In this article we propose an approach that models the truth behavior of cognitive entities (i.e., sets of connected propositions) by taking into account in a very explicit way the possible influence of the cognitive person (the one that interacts with the considered cognitive entity). Hereby we specifically apply the mathematical formalism of quantum mechanics because of the fact that this formalism allows the description of real contextual influences, i.e., the influence of the measuring apparatus on the physical entity. We concentrated on the typical situation of the liar paradox and have shown that (1) the true-false state of this liar paradox can be represented by a quantum vector of the nonproduct type in a finite-dimensional complex Hilbert space and the different cognitive interactions by the actions of the corresponding quantum projections, (2) the typical oscillations between false and true - the paradox - is now quantum dynamically described by a Schrödinger equation. We analyze possible philosophical implications of this result.