A Dialectic Approach to Problem-Solving

We analyze the dynamics of problem-solving in a framework which captures two key features of that activity. The first feature is that problem-solving is a social game where a number of problem-solvers interact, rely on other agents to tackle parts of a problem, and regularly communicate the outcomes of their investigations. The second feature is that problem-solving requires a careful control over the set of hypotheses that might be needed at various stages of the investigation for the problem to be solved; more particularly, that any incorrect hypothesis be eventually refuted in the face of some evidence: all agents can expect such evidence to be brought to their knowledge whenever it holds. Our presentation uses a very general form of logic programs, viewed as sets of rules that can be activated and fire, depending on what a problem-solver is willing to explore, what a problem-solver is willing to hypothesize, and what a problem-solver knows about the problem to be solved in the form of data or background knowledge. Our framework supports two fundamental aspects of problem-solving. The first aspect is that no matter how the work is being distributed amongst agents, exactly the same knowledge is guaranteed to be discovered eventually. The second aspect is that any group of agents (with at one end, one agent being in charge of all rules and at another end, one agent being in charge of one and only one rule) might need to sometimes put forward some hypotheses to allow for the discovery of a particular piece of knowledge in finite time.