Abstract. This paper serves to bring three independent but important areas of computer science to a common meeting point: Formal Concept Analysis (FCA), Chu Spaces, and Domain Theory (DT). Each area is given a perspective or reformulation that is conducive to the flow of ideas and to the exploration of cross-disciplinary connections. Among other results, we show that the notion of state in Scott’s information system corresponds precisely to that of formal concepts in FCA with respect to all finite Chu spaces, and the entailment relation corresponds to “association rules”. We introduce, moreover, the notion of approximable concept and show that approximable concepts represent algebraic lattices which are identical to Scott domains except the inclusion of a top element. This notion serves as a stepping stone in the recent work [Hitzler and Zhang, 2004] in which a new notion of morphism on formal contexts results in a category

W.C. Rounds and G.-Q. Zhang have proposed to study a form of disjunctive logic programming generalized to algebraic domains [1]. This system allows reasoning with information which is hierarchically structured and forms a (suitable) domain. We extend this framework to include reasoning with default negation, giving rise to a new nonmonotonic reasoning framework on hierarchical knowledge which encompasses answer set programming with extended disjunctive logic programs. We also show that the hierarchically structured knowledge on which programming in this paradigm can be done, arises very naturally from formal concept analysis. Together, we obtain a default reasoning paradigm for conceptual knowledge which is in accordance with mainstream developments in nonmonotonic reasoning.

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.

Abstract. Much recent research has focused on using situations rather than individual pieces of context as a means to trigger adaptive system behaviour. While current research on situations emphasises their representation and composition, they do not provide an approach on how to organise and identify their occurrences efficiently. This paper describes how lattice theory can be utilised to organise situations, which reflects the internal structure of situations such as generalisation and dependence. We claim that situation lattices will prove beneficial in identifying situations, and maintaining the consistency and integrity of situations. They will also help in resolving the uncertainty issues inherent in context and situations by working with Bayesian Networks. 1

W.C. Rounds and G.-Q. Zhang have recently proposed to study a form of resolution on algebraic domains [1]. This framework allows reasoning with knowledge which is hierarchically structured and forms a (suitable) domain, more precisely, a coherent algebraic cpo as studied in domain theory. In this paper, we give conditions under which a resolution theorem --- in a form underlying resolution-based logic programming systems --- can be obtained. The investigations bear potential for engineering new knowledge representation and reasoning systems on a firm domain-theoretic background.