Proof Orders for Decreasing Diagrams

We present and compare some well-founded proof orders for decreasing diagrams. These proof orders order a conversion above another conversion if the latter is obtained by filling any peak in the former by a (locally) decreasing diagram. Therefore each such proof order entails the decreasing diagrams technique for proving confluence. The proof orders differ with respect to monotonicity and complexity. Our results are developed in the setting of involutive monoids. We extend these results to obtain a decreasing diagrams technique for confluence modulo

Higher-Order Interpretations and Program Complexity

Polynomial interpretations and their generalizations like quasi-interpretations have been used in the setting of first-order functional languages to design criteria ensuring statically some complexity bounds on programs. This fits in the area of implicit computational complexity, which aims at giving machine-free characterizations of complexity classes. In this paper, we extend this approach to the higher-order setting. For that we consider the notion of simply-typed term rewriting systems, we define higher-order polynomial interpretations for them and give a criterion ensuring that a program can be executed in polynomial time. In order to obtain a criterion flexible enough to validate interesting programs using higher-order primitives, we introduce a notion of polynomial quasi-interpretations, coupled with a simple termination criterion based on linear types and path-like orders

Verifying Recursive Active Documents with Positive Data Tree Rewriting

This paper proposes a data tree-rewriting framework for modeling evolving documents. The framework is close to Guarded Active XML, a platform used for handling XML repositories evolving through web services. We focus on automatic verification of properties of evolving documents that can contain data from an infinite domain. We establish the boundaries of decidability, and show that verification of a {\em positive} fragment that can handle recursive service calls is decidable. We also consider bounded model-checking in our data tree-rewriting framework and show that it is \nexptime-complete

Inconsistency-tolerant Query Answering in Ontology-based Data Access

Ontology-based data access (OBDA) is receiving great attention as a new paradigm for managing information systems through semantic technologies. According to this paradigm, a Description Logic ontology provides an abstract and formal representation of the domain of interest to the information system, and is used as a sophisticated schema for accessing the data and formulating queries over them. In this paper, we address the problem of dealing with inconsistencies in OBDA. Our general goal is both to study DL semantical frameworks that are inconsistency-tolerant, and to devise techniques for answering unions of conjunctive queries under such inconsistency-tolerant semantics. Our work is inspired by the approaches to consistent query answering in databases, which are based on the idea of living with inconsistencies in the database, but trying to obtain only consistent information during query answering, by relying on the notion of database repair. We first adapt the notion of database repair to our context, and show that, according to such a notion, inconsistency-tolerant query answering is intractable, even for very simple DLs. Therefore, we propose a different repair-based semantics, with the goal of reaching a good compromise between the expressive power of the semantics and the computational complexity of inconsistency-tolerant query answering. Indeed, we show that query answering under the new semantics is first-order rewritable in OBDA, even if the ontology is expressed in one of the most expressive members of the DL-Lite family