Frithjof Dau

Concept Similarity and Related Categories in SearchSleuth

SearchSleuth is a program developed to experiment with the automated local analysis of Web search using formal concept analysis. SearchSleuth extends a standard search interface to include a conceptual neighborhood centered on a formal concept derived from the initial query. This neighborhood of the concept derived from the search terms is decorated with its upper and lower neighbors representing more general and specialized concepts respectively. In SearchSleuth, the notion of related categories --- which are themselves formal concepts --- is also introduced. This allows the retrieval focus to shift to a new formal concept called a sibling. This movement across the concept lattice needs to relate one formal concept to another in a principled way. This paper presents the issues concerning exploring and ordering the space of related categories.

A diagrammatic reasoning system for the description logic ALC

Diagrammatic reasoning is a tradition of visual logic that allows sentences that are equivalent to first order logic to be written in a visual or structural form: usually for improved usability. A calculus for the diagram can then be defined that allows well-formed formulas to be derived. This calculus is intended in the analog of logical inference. Description logics (DLs) have become a popular knowledge representation and processing language. DLs correspond to decidable fragments of first order logic; their notation is in the style of symbolic, variable-free formulas. Moreover, DLs are equipped with table au theorem provers that are proven to be sound and complete. Although DLs have roots in diagrammatic languages (such as semantic networks), they are elaborated in a purely symbolic manner. This paper discusses how DLs can be equivalently represented in terms of a diagrammatic reasoning system. First, existing diagrammatic reasoning systems, namely spider- and constraint diagrams, as well as existential and conceptual graphs, are investigated to determine if they are compatible with DLs. It turns out that Peirces existential graphs are better suited for this purpose than the alternatives we examine. The paper then redevelops the DL ALC, which is the smallest propositional DL, by means of labeled trees, and provides a diagrammatic representation for these trees in the style of Peircean graphs. We provide a calculus based on C.S. Peirces calculus for existential graphs and prove the soundness and completeness of the calculus. The calculus acts on labeled trees, but can be best understood as a diagrammatic calculus whose rules modify the Peircean-style representation of ALC.

Concept similarity and related categories in information retrieval using formal concept analysis

The application of formal concept analysis to the problem of information retrieval has been shown useful but has lacked any real analysis of the idea of relevance ranking of search results. SearchSleuth is a program developed to experiment with the automated local analysis of Web search using formal concept analysis. SearchSleuth extends a standard search interface to include a conceptual neighbourhood centred on a formal concept derived from the initial query. This neighbourhood of the concept derived from the search terms is decorated with its upper and lower neighbours representing more general and special concepts, respectively. SearchSleuth is in many ways an archetype of search engines based on formal concept analysis with some novel features. In SearchSleuth, the notion of related categories – which are themselves formal concepts – is also introduced. This allows the retrieval focus to shift to a new formal concept called a sibling. This movement across the concept lattice needs to relate one formal concept to another in a principled way. This paper presents the issues concerning exploring, searching, and ordering the space of related categories. The focus is on understanding the use and meaning of proximity and semantic distance in the context of information retrieval using formal concept analysis.

Conceptual Spider Diagrams

Conceptual Graphs are a common knowledge representation system which are used in conjunction with an explicit type hierarchy of the domain. However, this means the interpretation of information expressed in conceptual graphs requires the combined use of information from different sources, which is not always an easy cognitive task. Though it is possible to explicitly represent the type hierarchy with Conceptual Graphs with Cuts, this less natural expression of the type hierarchy information is not as easy to interpret and soon takes up a lot of space. Now, one of the main advantages of Euler diagram-based notations like Spider diagrams is the natural diagrammatic representation of hierarchies. However, Spider diagrams lack facilities such as the ability to represent general relationships between objects which is necessary for knowledge representation tasks. We bring together the most pertinent features of both of these notations, creating a new hybrid notation called Conceptual Spider Diagrams. We provide formal syntax and semantics of this new notation, together with examples demonstrating its capabilities.

Constants and Functions in Peirce's Existential Graphs

The system of Peirces existential graphs is a diagrammatic version of first order logic. To be more precise: As Peirce wanted to develop a logic of relatives(i.e., relations), existential graphs correspond to first order logic with relations and identity, but without constants or functions. In contemporary elaborations of first order logic, constants and functions are usually employed. In this paper, it is described how the syntax, semantics and calculus for Peirces existential graphs has to be extended in order to encompass constants and functions as well.

Xeena for schema: creating XML documents with a coordinated grammar tree

The vast heterogeneous network that is the World Wide Web requires common languages to facilitate the exchange and display of data and information in many forms. The Word Wide Web Consortium (W3C) developed the extensible markup language (XML) for this purpose. XML documents are produced automatically by applications or manually by users. When users do not produce documents regularly or when document languages are large and complex, manual editing can be a challenge. In these situations, better manual editing facilities that guide users and ease the burden of learning and recalling XML languages are needed. We present an XML editor design implemented in our Xeena for schema editor that addresses these needs. It is based on a new tree based grammar view that guides novice users and empowers experienced users to build XML documents. It lets users see and edit multiple levels of potential elements, unlike existing editors that present only one level of potential elements. We demonstrate its key features, present our grammar tree view design both informally and formally, and describe a user evaluation that supports the usability of our design.

A diagrammatic reasoning system for ALC

Description logics (DLs) are a well-known family of knowledge representation (KR) languages. The notation of DLs has the style of a variable-free first order predicate logic. In this paper a diagrammatic representation of the DL ALC- based on Peirces existential graphs - is presented and a set of transformation rules on these graphs provided. As the transformation rules modify the diagrammatic representation of ALC this produces a diagrammatic calculus. Some examples present in the paper illustrate the use and properties of this calculus.

A formalism for navigating and editing XML document structure

The use of XML has become pervasive. It is used in a range of data storage and data exchange applications. In many cases such XML data is captured from users via forms or transformed automatically from databases. However, there are still many situations where users must read and possibly write their own XML documents. There are a variety of both commercial and free XML editors that address this need. A limitation of most editors is that they require users to be familar with the grammar of the XML document they are creating. A better approach is to provide users with a view of a documents grammar that is integrated in some way to aid the user. In this paper, we formalise and extend the design of such an editor, Xeena for Schema. It uses a grammar tree view to explicitly guide user navigation and editing. We identify a key property that such an editor should have, stable reversable navigation, then via our formal treatment extend the Xeena for Schema design to satisfy it.