The quantum model of the two-sentence liar paradox proposed by Aerts, Broekaert, and Smets is an early example of the use of quantum formalism to describe cognitive dynamics. We revisit the model, clarifying the distinction between truth values originating from measurement and from semantic inference and the associated enlargement of the state space. This origin-truth factorization shows that the paradoxical state can be described as an entangled coupling of the two states associated with the non-paradoxical cases. We also derive the Hamiltonian generating the four-state cyclic evolution and express it in compact operator form. We show that the original 16-dimensional construction is not required for the standard liar dynamics, which admits an equivalent representation in the 4-dimensional truth-only space, where the initial liar state is separable. The extended representation becomes dynamically relevant, however, for more general processes in which states with identical truth values but different measurement/semantic origins can have different successors, with the origin degree of freedom then acting as a form of cognitive memory. We conclude by briefly discussing the possible relationship between the model and more general deliberative processes.