Visualizing Defeasible Logic Rules for the Semantic Web

Abstract

Abstract. Defeasible reasoning is a rule-based approach for efficient reasoning with incomplete and conflicting information. Such reasoning is useful in many Semantic Web applications, like policies, business rules, brokering, bargaining and agent negotiations. Nevertheless, defeasible logic is based on solid mathematical formulations and is, thus, not fully comprehensible by end users, who often need graphical trace and explanation mechanisms for the derived conclusions. Directed graphs can assist in confronting this drawback. They are a powerful and flexible tool of information visualization, offering a convenient and comprehensible way of representing relationships between entities. Their applicability, however, is balanced by the fact that it is difficult to associate data of a variety of types with the nodes and the arcs in the graph. In this paper we try to utilize digraphs in the graphical representation of defeasible rules, by exploiting the expressiveness and comprehensibility they offer, but also trying to leverage their major disadvantage, by defining two distinct node types, for rules and atomic formulas, and four distinct connection types for each rule type in defeasible logic and for superiority relationships. The paper also briefly presents a tool that implements this representation methodology.

Visualization of Proofs in Defeasible Logic

“…Each node is considered to be either an atom that participates in the body or the head of some rule or the rule itself. For the visualization of the components of the rules , we used the library of [14] which renders each node and the connections between them.…”

“…The proposed system is based on the implementation presented in [11], [12], which uses defeasible logic [13], a member of the non-monotonic logics family, as the underlying inference system. The proof representation schema adopted by our approach is based on [14], a graph-based methodology for visualizing defeasible logic rule bases.…”

Visual Stratification of Defeasible Logic Rule Bases

“…The full theoretical approach, regarding the graphical representation of defeasible reasoning elements is thoroughly described in [7]; here only a brief outline will be made. Thus, the first rule type in defeasible reasoning is strict rules, which are denoted by A → p and are interpreted in the typical sense: whenever the premises are indisputable, then so is the conclusion.…”

“…The basic theoretical principles for representing defeasible logic rules using digraphs were presented in a previous work of ours [7]. By applying digraphs, we attempt to exploit their expressiveness, but also try to mitigate their main disadvantage, mentioned above, by proposing distinct node types for rules and atomic formulas and distinct connection types for each rule type in defeasible logic and for superiority relationships.…”

Proof Explanation in the DR-DEVICE System

“…This effort includes proof visualization and visual rule execution tracing through integrating the work described in this paper with a tool for rule visualization [15] we have developed. Also, integration with the Inference Web infrastructure will be explored.…”