Guest Editor’s Forward
Mirosław Truszczyński · Fundamenta Informaticae · 1992
This special issue of Fundamenta Informaticae contains seven papers on modal logics and their applications in knowledge representation.Most of the papers discuss nonmonotonic modal logics, especially those related to autoepistemic logic of Moore and Levesque.Boutilier studies a generalization of autoepistemic logic which allows him to introduce a gradation of beliefs and talk about the degree of entrenchment.Schwarz introduces an attractive alternative to autoepistemic logic, the logic of reflexive knowledge.Lakemeyer investigates a variant of first-order autoepistemic logic in which objective formulas uniquely determine the set of agents beliefs.Marek and Truszczynski study connections between autoepistemic and default logics.Finally, the papers by Eiter and Gottlob, and by iemela.contain a discussion of complexity issues in autoepistemic reasoning.The only paper not directly related to autoepistemic reasoning is the paper by Fitting, where a certain multi valued logic is proposed to formalize reasonings of several experts some of whom may dominate others.The papers provide an ample evidence that modal logics are quickly becoming a standard tool to study problems in Artificial Intelligence and often offer elegant solutions to a wide range of problems from belief revision to multi-agent reasoning.We hope that this issue will raise reader's interest in the area of modal logics and their applications, and will contribute to its fu rther development.I will now briefly discuss each of the papers in this issue.The first of them, by Boutilier, deals with the notion of entrenchment of beliefs in logics of self-knowledge.Default and autoepisternic logics do not have any means for gradation of beliefs.Hence, all beliefs in belief sets constructed in these logics are regarded as equally plausible.Boutilier argues that this is a serious drawback of "classical nonmonotonic logics.He proposes a formalism which alleviates this problem.The logic of Boutilier is based on a class of Kripke models.The worlds in the models are arranged into totally ordered collections of clusters (hence, a close relation to the logic S4.3).In addition , it is required that (1) the frame of a model has a terminal cluster, and t hat (2) each propositional valuation appears in a model.Formulas true in the terminal cluster of a model are exactly those the ~gent believes in .The difference between Boutilier's approach and autoepistemic logic of "only believing" by Levesque is that while Levesque allows only two clusters (hence, a formula is either believed or disbelieved) Boutilier allows arbitrarily many.This richer structure of models allows him to specify the hierarchy on beliefs according to agent's willingness to give them up.The paper contains a thorough study of the properties of this hierarchy.Eiter and Gottlob study the complexity of brave and cautious reasoning with parsimonious and moderately grounded expansions.They prove that the problem