When Logical Conclusions Do Not Hold True. Inference rules are called nonmonotonic when they allow intelligent systems "to augment their beliefs by new ones that do not logically follow from their explicit ones" and this or another inference may have to be retracted.
Ordinary inference rules are monotonic "because the set of theorems derivable from premises is not reduced by adding to the premises."
– from Logical foundations of artificial intelligence by MR Genesereth and NJ Nilsson (1987)
We propose analyzing conditional reasoning by appeal to a notion of intervention on a simulation program, formalizing and subsuming a number of approaches to conditional thinking in the recent AI literature. Our main results include a series of axiomatizations, allowing comparison between this framework and existing frameworks (normality-ordering models, causal structural equation models), and a complexity result establishing NP-completeness of the satisfiability problem. Perhaps surprisingly, some of the basic logical principles common to all existing approaches are invalidated in our causal simulation approach. We suggest that this additional flexibility is important in modeling some intuitive examples.
Conditional information is an integral part of representation and inference processes of causal relationships, temporal events, and even the deliberation about impossible scenarios of cognitive agents. For formalizing these inferences, a proper formal representation is needed. Psychological studies indicate that classical, monotonic logic is not the approriate model for capturing human reasoning: There are cases where the participants systematically deviate from classically valid answers, while in other cases they even endorse logically invalid ones. Many analyses covered the independent analysis of individual inference rules applied by human reasoners. In this paper we define inference patterns as a formalization of the joint usage or avoidance of these rules. Considering patterns instead of single inferences opens the way for categorizing inference studies with regard to their qualitative results. We apply plausibility relations which provide basic formal models for many theories of conditionals, nonmonotonic reasoning, and belief revision to asses the rationality of the patterns and thus the individual inferences drawn in the study. By this replacement of classical logic with formalisms most suitable for conditionals, we shift the basis of judging rationality from compatibility with classical entailment to consistency in a logic of conditionals. Using inductive reasoning on the plausibility relations we reverse engineer conditional knowledge bases as explanatory model for and formalization of the background knowledge of the participants. In this way the conditional knowledge bases derived from the inference patterns provide an explanation for the outcome of the study that generated the inference pattern.
The Sixth International Workshop on Nonmonotonic Reasoning was held 10 to 12 June 1996 in Timberline, Oregon. The aim of the workshop was to bring together active researchers interested in nonmonotonic reasoning to discuss current research, results, and problems of both a theoretical and a practical nature. The aim of the workshop was to bring together active researchers interested in nonmonotonic reasoning to discuss current research, results, and problems of both a theoretical and a practical nature. The authors of the technical papers accepted for the workshop represented 10 countries: Austria, Brazil, Canada, France, Germany, Israel, Italy, the Netherlands, the United States, and Venezuela. The papers described new work on default logic; circumscription; modal nonmonotonic logics; logic programming; abduction; the frame problem; and other subjects, including qualitative probabilities.
The contributions to this workshop indicate substantial advances in the technical foundations of the field. They also show that it is time to evaluate the existing approaches to commonsense reasoning problems. The Second International Workshop on Nonmonotonic Reasoning was held from 12-16 June 1988 in Grassau, a small village near Lake Chiemsee in southern Germany. It was jointly organized by Johan de Kleer, Matthew Ginsberg, Erik Sandewall, and myself. Financial support for the workshop came from the American Association for Artificial Intelligence (AAAI), Deutsche Forschungsgemeinschaft (DFG), The European Communities (Project Cost-13), Linköping University, and SIEMENS AG.
