Connectionist Approach to Finding Stable Models and Other Structures in Nonmonotonic Reasoning

In this paper, a connection between Multilayer Feedforward Networks, propositional first order well formed formulas and pseudolinear functions is established. Due to this link, it is possible to formulate optimization problems in first order propositional metalanguage, obtaining the objective function and MFN structure with relative ease. This general technique is applied to solving two ∑2Pcomplete problems, finding a stable model of logic program and a stable answer set of CN-program. A connectionist model for minimization of the objective functions based on gradient descent in the space of inputs of a muitilayer feedforward network is proposed. The model's massive parallelism gives raise to a hope that even real world size instances of the two problems might he solved. It is also pointed out that due to mutual relationship between stable semantics of logic programs and extensions of default theories another important problem in nonmonotonic reasoning can be solved with a relative efficiency.