Defeasible Systems in Legal Reasoning: A Comparative Assessment

Different formalisms for defeasible reasoning have been used to represent legal knowledge and to reason with it. In this work, we provide an overview of the following logic-based approaches to defeasible reasoning: Defeasible Logic, Answer Set Programming, ABA+, ASPIC+, and DeLP. We compare features of these approaches from three perspectives: the logical model (knowledge representation), the method (computational mechanisms), and the technology (available software). On this basis, we identify and apply criteria for assessing their suitability for legal applications. We discuss the different approaches through a legal running example

Argumentation and Defeasible Reasoning in the Law

Different formalisms for defeasible reasoning have been used to represent knowledge and reason in the legal field. In this work, we provide an overview of the following logic-based approaches to defeasible reasoning: defeasible logic, Answer Set Programming, ABA+, ASPIC+, and DeLP. We compare features of these approaches under three perspectives: the logical model (knowledge representation), the method (computational mechanisms), and the technology (available software resources). On top of that, two real examples in the legal domain are designed and implemented in ASPIC+ to showcase the benefit of an argumentation approach in real-world domains. The CrossJustice and Interlex projects are taken as a testbed, and experiments are conducted with the Arg2P technology

Counterfactual Explanation Generation with s(CASP)

Machine learning models that automate decision-making are increasingly being used in consequential areas such as loan approvals, pretrial bail, hiring, and many more. Unfortunately, most of these models are black-boxes, i.e., they are unable to reveal how they reach these prediction decisions. A need for transparency demands justification for such predictions. An affected individual might desire explanations to understand why a decision was made. Ethical and legal considerations may further require informing the individual of changes in the input attribute that could be made to produce a desirable outcome. This paper focuses on the latter problem of automatically generating counterfactual explanations. Our approach utilizes answer set programming and the s(CASP) goal-directed ASP system. Answer Set Programming (ASP) is a well-known knowledge representation and reasoning paradigm. s(CASP) is a goal-directed ASP system that executes answer-set programs top-down without grounding them. The query-driven nature of s(CASP) allows us to provide justifications as proof trees, which makes it possible to analyze the generated counterfactual explanations. We show how counterfactual explanations are computed and justified by imagining multiple possible worlds where some or all factual assumptions are untrue and, more importantly, how we can navigate between these worlds. We also show how our algorithm can be used to find the Craig Interpolant for a class of answer set programs for a failing query.Comment: 18 Page

Defeasible Logic Programming: An Argumentative Approach

The work reported here introduces Defeasible Logic Programming (DeLP), a formalism that combines results of Logic Programming and Defeasible Argumentation. DeLP provides the possibility of representing information in the form of weak rules in a declarative manner, and a defeasible argumentation inference mechanism for warranting the entailed conclusions. In DeLP an argumentation formalism will be used for deciding between contradictory goals. Queries will be supported by arguments that could be defeated by other arguments. A query q will succeed when there is an argument A for q that is warranted, ie, the argument A that supports q is found undefeated by a warrant procedure that implements a dialectical analysis. The defeasible argumentation basis of DeLP allows to build applications that deal with incomplete and contradictory information in dynamic domains. Thus, the resulting approach is suitable for representing agent's knowledge and for providing an argumentation based reasoning mechanism to agents.Comment: 43 pages, to appear in the journal "Theory and Practice of Logic Programming

A Logic Programming Approach to Knowledge-State Planning: Semantics and Complexity

We propose a new declarative planning language, called K, which is based on principles and methods of logic programming. In this language, transitions between states of knowledge can be described, rather than transitions between completely described states of the world, which makes the language well-suited for planning under incomplete knowledge. Furthermore, it enables the use of default principles in the planning process by supporting negation as failure. Nonetheless, K also supports the representation of transitions between states of the world (i.e., states of complete knowledge) as a special case, which shows that the language is very flexible. As we demonstrate on particular examples, the use of knowledge states may allow for a natural and compact problem representation. We then provide a thorough analysis of the computational complexity of K, and consider different planning problems, including standard planning and secure planning (also known as conformant planning) problems. We show that these problems have different complexities under various restrictions, ranging from NP to NEXPTIME in the propositional case. Our results form the theoretical basis for the DLV^K system, which implements the language K on top of the DLV logic programming system.Comment: 48 pages, appeared as a Technical Report at KBS of the Vienna University of Technology, see http://www.kr.tuwien.ac.at/research/reports

Answer Set Planning Under Action Costs

Recently, planning based on answer set programming has been proposed as an approach towards realizing declarative planning systems. In this paper, we present the language Kc, which extends the declarative planning language K by action costs. Kc provides the notion of admissible and optimal plans, which are plans whose overall action costs are within a given limit resp. minimum over all plans (i.e., cheapest plans). As we demonstrate, this novel language allows for expressing some nontrivial planning tasks in a declarative way. Furthermore, it can be utilized for representing planning problems under other optimality criteria, such as computing ``shortest'' plans (with the least number of steps), and refinement combinations of cheapest and fastest plans. We study complexity aspects of the language Kc and provide a transformation to logic programs, such that planning problems are solved via answer set programming. Furthermore, we report experimental results on selected problems. Our experience is encouraging that answer set planning may be a valuable approach to expressive planning systems in which intricate planning problems can be naturally specified and solved