A decidable subclass of finitary programs

Answer set programming - the most popular problem solving paradigm based on logic programs - has been recently extended to support uninterpreted function symbols. All of these approaches have some limitation. In this paper we propose a class of programs called FP2 that enjoys a different trade-off between expressiveness and complexity. FP2 programs enjoy the following unique combination of properties: (i) the ability of expressing predicates with infinite extensions; (ii) full support for predicates with arbitrary arity; (iii) decidability of FP2 membership checking; (iv) decidability of skeptical and credulous stable model reasoning for call-safe queries. Odd cycles are supported by composing FP2 programs with argument restricted programs

Partial Preferences for Mediated Bargaining

In this work we generalize standard Decision Theory by assuming that two outcomes can also be incomparable. Two motivating scenarios show how incomparability may be helpful to represent those situations where, due to lack of information, the decision maker would like to maintain different options alive and defer the final decision. In particular, a new axiomatization is given which turns out to be a weakening of the classical set of axioms used in Decision Theory. Preliminary results show how preferences involving complex distributions are related to judgments on single alternatives.Comment: In Proceedings SR 2014, arXiv:1404.041

On finitely recursive programs

Disjunctive finitary programs are a class of logic programs admitting function symbols and hence infinite domains. They have very good computational properties, for example ground queries are decidable while in the general case the stable model semantics is highly undecidable. In this paper we prove that a larger class of programs, called finitely recursive programs, preserves most of the good properties of finitary programs under the stable model semantics, namely: (i) finitely recursive programs enjoy a compactness property; (ii) inconsistency checking and skeptical reasoning are semidecidable; (iii) skeptical resolution is complete for normal finitely recursive programs. Moreover, we show how to check inconsistency and answer skeptical queries using finite subsets of the ground program instantiation. We achieve this by extending the splitting sequence theorem by Lifschitz and Turner: We prove that if the input program P is finitely recursive, then the partial stable models determined by any smooth splitting omega-sequence converge to a stable model of P.Comment: 26 pages, Preliminary version in Proc. of ICLP 2007, Best paper awar

The Complexity of Enriched Mu-Calculi

The fully enriched μ-calculus is the extension of the propositional μ-calculus with inverse programs, graded modalities, and nominals. While satisfiability in several expressive fragments of the fully enriched μ-calculus is known to be decidable and ExpTime-complete, it has recently been proved that the full calculus is undecidable. In this paper, we study the fragments of the fully enriched μ-calculus that are obtained by dropping at least one of the additional constructs. We show that, in all fragments obtained in this way, satisfiability is decidable and ExpTime-complete. Thus, we identify a family of decidable logics that are maximal (and incomparable) in expressive power. Our results are obtained by introducing two new automata models, showing that their emptiness problems are ExpTime-complete, and then reducing satisfiability in the relevant logics to these problems. The automata models we introduce are two-way graded alternating parity automata over infinite trees (2GAPTs) and fully enriched automata (FEAs) over infinite forests. The former are a common generalization of two incomparable automata models from the literature. The latter extend alternating automata in a similar way as the fully enriched μ-calculus extends the standard μ-calculus.Comment: A preliminary version of this paper appears in the Proceedings of the 33rd International Colloquium on Automata, Languages and Programming (ICALP), 2006. This paper has been selected for a special issue in LMC

Big Data and Analytics in the Age of the GDPR

The new European General Data Protection Regulation places stringent restrictions on the processing of personally identifiable data. The GDPR does not only affect European companies, as the regulation applies to all the organizations that track or provide services to European citizens. Free exploratory data analysis is permitted only on anonymous data, at the cost of some legal risks.We argue that for the other kinds of personal data processing, the most flexible and safe legal basis is explicit consent. We illustrate the approach to consent management and compliance with the GDPR being developed by the European H2020 project SPECIAL, and highlight some related big data aspects

Expressive Non-Monotonic Description Logics Based on Circumscription

Recent applications of description logics (DLs) strongly suggest the integration of non-monotonic features into DLs, with particular attention to defeasible inheritance. However, the existing non-monotonic extensions of DLs are usually based on default logic or autoepistemic logic, and have to be seriously restricted in expressive power to preserve the decidability of reasoning. In particular, such DLs allow the modelling of defeasible inheritance only in a very restricted form, where non-monotonic reasoning is limited to individuals that are explicitly identified by constants in the knowledge base. In this paper, we consider non-monotonic extensions of expressive DLs based on circumscription. We prove that reasoning in such DLs is decidable even without the usual, strong restrictions in expressive power. We pinpoint the exact computational complexity of reasoning as complete for NPNEXP and NEXPNP, depending on whether or not the number of minimized and fixed predicates is assumed to be bounded by a constant. These results assume that only concept names (and no role names) can be minimized and fixed during minimization. On the other hand, we show that fixing role names during minimization makes reasoning undecidable

Transparent Personal Data Processing: The Road Ahead

The European General Data Protection Regulation defines a set of obligations for personal data controllers and processors. Primary obligations include: obtaining explicit consent from the data subject for the processing of personal data, providing full transparency with respect to the processing, and enabling data rectification and erasure (albeit only in certain circumstances). At the core of any transparency architecture is the logging of events in relation to the processing and sharing of personal data. The logs should enable verification that data processors abide by the access and usage control policies that have been associated with the data based on the data subject's consent and the applicable regulations. In this position paper, we: (i) identify the requirements that need to be satisfied by such a transparency architecture, (ii) examine the suitability of existing logging mechanisms in light of said requirements, and (iii) present a number of open challenges and opportunities

Machine Understandable Policies and GDPR Compliance Checking

The European General Data Protection Regulation (GDPR) calls for technical and organizational measures to support its implementation. Towards this end, the SPECIAL H2020 project aims to provide a set of tools that can be used by data controllers and processors to automatically check if personal data processing and sharing complies with the obligations set forth in the GDPR. The primary contributions of the project include: (i) a policy language that can be used to express consent, business policies, and regulatory obligations; and (ii) two different approaches to automated compliance checking that can be used to demonstrate that data processing performed by data controllers / processors complies with consent provided by data subjects, and business processes comply with regulatory obligations set forth in the GDPR