Reason Maintenance - State of the Art

This paper describes state of the art in reason maintenance with a focus on its future usage in the KiWi project. To give a bigger picture of the field, it also mentions closely related issues such as non-monotonic logic and paraconsistency. The paper is organized as follows: first, two motivating scenarios referring to semantic wikis are presented which are then used to introduce the different reason maintenance techniques

Characterizing and Extending Answer Set Semantics using Possibility Theory

Answer Set Programming (ASP) is a popular framework for modeling combinatorial problems. However, ASP cannot easily be used for reasoning about uncertain information. Possibilistic ASP (PASP) is an extension of ASP that combines possibilistic logic and ASP. In PASP a weight is associated with each rule, where this weight is interpreted as the certainty with which the conclusion can be established when the body is known to hold. As such, it allows us to model and reason about uncertain information in an intuitive way. In this paper we present new semantics for PASP, in which rules are interpreted as constraints on possibility distributions. Special models of these constraints are then identified as possibilistic answer sets. In addition, since ASP is a special case of PASP in which all the rules are entirely certain, we obtain a new characterization of ASP in terms of constraints on possibility distributions. This allows us to uncover a new form of disjunction, called weak disjunction, that has not been previously considered in the literature. In addition to introducing and motivating the semantics of weak disjunction, we also pinpoint its computational complexity. In particular, while the complexity of most reasoning tasks coincides with standard disjunctive ASP, we find that brave reasoning for programs with weak disjunctions is easier.Comment: 39 pages and 16 pages appendix with proofs. This article has been accepted for publication in Theory and Practice of Logic Programming, Copyright Cambridge University Pres

Risk management in intelligent agents

University of Technology, Sydney. Faculty of Engineering and Information Technology.This thesis presents the development of a generalised risk analysis, modelling and management framework for intelligent agents based on the state-of-art techniques from knowledge representation and uncertainty management in the field of Artificial Intelligence (AI). Assessment and management of risk are well established common practices in human society. However, formal recognition and treatment of risk are not usually considered in the design and implementation of (most existing) intelligent agents and information systems. This thesis aims to fill this gap and improve the overall performance of an intelligent agent. By providing a formal framework that can be easily implemented in practice, my work enables an agent to assess and manage relevant domain risks in a consistent, systematic and intelligent manner. In this thesis, I canvas a wide range of theories and techniques in AI research that deal with uncertainty representation and management. I formulated a generalised concept of risk for intelligent agents and developed formal qualitative and quantitative representations of risk based on the Possible Worlds paradigm. By adapting a selection of mature knowledge modelling and reasoning techniques, I develop a qualitative and a quantitative approach of modelling domains for risk assessment and management. Both approaches are developed under the same theoretical assumptions and use the same domain analysis procedure; both share a similar iterative process to maintain and improve domain knowledge base continuously over time. Most importantly, the knowledge modelling and reasoning techniques used in both approaches share the same underlying paradigm of Possible Worlds. The close connection between the two risk modelling and reasoning approaches leads us to combine them into a hybrid, multi-level, iterative risk modelling and management framework for intelligent agents, or HiRMA, that is generalised for risk modelling and management in many disparate problem domains and environments. Finally, I provide a top-level guide on how HiRMA can be implemented in a practical domain and a software architecture for such an implementation. My work lays a solid foundation for building better decision support tools (with respect to risk management) that can be integrated into existing or future intelligent agents

In search of a “true” logic of knowledge: the nonmonotonic perspective

AbstractModal logics are currently widely accepted as a suitable tool of knowledge representation, and the question what logics are better suited for representing knowledge is of particular importance. Usually, some axiom list is given, and arguments are presented justifying that suggested axioms agree with intuition. The question why the suggested axioms describe all the desired properties of knowledge remains answered only partially, by showing that the most obvious and popular additional axioms would violate the intuition.We suggest the general paradigm of maximal logics and demonstrate how it can work for nonmonotonic modal logics. Technically, we prove that each of the modal logics KD45, SW5, S4F and S4.2 is the strongest modal logic among the logics generating the same nonmonotonic logic. These logics have already found important applications in knowledge representation, and the obtained results contribute to the explanation of this fact

Reasoning about uncertainty and explicit ignorance in generalized possibilistic logic

© 2014 The Authors and IOS Press. Generalized possibilistic logic (GPL) is a logic for reasoning about the revealed beliefs of another agent. It is a two-tier propositional logic, in which propositional formulas are encapsulated by modal operators that are interpreted in terms of uncertainty measures from possibility theory. Models of a GPL theory represent weighted epistemic states and are encoded as possibility distributions. One of the main features of GPL is that it allows us to explicitly reason about the ignorance of another agent. In this paper, we study two types of approaches for reasoning about ignorance in GPL, based on the idea of minimal specificity and on the notion of guaranteed possibility, respectively. We show how these approaches naturally lead to different flavours of the language of GPL and a number of decision problems, whose complexity ranges from the first to the third level of the polynomial hierarchy

A simple logic for reasoning about incomplete knowledge

International audienceThe semantics of modal logics for reasoning about belief or knowledge is often described in terms of accessibility relations, which is too expressive to account for mere epistemic states of an agent. This paper proposes a simple logic whose atoms express epistemic attitudes about formulae expressed in another basic propositional language, and that allows for conjunctions, disjunctions and negations of belief or knowledge statements. It allows an agent to reason about what is known about the beliefs held by another agent. This simple epistemic logic borrows its syntax and axioms from the modal logic KD. It uses only a fragment of the S5 language, which makes it a two-tiered propositional logic rather than as an extension thereof. Its semantics is given in terms of epistemic states understood as subsets of mutually exclusive propositional interpretations. Our approach offers a logical grounding to uncertainty theories like possibility theory and belief functions. In fact, we define the most basic logic for possibility theory as shown by a completeness proof that does not rely on accessibility relations