A general formulation of abduction algorithms

Abstract

The paper offers a general formulation of abduction algorithms, referred to as minimum length solution algorithms, which are based on all observable states. The algorithms compute the necessary evidence to derive the correct hypothesis in minimum steps. A first version of algorithms is proposed such that to deal with situations when not all states are observable. The development of fuzzy inference systems is presented in order to apply the minimum length solution algorithms to sets of imprecise observations. I.INTRODUCTION Cognitive reasoning represents the particular case of reasoning based on incomplete information. It is accepted that reasoning means to process and infer the premise information into conclusions. Several forms of logic inference are used in this context; they include the deduction, the induction and the abduction. The deduction is characterized by setting the necessity of the consequence. Two conditions are needed in this context, the observation of the premise and the knowledge on the fact that the premise causes the consequences. The induction states a necessary relation between two observations, the premise and the consequence. This statement is supported by several observations which link together the premise and the consequences.The abduction assumes the causal relation between two events. The abduction is needed when the causes of an observation are unknown, and that is possible if a set of hypotheses is available. The quality of this assumption can be a subject to a certain strategy and the well acknowledged Occam's razor principle is suggested in this framework. A hypothesis is based on the assumption that a certain premise is related to a particular observation. Using the previous experience each hypothesis has a certain degree of truth named the plausibility. Usually, several hypotheses can be proposed for a particular observation. These hypotheses form the observation's set of possible explanations.The ignorance can be classified in terms of incompleteness, imprecision and uncertainty. The incompleteness is the subject of non monotonic logic, the imprecision is the subject of fuzzy logic, and the uncertainty is the subject of probability theory. The combination of imprecision and uncertainty becomes the subject of evidence theory [1] or of possibility theory [2].The induction process in the machine learning theory employs input-output correspondences that are known, and the query is to find the function (the law) according to this correspondences. Using these correspondences one can predict future outputs caused by the not yet

Applications of Signatures to Expert Systems Modelling

“…If Y is observed, then rule 1 will be fired and the knowledge on Z will be obtained. If not, Y will be replaced by rule 2: , ) ( Z Then Y Then X If If (11) and we will ask about the observability of the fact X.…”

“…Successful implementations of expert systems include evolving classification and fuzzy systems [1,2], multi-agent systems [3,4], data mining [5,6], and meta-heuristic engines [7][8][9]. As mentioned in [10,11], the better understanding of how natural cognitive processes can effectively co-evolve with processes in artificially cognitive systems in the framework of Cognitive Infocommunications (CogInfoCom) [12][13][14]. Rule-based expert systems will be addressed in this paper as a step in the context of cognitive processes modelling.…”