Reasoning under incomplete information in artificial intelligence: A comparison of formalisms using a single example

Abstract

Man is capable of reasoning when the available information is incomplete. the conclusions obtained are based on knowledge considered as “generally true.” These conclusions are temporary as they are liable to be challenged by the arrival of new pieces of information which will refine the information previously available (without necessarily contradicting it). Numerous studies have independently dealt with the formalization of this kind of revisable reasoning over the last ten years. the approaches used have been very diverse: some are purely symbolic, others make use of numbers to quantify the uncertainty; some are close to formal logic, and others are much less formalized; some only deal with exceptions, a smaller number which are somewhat more ambitious tackle the problem of knowledge base revision. This work presents the above approaches and compares them on a single example in order to better evaluate their similarities, their differences, their abilities to formalize certain aspects of so-called “commonsense” reasoning, and also in order to try to lay bare the fundamental principles that underlie the different approaches. the logics considered in this work are default logic, nonmonotonic modal logics, including autoepistemic logic, circumscription, circumscription-like approaches, supposition-based logic, conditional logics, logics of uncertainty, i.e., probabilistic, and possibilistic logics as well as belief functions, numerical quantifier logic, and fuzzy logics. We also consider formalisms oriented towards causal reasoning and analogical reasoning. Lastly, we study the contribution of works on truth maintenance, action logic, as well as recent attempts to formalize the process of revision of a set of formulae closed by deduction. the systematic use of a single example and of the same evaluation criteria for each formalism, will enable the reader to better perceive the rationale behind the various approaches as well as to appreciate their interest.