Semantics for possibilistic answer set programs: uncertain rules versus rules with uncertain conclusions

Although Answer Set Programming (ASP) is a powerful framework for declarative problem solving, it cannot in an intuitive way handle situations in which some rules are uncertain, or in which it is more important to satisfy some constraints than others. Possibilistic ASP (PASP) is a natural extension of ASP in which certainty weights are associated with each rule. In this paper we contrast two different views on interpreting the weights attached to rules. Under the first view, weights reflect the certainty with which we can conclude the head of a rule when its body is satisfied. Under the second view, weights reflect the certainty that a given rule restricts the considered epistemic states of an agent in a valid way, i.e. it is the certainty that the rule itself is correct. The first view gives rise to a set of weighted answer sets, whereas the second view gives rise to a weighted set of classical answer sets.

Interpretable and Reconfigurable Clustering of Document Datasets by Deriving Word-based Rules

Clusters of text documents output by clustering algorithms are often hard to interpret. We describe motivating real-world scenarios that necessitate reconfigurability and high interpretability of clusters and outline the problem of generating clusterings with interpretable and reconfigurable cluster models. We develop two clustering algorithms toward the outlined goal of building interpretable and reconfigurable cluster models. They generate clusters with associated rules that are composed of conditions on word occurrences or nonoccurrences. The proposed approaches vary in the complexity of the format of the rules; RGC employs disjunctions and conjunctions in rule generation whereas RGC-D rules are simple disjunctions of conditions signifying presence of various words. In both the cases, each cluster is comprised of precisely the set of documents that satisfy the corresponding rule. Rules of the latter kind are easy to interpret, whereas the former leads to more accurate clustering. We show that our approaches outperform the unsupervised decision tree approach for rule-generating clustering and also an approach we provide for generating interpretable models for general clusterings, both by significant margins. We empirically show that the purity and f-measure losses to achieve interpretability can be as little as 3 and 5%, respectively using the algorithms presented herein.

Answer set programs with optional rules: a possibilistic approach

Many problems in artificial intelligence can be encoded as answer set programs (ASP) in which some rules are uncertain. ASP programs with incorrect rules may have erroneous conclusions, but due to the non-monotonic nature of ASP, omitting a correct rule may also lead to errors. To derive the most certain conclusions from an uncertain ASP program, we thus need to consider all situations in which some, none, or all of the least certain rules are omitted. This corresponds to treating some rules as optional and reasoning about which conclusions remain valid regardless of the inclusion of these optional rules. While a version of possibilistic ASP (PASP) based on this view has recently been introduced, no implementation is currently available. In this paper we propose a simulation of the main reasoning tasks in PASP using (disjunctive) ASP programs, allowing us to take advantage of state-of-the-art ASP solvers. Furthermore, we identify how several interesting AI problems can be naturally seen as special cases of the considered reasoning tasks, including cautious abductive reasoning and conformant planning. As such, the proposed simulation enables us to solve instances of the latter problem types that are more general than what current solvers can handle.

The basic principles of uncertain information fusion. An organised review of merging rules in different representation frameworks.

We propose and advocate basic principles for the fusion of incomplete or uncertain information items, that should apply regardless of the formalism adopted for representing pieces of information coming from several sources. This formalism can be based on sets, logic, partial orders, possibility theory, belief functions or imprecise probabilities. We propose a general notion of information item representing incomplete or uncertain information about the values of an entity of interest. It is supposed to rank such values in terms of relative plausibility, and explicitly point out impossible values. Basic issues affecting the results of the fusion process, such as relative information content and consistency of information items, as well as their mutual consistency, are discussed. For each representation setting, we present fusion rules that obey our principles, and compare them to postulates specific to the representation proposed in the past. In the crudest (Boolean) representation setting (using a set of possible values), we show that the understanding of the set in terms of most plausible values, or in terms of non-impossible ones matters for choosing a relevant fusion rule. Especially, in the latter case our principles justify the method of maximal consistent subsets, while the former is related to the fusion of logical bases. Then we consider several formal settings for incomplete or uncertain information items, where our postulates are instantiated: plausibility orderings, qualitative and quantitative possibility distributions, belief functions and convex sets of probabilities. The aim of this paper is to provide a unified picture of fusion rules across various uncertainty representation settings.