Towards a Logical Analysis of Biochemical Reactions

Suppose one is given a (incomplete) specification of a set of interacting reactions. We would use this set of formulas as the background theory T . Suppose additionally, that a number of observations are made referring to reactions known to have occurred, or compounds known to be available for participation in a reaction, etc. Let α denote the formula representing these observations. Generally, it will not be the case that T |= α because T only provides an incomplete specification of the reactions. We would like to generate a formula (candidate hypotheses) φ in a restricted subset of the language of reactions P such that φ together with the background theory T does entail the observations α. It is important that we do not over commit otherwise we could just as easily choose α itself as the hypothesis which wouldn’t do much good. In fact, the WSC(α;T ;P ) does just the right thing since we know that T∧WSC(α;T ;P ) |= α and it is the weakest such formula by definition. The wsc’s and snc’s can be calculated efficiently for a large class of formulas by expressing them as second-order formulas, using an equivalence proved in [3], and obtaining logically equivalent firstorder formulas by applying the DLS∗ algorithm described, e.g., in [2].