The workshop was sponsored by the American Association for Artificial Intelligence, Compulog, Associazione Italiana per l'Intelligenza Artificiale, and the Prolog Development Center. This year's workshop, organized by Gerhard Brewka and Ilkka Niemela (local chair: Enrico Giunchiglia, honorary chair: Ray Reiter), was different from earlier workshops in this series in an important aspect: It consisted of several specialized tracks, held partially in parallel, embedded in a plenary program that comprised invited talks and a panel. The following five tracks were organized: (1) Formal Aspects and Applications of Nonmonotonic Reasoning (cochairs: Jim Delgrande, Mirek Truszczynski), (2) Computational Aspects of Nonmonotonic Reasoning (cochairs: Niemela, Torsten Schaub), (3) Logic Programming (cochairs: Jürgen Dix, Jorge Lobo), (4) Action and Causality (cochairs: Vladimir Lifschitz, Hector Geffner), and (5) Belief Revision (cochairs: Hans Rott, Mary-Anne Williams). Both the new format and the scheduling of the workshop in conjunction with the KR Conference proved to be highly fruitful. The Seventh International Workshop on Nonmonotonic Reasoning was held in Trento, Italy, on 30 May to 1 June 1998 in conjunction with the Sixth International Conference on the Principles of Knowledge Representation and Reasoning (KR'98).
Decision theory and nonmonotonic logics are formalisms that can be employed to represent and solve problems of planning under uncertainty. We analyze the usefulness of these two approaches by establishing a simple correspondence between the two formalisms. The analysis indicates that planning using nonmonotonic logic comprises two decision-theoretic concepts: probabilities (degrees of belief in planning hypotheses) and utilities (degrees of preference for planning outcomes). We present and discuss examples of the following lessons from this decision-theoretic view of nonmonotonic reasoning: (1) decision theory and nonmonotonic logics are intended to solve different components of the planning problem; (2) when considered in the context of planning under uncertainty, nonmonotonic logics do not retain the domain-independent characteristics of classical (monotonic) logic; and (3) because certain nonmonotonic programming paradigms (for example, frame-based inheritance, nonmonotonic logics) are inherently problem specific, they might be inappropriate for use in solving certain types of planning problems. We discuss how these conclusions affect several current AI research issues.
We give an overview of the multifaceted relationship between nonmonotonic logics and preferences. We discuss how the nonmonotonicity of reasoning itself is closely tied to preferences reasoners have on models of the world or, as we often say here, possible belief sets. Selecting extended logic programming with answer-set semantics as a generic nonmonotonic logic, we show how that logic defines preferred belief sets and how preferred belief sets allow us to represent and interpret normative statements. Conflicts among program rules (more generally, defaults) give rise to alternative preferred belief sets. We discuss how such conflicts can be resolved based on implicit specificity or on explicit rankings of defaults.
Once the topic has become well enough understood that it can be explained easily to paying customers, and stable enough that anyone teaching it is not likely to have to update his/her teaching materials every few months as new developments are reported, it can be considered to have arrived. Another reasonable indicator of the maturity of a subject, a milestone along the road to academic respectability, is the publication of a really good book on the subject--not another research monograph but a book that consolidates what is already known, surveys and relates existing ideas, and maybe even unifies some of them. Grigoris Antoniou's Nonmonotonic Reasoning is just such a milestone--well written, informative, and a good source of information on an important and complex subject. Neither is it surprising nor unreasonable that he devotes a lot of space to Reiter's (1980) default logic, which, along with Mc-Carthy's (1980) circumscription and Moore's (1985) autoepistemic logic, is one of the holy trinity of nonmonotonic reasoning. AI Magazine Volume 20 Number 3 (1999) ( AAAI) and it has been the basis of a number of different variants, all with their own strengths and weaknesses.
Bilattice-based triangle provides an elegant algebraic structure for reasoning with vague and uncertain information. But the truth and knowledge ordering of intervals in bilattice-based triangle can not handle repetitive belief revisions which is an essential characteristic of nonmonotonic reasoning. Moreover the ordering induced over the intervals by the bilattice-based triangle is not sometimes intuitive. In this work, we construct an alternative algebraic structure, namely preorder-based triangle and we formulate proper logical connectives for this. It is also demonstrated that Preorder-based triangle serves to be a better alternative to the bilattice-based triangle for reasoning in application areas, that involve nonmonotonic fuzzy reasoning with uncertain information.