Odile Papini

Iterated Revision Operations Stemming from the History of an Agent’s Observations

Knowledge bases can be used to represent an agent’s perception of the world. As an agent often has to deal with incomplete, uncertain or vague information, she has to revise her beliefs about the world. In order to model revision, one has to provide a mechanism to support the modification of the knowledge base in the presence of a new item of information. Since revision is a central topic in knowledge representation, it has been tackled in the literature according to several points of view, symbolic or numerical, logical or probabilistic. Among the logical approaches, the AGM paradigm [Alchourron et al., 1985], in which revision is interpreted as beliefs change, has become a standard. Although very elegant, this framework does not support iterated revision because the underlying preference relation between beliefs is lost in the process of change. In fact, in this approach an epistemic state is represented by a beliefs set, i.e. a deductively closed set of sentences of a logical language, that represents the agent’s current beliefs. However, an epistemic state does not only consist of the agent’s current beliefs but also encodes the strategy that the agent uses to modify his beliefs after learning a new piece of information. A revision operator satisfying the AGM postulates is equivalent to a set of pre-orders ≤Ψ, where each pre-order corresponds to an epistemic state Ψ and is used for the revision of this state in the presence of a new observation. However the total pre-orders associated with two successive epistemic states are not related, the only requirement is that these pre-orders are faithful.

Reasoning with Partially Ordered Information in a Possibilistic Logic Framework

In many applications, the reliability relation associated with available information is only partially defined, while most of existing uncertainty frameworks deal with totally ordered pieces of knowledge. Partial pre-orders offer more flexibility than total pre-orders to represent incomplete knowledge. Possibilistic logic, which is an extension of classical logic, deals with totally ordered information. It offers a natural qualitative framework for handling uncertain information. Priorities are encoded by means of weighted formulas, where weights are lower bounds of necessity measures. This paper proposes an extension of possibilistic logic for dealing with partially ordered pieces of knowledge. We show that there are two different ways to define a possibilistic logic machinery which both extend the standard one.

Belief revision within fragments of propositional logic

Belief revision has been extensively studied in the framework of propositional logic, but just recently revision within fragments of propositional logic has gained attention. Hereby it is not only the belief set and the revision formula which are given within a certain language fragment, but also the result of the revision has to be located in the same fragment. So far, research in this direction has been mainly devoted to the Horn fragment of classical logic. In this work, we present a general approach to define new revision operators derived from known operators (as for instance, Satohs and Dalals revision operators), such that the result of the revision remains in the fragment under consideration. Our approach is not limited to the Horn case but applicable to any fragment of propositional logic where the models of the formulas are closed under a Boolean function. Thus we are able to uniformly treat cases as dual-Horn, Krom and affine formulas, as well.

Methods for Handling Imperfect Spatial Information

Spatial information is pervaded by uncertainty. Indeed, geographical data is often obtained by an imperfect interpretation of remote sensing images, while people attach ill-defined or ambiguous labels to places and their properties. As another example, medical images are often the result of measurements by imprecise sensors (e.g. MRI scans). Moreover, by processing spatial information in real-world applications, additional uncertainty is introduced, e.g. due to the use of interpolation/extrapolation techniques or to conflicts that are detected in an information fusion step. To the best of our knowledge, this book presents the first overview of spatial uncertainty which goes beyond the setting of geographical information systems. Uncertainty issues are especially addressed from a representation and reasoning point of view. In particular, the book consists of 14 chapters, which are clustered around three central topics. The first of these topics is about the uncertainty in meaning of linguistic descriptions of spatial scenes. Second, the issue of reasoning about spatial relations and dealing with inconsistency in information merging is studied. Finally, interpolation and prediction of spatial phenomena are investigated, both at the methodological level and from an application-oriented perspective. The concept of uncertainty by itself is understood in a broad sense, including both quantitative and more qualitative approaches, dealing with variability, epistemic uncertainty, as well as with vagueness of terms.

Knowledge-base revision

This paper surveys the most representative approaches of knowledge-base revision. After a description of the revision characterization according to the AGM paradigm, the paper reviews different revision methods. In each case, the same example is used, as a reference example, to illustrate the different approaches. Closely connected with revision, some other non-monotonic approaches, like update, are briefly presented.

Merging Belief Bases Represented by Logic Programs

This paper presents a method which allows for merging beliefs expressed thanks to logic programming with stable model semantics. This method is based on the syntactic merging operators described in the framework of propositional logic. The study of these operators leads to a new definition of the consequence relation between logic programs which is based on the logic of Here-and-There brought by Turner. Moreover, the specificity of the non-monotonic framework given by logic programming with stable model semantics allows for describing a weakened version of the merging operation. Once the operators are defined, their behaviour with respect to the Konieczny and Pino-Perez postulates for merging are examined and discussed.

Syntactic Propositional Belief Bases Fusion with Removed Sets

The problem of merging multiple sources information is central in several domains of computer science. In knowledge representation for artificial intelligence, several approaches have been proposed for propositional bases fusion, however, most of them are defined at a semantic level and are untractable. This paper proposes a new syntactic approach of belief bases fusion, called Removed Sets Fusion (RSF). The notion of removed-set, initially defined in the context of belief revision is extended to fusion and most of the classical fusion operations are syntactically captured by RSF. In order to efficiently implement RSF, the paper shows how RSF can be encoded into a logic program with answer set semantics, then presents an adaptation of the smodels system devoted to efficiently compute the removed sets in order to perform RSF. Finally a preliminary experimental study shows that the answer set programming approach seems promising for performing belief bases fusion on real scale applications.

Spatial Information Revision: A Comparison between 3 Approaches

The present paper deals with spatial information revision in geographical information system (GIS). These systems use incomplete and uncertain information and inconsistency can result, therefore the definition of revision operations is required. Most of the proposed belief revision operations are characterized by a high complexity and since GIS use large amount of data, adjustments of existing strategies are necessary. Taking advantage of the specificity of spatial information allows to define heuristics which speed up the general algorithms. We illustrate some suitable adjustments on 3 approaches of revision: binary decision diagrams, preferred models and Reiters algorithm for diagnostic. We formally compare them and we experiment them on a real application. In order to deal with huge amount of data we propose a divide and revise strategy in the case where inconsistencies are local.

Belief Merging within Fragments of Propositional Logic

Recently, belief change within the framework of fragments of propositional logic has gained increasing attention. Previous research focused on belief contraction and belief revision on the Horn fragment. However, the problem of belief merging within fragments of propositional logic has been mostly neglected so far. We present a general approach to defining new merging operators derived from existing ones such that the result of merging remains in the fragment under consideration. Our approach is not limited to the case of Horn fragment; it is applicable to any fragment of propositional logic characterized by a closure property on the sets of models of its formulæ. We study the logical properties of the proposed operators regarding satisfaction of merging postulates, considering, in particular, distance-based merging operators for Horn and Krom fragments.

Underwater archaeological 3D surveys validation within the removed sets framework

This paper presents the results of the VENUS european project aimed at providing scientific methodologies and technological tools for the virtual exploration of deep water archaeological sites. We focused on underwater archaeological 3D surveys validation problem. This paper shows how the validation problem has been tackled within the Removed Sets framework, according to Removed Sets Fusion (RSF) and to the Partially Preordered Removed Sets Inconsistency Handling (PPRSIH). Both approaches have been implemented thanks to ASP and the good behaviour of the Removed Sets operations is presented through an experimental study on two underwater archaeological sites.