An anhomomorphic logic $\ascript ^*$ is the set of all possible realities for a quantum system. Our main goal is to find the "actual reality" $ϕ_a\in\ascript ^*$ for the system. Reality filters are employed to eliminate unwanted potential realities until only
ϕa remains. In this paper, we consider three reality filters that are constructed by means of quantum integrals. A quantum measure
μ can generate or actualize a $ϕ\in\ascript ^*$ if
μ(A) is a quantum integral with respect to
ϕ for a density function
f over events
A. In this sense,
μ is an "average" of the truth values of
ϕ with weights given by
f. We mainly discuss relations between these filters and their existence and uniqueness properties. For example, we show that a quadratic reality generated by a quantum measure is unique. In this case we obtain the unique actual quadratic reality.
After a very successful flurry of activities for a few decades to maximize the benefits of the formalism of Quantum Mechanics to connect the micro and macro universe, the applied physics community has successfully engineered sustained technological innovations for human social advancements. However, a significant segment of the theoretical physics community put their endeavors essentially in inventing realities that are esthetically pleasing to our human logics (epistemology) rather than staying focused on discovering the actual physical realities in nature driven by cosmic logics (ontology). The purpose of this paper is an attempt to formulate a Reality Epistemology that can leverage our enormous successes in science to re‐focus our attention to discovering nature's realities by understanding the physical processes behind all natural interactions that collectively make the cosmic evolution progressing forward. We underscore the deviation from seeking reality to justify the key premise of the paper. We can “see” (measure) the universe only through the “eyes” of the various sensors (detectors). None of these sensors are completely known to us as yet. All sensors also have inherently limited capabilities to respond to input signals and limited capabilities to “report” only a part of all that it experiences. We are thus forced to develop our mathematical theories mixing our human logics and incomplete information and hence they are all provisional and incomplete since they are predicting only correctly measured but limited report by the detector. Thus, we should be careful not to jump into conclusion that we have captured all the necessary cosmic logics behind the interactions involved. We dissect the measurement process in a generic way along with well defined steps to apply Reality Epistemology, which will jointly allow us to develop a scientific methodology of iteratively refining our “successful” human logics that can evolve towards our goal of capturing the cosmic logics. The core content of this paper was first presented at the 2007 QTRF‐4 conference at the Vaxjo University [1].