Let W be the weight of the partition, that is, the sum of the weights of the satisfied constraints. The coherence problem is then to partition E into A and R in a way that maximizes W . By itself, this characterization has no philosophical or psychological applications, because it does not state the nature of the elements, the nature of the constraints, or the algorithms to be used to maximize satisfaction of the constraints. Once these elements and constraints are specified, then the algorithms that solve the general coherence problem can be used to compute coherence in ways that apply to philosophical problems. Epistemic coherence is a combination of the first five kinds of coherence, and ethics involves deliberative coherence as well.
Explanatory coherence is a symmetric relation, unlike, say, conditional probability.
That is, two propositions p and q cohere with each other equally. Similar hypotheses that explain similar pieces of evidence cohere. Propositions that describe the results of observations have a degree of acceptability on their own. Contradictory propositions are incoherent with each other. If P and Q both explain a proposition, and if P and Q are not explanatorily connected, then P and Q are incoherent with each other.