We tackle the problem of semantic heterogeneity in the context of agent communication and argue that solutions based solely on ontologies and ontology matching do not capture adequately the richness of semantics as it arises in dynamic and open multiagent systems. Current solutions to the semantic heterogeneity problem in distributed systems usually do not address the contextual nuances of the interaction underlying an agent communication. The meaning an agent attaches to its utterances is, in our view, very relative to the particular dialogue in which it may be engaged, and that the interaction model specifying its dialogical structure and its unfolding should not be left out of the semantic alignment mechanism. In this article we provide the formal foundation of a novel, interaction-based approach to semantic alignment, drawing from a mathematical construct inspired from category theory that we call the communication product. In addition, we describe a simple alignment protocol which, combined with a probabilistic matching mechanism, endows an agent with the capacity of bootstrapping --by repeated successful interaction-- the basic semantic relationship between its local vocabulary and that of another agent. We have also implemented the alignment technique based on this approach and prove its viability by means of an abstract experimentation and a thorough statistical analysis.