A heuristic calculus for transformative reasoning about social information

Social computing needs a capability to reason with qualitatively fuzzy relations and analogy if it is to be capable of pattern matching using commonsense reasoning. The paper proper begins with an introduction to the first-order predicate calculus and heuristics. Using everyday simple examples, it shows where heuristic reasoning can be invaluable and where deductive reasoning falls short. The ∀ qualifier is replaced with Ψ (i.e., for most) and the ∃ qualifier is replaced with E (i.e., for some). That is, the realization of a heuristic calculus necessarily fuzzifies the predicate calculus. Moreover, computational analogy is shown to be possible through the use of multiple analogies. These may be defined by way of a (non-square) matrix, which serves to explain the predicates in terms of one or more disjoint predicates - including various permutations of arguments. These predicates are also subject to composition. Union and intersection operations are used to define predicates in terms of other predicates having common defining heuristic matrices. Finally, an introductory heuristic calculus is defined and exemplified. In particular, context-sensitive left and right-hand transformations are developed for the creation of knowledge, which is open under deduction. Local knowledge is validated through constraint checking and converges just short of validity.