Towards Collaborative Conceptual Exploration

In domains with high knowledge distribution a natural objective is to create principle foundations for collaborative interactive learning environments. We present a first mathematical characterization of a collaborative learning group, a consortium, based on closure systems of attribute sets and the well-known attribute exploration algorithm from formal concept analysis. To this end, we introduce (weak) local experts for subdomains of a given knowledge domain. These entities are able to refute and potentially accept a given (implicational) query for some closure system that is a restriction of the whole domain. On this we build up a consortial expert and show first insights about the ability of such an expert to answer queries. Furthermore, we depict techniques on how to cope with falsely accepted implications and on combining counterexamples. Using notions from combinatorial design theory we further expand those insights as far as providing first results on the decidability problem if a given consortium is able to explore some target domain. Applications in conceptual knowledge acquisition as well as in collaborative interactive ontology learning are at hand.Comment: 15 pages, 2 figure

Formal Concept Analysis and Resolution in Algebraic Domains

We relate two formerly independent areas: Formal concept analysis and logic of domains. We will establish a correspondene between contextual attribute logic on formal contexts resp. concept lattices and a clausal logic on coherent algebraic cpos. We show how to identify the notion of formal concept in the domain theoretic setting. In particular, we show that a special instance of the resolution rule from the domain logic coincides with the concept closure operator from formal concept analysis. The results shed light on the use of contexts and domains for knowledge representation and reasoning purposes.Comment: 14 pages. We have rewritten the old version according to the suggestions of some referees. The results are the same. The presentation is completely differen

Learning definite Horn formulas from closure queries

A definite Horn theory is a set of n-dimensional Boolean vectors whose characteristic function is expressible as a definite Horn formula, that is, as conjunction of definite Horn clauses. The class of definite Horn theories is known to be learnable under different query learning settings, such as learning from membership and equivalence queries or learning from entailment. We propose yet a different type of query: the closure query. Closure queries are a natural extension of membership queries and also a variant, appropriate in the context of definite Horn formulas, of the so-called correction queries. We present an algorithm that learns conjunctions of definite Horn clauses in polynomial time, using closure and equivalence queries, and show how it relates to the canonical Guigues–Duquenne basis for implicational systems. We also show how the different query models mentioned relate to each other by either showing full-fledged reductions by means of query simulation (where possible), or by showing their connections in the context of particular algorithms that use them for learning definite Horn formulas.Peer ReviewedPostprint (author's final draft

Attribute exploration with fuzzy attributes and background knowledge

Abstract. Attribute exploration is a formal concept analytical tool for knowledge discovery by interactive determination of the implications holding between a given set of attributes. The corresponding algorithm queries the user in an efficient way about the implications between the attributes. The result of the exploration process is a representative set of examples for the entire theory and a set of implications from which all implications that hold between the considered attributes can be deduced. The method was successfully applied in different real-life applications for discrete data. In many instances, the user may know some implications before the exploration starts. These are considered as background knowledge and their usage shortens the exploration process. In this paper we show that the handling of background information can be generalised to the fuzzy setting

Extending Attribute Exploration by Means of Boolean Derivatives

We present a translation of problems of Formal Context Analysis into ideals problems in F2[x] through the Boolean derivatives. The Boolean derivatives are introduced as a kind of operators on propositional formulas which provide a complete calculus. They are useful to refine stem basis as well as for extending attribute exploration

Non-Redundant Implicational Base of Many-Valued Context Using SAT

Some attribute implications in an implicational base of a derived context of many-valued context can be inferred from some other attribute implications together with its scales. The scales are interpretation of some values in the many-valued context therefore they are a prior or an existing knowledge. In knowledge discovery, the such attribute implications are redundant and cannot be considered as new knowledge. Therefore the attribute implicational should be eliminated. This paper shows that the redundancy problem exists and formalizes a model to check the redundancy

Towards semantic web mining

Semantic Web Mining aims at combining the two fast-developing research areas Semantic Web and Web Mining. The idea is to improve, on the one hand, the results of Web Mining by exploiting the new semantic structures in the Web; and to make use of Web Mining, on the other hand, for building up the Semantic Web. This paper gives an overview of where the two areas meet today, and sketches ways of how a closer integration could be profitable