contexts in formulating relations between properties of systems at di¤erent descriptive levels is addressed. Based on the distinction between necessary and su¢ cient conditions for interlevel relations, a comprehensive classi…cation of such relations is proposed, providing a transparent conceptual framework for discussing particular versions of reduction, emergence, and supervenience. One of these versions, contextual emergence, is demonstrated using two physical examples: molecular structure and chirality, and thermal equilibrium and temperature. The concept of stability is emphasized as a basic guiding principle of contextual property emergence.