A Logical Framework for XML Reference Specification

XML emerged as the (meta) mark-up language for representing, exchanging, or storing semistructured data. The structure of an XML document may be specified through DTD (Document Type Definition) language or through the specific XML language XSchema. While the expressiveness of XML Schema allows one to specify both the structure and constraints for XML documents, DTD does not allow the specification of integrity constraints for XML documents. On the other side, DTD has a very compact notation opposed to the complex notation and syntax of XML Schema. According to this scenario, in this paper we focus on a (as much as possible) simple logic, called XHyb, expressive enough to allow the specification of the most common integrity constraints in XML documents. In particular we will deal with constraints on ID and IDREF(S) attributes, which are the common way of logically connecting parts of XML documents, besides the usual containment relation of XML elements

Computer-Aided Reasoning about Knowledge and Justifications

In the first Chapter we compare two well-known type-based computer frameworks for computer aided logical reasoning and verification: MetaPRL and Coq. In particular, we implement in MetaPRL the Calculus of Inductive Constructions which is the theoretical base for Coq. This work has shown the common points of MetaPRL and Coq, and revealed their principal methodological differences. A possible application of this work is a possibility to perform re-validation in MetaPRL of the existing library of Coq proofs which could help to build more trust in the latter. Chapter 2 is the main contribution of the dissertation. It contains the description and testing results of an implementation of realization algorithm in epistemic modal logic that converts cut-free derivations in multi-agent epistemic modal logic into derivations in the corresponding Justification Logic where witnesses of knowledge (justification terms) are recovered for all instances of common knowledge. We also apply this algorithms to several well-known epistemic puzzles, such as Muddy Children, Wise Men, Wise Girls, etc

Pseudo-contractions as Gentle Repairs

Updating a knowledge base to remove an unwanted consequence is a challenging task. Some of the original sentences must be either deleted or weakened in such a way that the sentence to be removed is no longer entailed by the resulting set. On the other hand, it is desirable that the existing knowledge be preserved as much as possible, minimising the loss of information. Several approaches to this problem can be found in the literature. In particular, when the knowledge is represented by an ontology, two different families of frameworks have been developed in the literature in the past decades with numerous ideas in common but with little interaction between the communities: applications of AGM-like Belief Change and justification-based Ontology Repair. In this paper, we investigate the relationship between pseudo-contraction operations and gentle repairs. Both aim to avoid the complete deletion of sentences when replacing them with weaker versions is enough to prevent the entailment of the unwanted formula. We show the correspondence between concepts on both sides and investigate under which conditions they are equivalent. Furthermore, we propose a unified notation for the two approaches, which might contribute to the integration of the two areas