Modeling Information Retrieval by Formal Logic

Abstract

Several mathematical frameworks have been used to model the information retrieval (IR) process, among them, formal logics. Logic-based IR models upgrade the IR process from document-query comparison to an inference process, in which both documents and queries are expressed as sentences of the selected formal logic. The underlying formal logic also permits one to represent and integrate knowledge in the IR process. One of the main obstacles that has prevented the adoption and large-scale diffusion of logic-based IR systems is their complexity. However, several logic-based IR models have been recently proposed that are applicable to large-scale data collections. In this survey, we present an overview of the most prominent logical IR models that have been proposed in the literature. The considered logical models are categorized under different axes, which include the considered logics and the way in which uncertainty has been modeled, for example, degrees of belief or degrees of truth. Accordingly, the main contribution of the article is to categorize the state-of-theart logical models on a fine-grained basis, and for the considered models the related implementation aspects are described. Consequently, the proposed survey is finalized to better understand and compare the different logical IR models. Last, but not least, this article aims at reconsidering the potentials of logical approaches to IR by outlining the advances of logic-based approaches in close research areas.K. Abdulahhad et al. information need, formulated by a query. Based on this definition, an IRS has to deal with a collection of documents, with users' information needs, and with the notion of relevance.In IR, documents are carriers of information; in their original forms, they are humanunderstandable objects (e.g., Web pages, articles, books, and images), which an IRS must transform into machine-understandable objects. This process is called indexing, and its outcome is the association of a set of features (terms in textual documents) with documents. These features constitute the basic elements employed to formally represent a document. A user's information needs are motivated by a user's information gap; a query is a representation of these needs. Once formal representations have been provided for both documents and queries, the system compares them to assess the relevance of each document to the considered query.Relevance is a complex notion composed of several dimensions, such as topicality, popularity, and novelty, as has been well pointed out in the literature [33,65,95,96]. An IRS can only estimate relevance, and generally topicality is the core relevance dimension. The assessment of topical relevance 1 relies on the definition of a model, the IR model, which provides a formal means to represent and compare both documents and queries. In this survey we use the term retrieval status value (RSV) to indicate the numerical value produced by the estimate of topical relevance.Different mathematical theories have been employed to define IR models, w...

Usefulness of Information for Achieving Goals with Disjunctive Premises

“…We will then compare those dimensions with the usefulness measure we are proposing here. However, to have a fair comparison, we need to reformulate those dimensions in a logical setting (Abdulahhad et al ., 2019; Lalmas, 1998; Chen, 1994).…”

Usefulness of Information for Goal Achievement

“…We will then compare those dimensions with the usefulness measure we are proposing here. However, to have a fair comparison, we need to reformulate those dimensions in a logical setting [1].…”