Characterization, definability and separation via saturated models

Three important results about the expressivity of a modal logic L are the Characterization Theorem (that identifies a modal logic L as a fragment of a better known logic), the Definability theorem (that provides conditions under which a class of L-models can be defined by a formula or a set of formulas of L), and the Separation Theorem (that provides conditions under which two disjoint classes of L-models can be separated by a class definable in L). We provide general conditions under which these results can be established for a given choice of model class and modal language whose expressivity is below first order logic. Besides some basic constraints that most modal logics easily satisfy, the fundamental condition that we require is that the class of ω-saturated models in question has the Hennessy-Milner property with respect to the notion of observational equivalence under consideration. Given that the Characterization, Definability and Separation theorems are among the cornerstones in the model theory of L, this property can be seen as a test that identifies the adequate notion of observational equivalence for a particular modal logic.submittedVersionFil: Areces, Carlos Eduardo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Areces, Carlos Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.Fil: Carreiro, Facundo. Universidad de Ámsterdam. Instituto de Lógica, Lenguaje y Computación; Países Bajos.Fil: Figueira, Santiago. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina.Fil: Figueira, Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.Ciencias de la Computació

KeyQuery : improving the preciseness of search engines by automatic translation of keywords into structured queries

We demonstrate an approach to transform keyword queries automatically into queries that combine keywords appropriately by boolean operations, such as and and or. Most current search engines will preprocess the queries before they really use these queries to search locally stored files or web pages. However, the search engines usually only provide spell-check or word subsumption. Some search engines support boolean operators. However, typical users do not use them or use them incorrectly. Our approach helps to improve the precision of keyword queries. It is based on the analysis of keywords in a taxonomy. The transformed queries will be sent to search engines and the returned results will be presented to users. We evaluate the effectiveness of our approach by comparing the precision of the returned results with the precision of original results.Keywords: Search engine, boolean operator, query translation, taxonomy, precisio

Model-theoretic characterisations of description logics

The growing need for computer aided processing of knowledge has led to an increasing interest in description logics (DLs), which are applied to encode knowledge in order to make it explicit and accessible to logical reasoning. DLs and in particular the family around the DL ALC have therefore been thoroughly investigated w.r.t. their complexity theory and proof theory. The question arises which expressiveness these logics actually have. The expressiveness of a logic can be inferred by a model theoretic characterisation. On concept level, these DLs are akin to modal logics whose model theoretic properties have been investigated. Yet the model theoretic investigation of the DLs with their TBoxes, which are an original part of DLs usually not considered in context of modal logics, have remained unstudied. This thesis studies the model theoretic properties of ALC, ALCI, ALCQ, as well as ALCO, ALCQO, ALCQIO and EL. It presents model theoretic properties, which characterise these logics as fragments of the first order logic (FO). The characterisations are not only carried out on concept level and on concept level extended by the universal role, but focus in particular on TBoxes. The properties used to characterise the logics are `natural' notions w.r.t. the logic under investigation: On the concept-level, each of the logics is characterised by an adapted form of bisimulation and simulation, respectively. TBoxes of ALC, ALCI and ALCQ are characterised as fragments of FO which are invariant under global bisimulation and disjoint unions. The logics ALCO, ALCQO and ALCQIO, which incorporate individuals, are characterised w.r.t. to the class K of all interpretations which interpret individuals as singleton sets. The characterisations for TBoxes of ALCO and ALCQO both require, additionally to being invariant under the appropriate notion of global bisimulation and an adapted version of disjoint unions, that an FO-sentence is, under certain circumstances, preserved under forward generated subinterpretations. FO-sentences equivalent to ALCQIO-TBoxes, are - due to ALCQIO's inverse roles - characterised similarly to ALCO and ALCQO but have as third additional requirement that they are preserved under generated subinterpretations. EL as sub-boolean DL is characterised on concept level as the FO-fragment which is preserved under simulation and preserved under direct products. Equally valid is the characterisation by being preserved under simulation and having minimal models. For EL-TBoxes, a global version of simulation was not sufficient but FO-sentences of EL-TBoxes are invariant under global equi-simulation, disjoint unions and direct products. For each of these description logics, the characteristic concepts are explicated and the characterisation is accompanied by an investigation under which notion of saturation the logic in hand enjoys the Hennessy-and-Milner-Property. As application of the results we determine the minimal globally bisimilar companion w.r.t. ALCQO-bisimulation and introduce the L1-to-L2-rewritability problem for TBoxes, where L1 and L2 are (description) logics. The latter is the problem to decide whether or not an L1-TBox can be equivalently expressed as L2-TBox. We give algorithms which decide ALCI-to-ALC-rewritability and ALC-to-EL-rewritability

Classifying Description Logics

We describe a method for characterizing the expressive power of description logics. The method is essentially model-theoretic in nature, and it is applied to obtain expressiveness results for a wide range of logics in the well-known FL \Gamma and AL hierarchies. As a corollary we obtain a complete classification of the relative expressive power of these logics