On the probabilistic logical modelling of quantum and geometrically-inspired IR

Information Retrieval approaches can mostly be classed into probabilistic, geometric or logic-based. Recently, a new unifying framework for IR has emerged that integrates a probabilistic description within a geometric framework, namely vectors in Hilbert spaces. The geometric model leads naturally to a predicate logic over linear subspaces, also known as quantum logic. In this paper we show the relation between this model and classic concepts such as the Generalised Vector Space Model, highlighting similarities and differences. We also show how some fundamental components of quantum-based IR can be modelled in a descriptive way using a well-established tool, i.e. Probabilistic Datalog

Declarative Rules for Annotated Expert Knowledge in Change Management

In this paper, we use declarative and domain-specific languages for representing expert knowledge in the field of change management in organisational psychology. Expert rules obtained in practical case studies are represented as declarative rules in a deductive database. The expert rules are annotated by information describing their provenance and confidence. Additional provenance information for the whole - or parts of the - rule base can be given by ontologies. Deductive databases allow for declaratively defining the semantics of the expert knowledge with rules; the evaluation of the rules can be optimised and the inference mechanisms could be changed, since they are specified in an abstract way. As the logical syntax of rules had been a problem in previous applications of deductive databases, we use specially designed domain-specific languages to make the rule syntax easier for non-programmers. The semantics of the whole knowledge base is declarative. The rules are written declaratively in an extension datalogs of the well-known deductive database language datalog on the data level, and additional datalogs rules can configure the processing of the annotated rules and the ontologies

Ontology Module Extraction via Datalog Reasoning

Module extraction - the task of computing a (preferably small) fragment M of an ontology T that preserves entailments over a signature S - has found many applications in recent years. Extracting modules of minimal size is, however, computationally hard, and often algorithmically infeasible. Thus, practical techniques are based on approximations, where M provably captures the relevant entailments, but is not guaranteed to be minimal. Existing approximations, however, ensure that M preserves all second-order entailments of T w.r.t. S, which is stronger than is required in many applications, and may lead to large modules in practice. In this paper we propose a novel approach in which module extraction is reduced to a reasoning problem in datalog. Our approach not only generalises existing approximations in an elegant way, but it can also be tailored to preserve only specific kinds of entailments, which allows us to extract significantly smaller modules. An evaluation on widely-used ontologies has shown very encouraging results.Comment: 13 pages. To appear in AAAI-1

Logics for Unranked Trees: An Overview

Labeled unranked trees are used as a model of XML documents, and logical languages for them have been studied actively over the past several years. Such logics have different purposes: some are better suited for extracting data, some for expressing navigational properties, and some make it easy to relate complex properties of trees to the existence of tree automata for those properties. Furthermore, logics differ significantly in their model-checking properties, their automata models, and their behavior on ordered and unordered trees. In this paper we present a survey of logics for unranked trees