Where Fail-Safe Default Logics Fail

Reiter's original definition of default logic allows for the application of a default that contradicts a previously applied one. We call failure this condition. The possibility of generating failures has been in the past considered as a semantical problem, and variants have been proposed to solve it. We show that it is instead a computational feature that is needed to encode some domains into default logic

The Toulmin Model and Non-monotonic Reasoning

While the nature of warrants is unclear in both Toulmin’s Uses of Argument and in textbook pedagogy based on it, the theory of non-monotonic reasoning could clarify and enhance our understanding of warrants

Towards an Enforceable GDPR Specification

While Privacy by Design (PbD) is prescribed by modern privacy regulations such as the EU's GDPR, achieving PbD in real software systems is a notoriously difficult task. One emerging technique to realize PbD is Runtime enforcement (RE), in which an enforcer, loaded with a specification of a system's privacy requirements, observes the actions performed by the system and instructs it to perform actions that will ensure compliance with these requirements at all times. To be able to use RE techniques for PbD, privacy regulations first need to be translated into an enforceable specification. In this paper, we report on our ongoing work in formalizing the GDPR. We first present a set of requirements and an iterative methodology for creating enforceable formal specifications of legal provisions. Then, we report on a preliminary case study in which we used our methodology to derive an enforceable specification of part of the GDPR. Our case study suggests that our methodology can be effectively used to develop accurate enforceable specifications

Grounded Fixpoints and Active Integrity Constraints

The formalism of active integrity constraints was introduced as a way to specify particular classes of integrity constraints over relational databases together with preferences on how to repair existing inconsistencies. The rule-based syntax of such integrity constraints also provides algorithms for finding such repairs that achieve the best asymptotic complexity. However, the different semantics that have been proposed for these integrity constraints all exhibit some counter-intuitive examples. In this work, we look at active integrity constraints using ideas from algebraic fixpoint theory. We show how database repairs can be modeled as fixpoints of particular operators on databases, and study how the notion of grounded fixpoint induces a corresponding notion of grounded database repair that captures several natural intuitions, and in particular avoids the problems of previous alternative semantics. In order to study grounded repairs in their full generality, we need to generalize the notion of grounded fixpoint to non-deterministic operators. We propose such a definition and illustrate its plausibility in the database context

Borhan: A Novel System for Prioritized Default Logic

Prioritized Default Logic presents an optimal solution for addressing real-world problems characterized by incomplete information and the need to establish preferences among diverse scenarios. Although it has reached great success in the theoretical aspect, its practical implementation has received less attention. In this article, we introduce Borhan, a system designed and created for prioritized default logic reasoning. To create an effective system, we have refined existing default logic definitions, including the extension concept, and introduced novel concepts. In addition to its theoretical merits, Borhan proves its practical utility by efficiently addressing a range of prioritized default logic problems. In addition, one of the advantages of our system is its ability to both store and report the explanation path for any inferred triple, enhancing transparency and interpretability. Borhan is offered as an open-source system, implemented in Python, and even offers a simplified Java version as a plugin for the Protege ontology editor. Borhan thus represents a significant step forward in bridging the gap between the theoretical foundations of default logic and its real-world applications