Computer theorem proving in math

We give an overview of issues surrounding computer-verified theorem proving in the standard pure-mathematical context. This is based on my talk at the PQR conference (Brussels, June 2003)

Deontic Logic and Natural Language

There has been a recent surge of work on deontic modality within philosophy of language. This work has put the deontic logic tradition in contact with natural language semantics, resulting in significant increase in sophistication on both ends. This chapter surveys the main motivations, achievements, and prospects of this work

The Anatomy and Facets of Dynamic Policies

Information flow policies are often dynamic; the security concerns of a program will typically change during execution to reflect security-relevant events. A key challenge is how to best specify, and give proper meaning to, such dynamic policies. A large number of approaches exist that tackle that challenge, each yielding some important, but unconnected, insight. In this work we synthesise existing knowledge on dynamic policies, with an aim to establish a common terminology, best practices, and frameworks for reasoning about them. We introduce the concept of facets to illuminate subtleties in the semantics of policies, and closely examine the anatomy of policies and the expressiveness of policy specification mechanisms. We further explore the relation between dynamic policies and the concept of declassification.Comment: Technical Report of publication under the same name in Computer Security Foundations (CSF) 201

Mixin Composition Synthesis based on Intersection Types

We present a method for synthesizing compositions of mixins using type inhabitation in intersection types. First, recursively defined classes and mixins, which are functions over classes, are expressed as terms in a lambda calculus with records. Intersection types with records and record-merge are used to assign meaningful types to these terms without resorting to recursive types. Second, typed terms are translated to a repository of typed combinators. We show a relation between record types with record-merge and intersection types with constructors. This relation is used to prove soundness and partial completeness of the translation with respect to mixin composition synthesis. Furthermore, we demonstrate how a translated repository and goal type can be used as input to an existing framework for composition synthesis in bounded combinatory logic via type inhabitation. The computed result is a class typed by the goal type and generated by a mixin composition applied to an existing class

Guidelines to Study Differences in Expressiveness between Ontology Specification Languages: A Case Of Study

We focus on our experiences on translating ontologies between two ontology languages, FLogic and Ontolingua, in the framework of Methontology and ODE. Rather than building "ad hoc" translators between languages or using KIF, our option consists of translating through ODE intermediate representations. So, we have built direct translators from ODE intermediate representations to Ontolingua and FLogic, and we have also built reverse translators from these two languages to ODE intermediate representations. Expressiveness of the target languages is the main feature to analyse when automatically generating ontologies from ODE intermediate representations. Therefore, we analyse the expressiveness of Ontolingua and FLogic for creating classes, instances, relations, functions and axioms, which are the essential components in ontologies. The motivation for this analysis can be found in the (KA)² initiative and can be easily extended to any other domains and languages

Formalization of the classification pattern: Survey of classification modeling in information systems engineering

Formalization is becoming more common in all stages of the development of information systems, as a better understanding of its benefits emerges. Classification systems are ubiquitous, no more so than in domain modeling. The classification pattern that underlies these systems provides a good case study of the move towards formalization in part because it illustrates some of the barriers to formalization; including the formal complexity of the pattern and the ontological issues surrounding the ‘one and the many’. Powersets are a way of characterizing the (complex) formal structure of the classification pattern and their formalization has been extensively studied in mathematics since Cantor’s work in the late 19th century. One can use this formalization to develop a useful benchmark. There are various communities within Information Systems Engineering (ISE) that are gradually working towards a formalization of the classification pattern. However, for most of these communities this work is incomplete, in that they have not yet arrived at a solution with the expressiveness of the powerset benchmark. This contrasts with the early smooth adoption of powerset by other Information Systems communities to, for example, formalize relations. One way of understanding the varying rates of adoption is recognizing that the different communities have different historical baggage. Many conceptual modeling communities emerged from work done on database design and this creates hurdles to the adoption of the high level of expressiveness of powersets. Another relevant factor is that these communities also often feel, particularly in the case of domain modeling, a responsibility to explain the semantics of whatever formal structures they adopt. This paper aims to make sense of the formalization of the classification pattern in ISE and surveys its history through the literature; starting from the relevant theoretical works of the mathematical literature and gradually shifting focus to the ISE literature. The literature survey follows the evolution of ISE’s understanding of how to formalize the classification pattern. The various proposals are assessed using the classical example of classification; the Linnaean taxonomy formalized using powersets as a benchmark for formal expressiveness. The broad conclusion of the survey is that (1) the ISE community is currently in the early stages of the process of understanding how to formalize the classification pattern, particularly in the requirements for expressiveness exemplified by powersets and (2) that there is an opportunity to intervene and speed up the process of adoption by clarifying this expressiveness. Given the central place that the classification pattern has in domain modeling, this intervention has the potential to lead to significant improvements.The UK Engineering and Physical Sciences Research Council (grant EP/K009923/1)