Conversation Theory is a theory of interaction. From interaction (the theory asserts) arises all individuals and all concepts. Interaction, if it is to allow for evolution, must perforce contain conflict, and, if concepts and individuals are to endure, resolution of conflict. Conversation Theory as developed by Pask led to the protologic called Lp which describes the interaction of conceptual entities. Lp contains injunctions as to how entities can and may interact, including how they may conflict and how their conflict may be resolved. Unlike existing software implementations based on Conversation Theory, Lp in its pure form is a logic of process as well as coherence and distinction. The hypothesis is that a low-level simulation of Lp, that of an internal and microscopic level in which topics are influenced by "forces" that are exerted by the topology of the conceptual space, would, in its activation as a dynamic process of appropriate dimension, produce as a result (and hence be a confirmation of) the macroscopically-observed behaviour of the system manifest as conflict and resolution of conflict. Without this confirmation, the relationships between Conversation Theory and Lp remain only proposed; with it, their mutual consistencies and validity as a model of cognition, are affirmed. The background of Conversation Theory and Lp necessary to support the thesis is presented a long with a comparison of other software approaches to related problems. A description of THOUGHTSTICKER, a current embodiment of Lp at the macro level, provides a detailed sense of the Lp operations. Then a computer program (developed to provide a proof by demonstration of the thesis) is described, in which a microscopic simulation of Lp processes confirms the macroscopic behaviour predicted by Conversation Theory. Conversation Theory thereby gains support f or its use as a valid observer's language for every-day experience owing to this confirmation and its protologic as a basis for psychological phenomena in the interaction of conceptual entities of mind.