Rethinking Defeasible Reasoning: A Scalable Approach

Abstract

<jats:title>Abstract</jats:title><jats:p>Recent technological advances have led to unprecedented amounts of generated data that originate from the Web, sensor networks, and social media. Analytics in terms of defeasible reasoning – for example, for decision making – could provide richer knowledge of the underlying domain. Traditionally, defeasible reasoning has focused on complex knowledge structures over small to medium amounts of data, but recent research efforts have attempted to parallelize the reasoning process over theories with large numbers of facts. Such work has shown that traditional defeasible logics come with overheads that limit scalability. In this work, we design a new logic for defeasible reasoning, thus ensuring scalability by design. We establish several properties of the logic, including its relation to existing defeasible logics. Our experimental results indicate that our approach is indeed scalable and defeasible reasoning can be applied to billions of facts.</jats:p>

Approximating Defeasible Logics to Improve Scalability

“…For definition of these logics and discussion of these classifications, see [8]. 1 We present below the definition of the logic DL(∂ || ) from [15], which is ambiguity propagating and uses team defeat.…”

“…The restriction should be clear from the context. [15] has a comprehensive statement of (unrestricted) relative inference power among the inference rules we will address.…”

“…Despite propositional defeasible logics having linear complexity [13,8], the implementation of conventional first-order defeasible logics faces scalability issues [21,15]. This led to the design of the defeasible logic DL(∂ || ) [15] as a more scalable alternative to DL(∂), which is better known [16,6,7,17,2]. DL(∂ || ) has particular advantages over DL(∂) [15,14], which gives it greater potential for scalable implementation.…”

“…This led to the design of the defeasible logic DL(∂ || ) [15] as a more scalable alternative to DL(∂), which is better known [16,6,7,17,2]. DL(∂ || ) has particular advantages over DL(∂) [15,14], which gives it greater potential for scalable implementation. On the other hand, other defeasible logics have better intuitions and justifications for the reasoning they support [17,4,8].…”

“…The remainder of the paper is structured as follows. Section 2 introduces concepts from defeasible reasoning, and defines the defeasible logic DL(∂ || ) from [15]. Section 3 identifies cases where a defeasible theory is decisive, that is, every literal can either be defeasibly inferred (D ⊢ +d q) or provably not defeasible inferred (D ⊢ −d q).…”