Study On Automated Reasoning Theory And Method Based On Neurol Network

Anficial Intelligent is based knowedge expressiOn. at the same tim it is depend onusing knowledge. We can get anaIysis and deeision and fOreCaSt by using knowedge. In logicsystem, using knowledge mearis logic chrence or deduction. So, stUdying inferenee is noonly one driportan part of logic system, but also is the core of the subect of whficialtalligen.In aUtomated theorem PIDving, auomated reasoning methods of propositional calculusProvide with edtersal naoning method fOr other Iogic Sywt. In proPOsbonal calculus, theProCessing ofresoluhon pdriciple have combination explosion naturally So, how to eltwcombinaion explosion in the processing of resolution (genetal showed comPUtationaily hardProblem) is an in1POrtan subject in automated theorem proving. Now netal netWOrk is aneffeCtive tOOl of intelligent technlogy in solving COInPUtalionally hard Problem. Alti1oughneuIal netWork gets a Satistw soluhon of Prob1em, it is not deted to use ned nedsolving problem of automated reasoning. In this thesis, reasning based medel and resolutionprinciple are deeply stUdied, and using netal network partly driplement automated reasoning.The special contentS are as fOllows fl. Evaluation proPositional calculusA drictiony f F(S) - [0,l] is given in proposihonal caIculus, and F(S) is a fOrmulaset of proposihonal calculus. The driction p is cal1ed an evaluation boon of F(S).(F(S), y) is called an evaluatio PrOPOsihonal calculus. Being comPared with mpsitionalcalculus, the PrOperty of model theOry of the evalUation twhonal calculus is StUdied. Theconclusion points out tha evaltalon PrOpositional calculus is sbole extension ofHsitional calculus. MNle, the aUthr deePly studies to get ch medl Sets, andgets some conclusion. The author also discusses a kind of extension neurn wh logicproperty and points out tha using extension mulhlayer Perceptrons can twlementsemantically deduction.2. NumeraIs syStem of PrOPOsitional calculusNend netwrk deals with data, but it is a formula set in ProPOsihonal calculus. In orderto mak neuha netWOr can deal with formuJa, in thes theis, numenis sySem of PIDpoihonalj,-ivcalculus is proposed. We can construct a "numerals system", and there is isomorphism of the numerals system into prepositional calculus, so, for a proof of prepositional calculus, by isomorphism, we can find a "numerals proof of the numerals system. To make the expression of the numerals system very simple, A simple expression of numerals system is given, and some property of the numerals system N is discussed. The conclusion points out N and P have the same ability in inference.3. Resolution principle of numerals system NBecause simple statements have order relation in N , The order relation makes complex statements of N have special property. It happens in the inside of a complex statement, no between two complex statements. In prepositional calculus, the property is new arrangement of simple statements in a clause or a term. So, resolution principle of N is clear and simple, and we can use the four fundamental operations of arithmetic in the procession of the resolution. Further, resolution principle based on matrix calculus is proposed.4 . A kind of resolution principle based on neural networkIn the procession of the resolution, computationally hard problem may happen. Because neural network has the advantage of learning and parallel algorithmic, we can use it to solve the problem. In this thesis, the author just discusses Horn clause sets, and gives how to transform Horn clause set into neural network. Go a step further, the author discusses how to get the learning algorithm of neural network that is equivalence with resolution principle, and proves completeness theorem and soundness theorem of the algorithm for resolution.