Observation and abstract behaviour in specification and implementation of state-based systems

Classical algebraic specification is an accepted framework for specification. A criticism which applies is the fact that it is functional, not based on a notion of state as most software development and implementation languages are. We formalise the idea of a state-based object or abstract machine using algebraic means. In contrast to similar approaches we consider dynamic logic instead of equational logic as the framework for specification and implementation. The advantage is a more expressive language allowing us to specify safety and liveness conditions. It also allows a clearer distinction of functional and state-based parts which require different treatment in order to achieve behavioural abstraction when necessary. We shall in particular focus on abstract behaviour and observation. A behavioural notion of satisfaction for state-elements is needed in order to abstract from irrelevant details of the state realisation

A Local Logic for Realizability in Web Service Choreographies

Web service choreographies specify conditions on observable interactions among the services. An important question in this regard is realizability: given a choreography C, does there exist a set of service implementations I that conform to C ? Further, if C is realizable, is there an algorithm to construct implementations in I ? We propose a local temporal logic in which choreographies can be specified, and for specifications in the logic, we solve the realizability problem by constructing service implementations (when they exist) as communicating automata. These are nondeterministic finite state automata with a coupling relation. We also report on an implementation of the realizability algorithm and discuss experimental results.Comment: In Proceedings WWV 2014, arXiv:1409.229

A Novel Approach to Multimedia Ontology Engineering for Automated Reasoning over Audiovisual LOD Datasets

Multimedia reasoning, which is suitable for, among others, multimedia content analysis and high-level video scene interpretation, relies on the formal and comprehensive conceptualization of the represented knowledge domain. However, most multimedia ontologies are not exhaustive in terms of role definitions, and do not incorporate complex role inclusions and role interdependencies. In fact, most multimedia ontologies do not have a role box at all, and implement only a basic subset of the available logical constructors. Consequently, their application in multimedia reasoning is limited. To address the above issues, VidOnt, the very first multimedia ontology with SROIQ(D) expressivity and a DL-safe ruleset has been introduced for next-generation multimedia reasoning. In contrast to the common practice, the formal grounding has been set in one of the most expressive description logics, and the ontology validated with industry-leading reasoners, namely HermiT and FaCT++. This paper also presents best practices for developing multimedia ontologies, based on my ontology engineering approach

Practical Reasoning for Very Expressive Description Logics

Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can be computationally problematical. We present an algorithm that decides satisfiability of the DL ALC extended with transitive and inverse roles and functional restrictions with respect to general concept inclusion axioms and role hierarchies; early experiments indicate that this algorithm is well-suited for implementation. Additionally, we show that ALC extended with just transitive and inverse roles is still in PSPACE. We investigate the limits of decidability for this family of DLs, showing that relaxing the constraints placed on the kinds of roles used in number restrictions leads to the undecidability of all inference problems. Finally, we describe a number of optimisation techniques that are crucial in obtaining implementations of the decision procedures, which, despite the worst-case complexity of the problem, exhibit good performance with real-life problems

Constructive interval temporal logic in Alf

This paper gives an implementation of an interval temporal logic in a constructive type theory, using the Alf proof system. After explaining the constructive approach, its relevance to interval temporal logic and potential applications of our work, we explain the fundamentals of the Alf system. We then present the implementation of the logic and give a number of examples of its use. We conclude by exploring how the work can be extended in the future

A Foundational View on Integration Problems

The integration of reasoning and computation services across system and language boundaries is a challenging problem of computer science. In this paper, we use integration for the scenario where we have two systems that we integrate by moving problems and solutions between them. While this scenario is often approached from an engineering perspective, we take a foundational view. Based on the generic declarative language MMT, we develop a theoretical framework for system integration using theories and partial theory morphisms. Because MMT permits representations of the meta-logical foundations themselves, this includes integration across logics. We discuss safe and unsafe integration schemes and devise a general form of safe integration

Towards MKM in the Large: Modular Representation and Scalable Software Architecture

MKM has been defined as the quest for technologies to manage mathematical knowledge. MKM "in the small" is well-studied, so the real problem is to scale up to large, highly interconnected corpora: "MKM in the large". We contend that advances in two areas are needed to reach this goal. We need representation languages that support incremental processing of all primitive MKM operations, and we need software architectures and implementations that implement these operations scalably on large knowledge bases. We present instances of both in this paper: the MMT framework for modular theory-graphs that integrates meta-logical foundations, which forms the base of the next OMDoc version; and TNTBase, a versioned storage system for XML-based document formats. TNTBase becomes an MMT database by instantiating it with special MKM operations for MMT.Comment: To appear in The 9th International Conference on Mathematical Knowledge Management: MKM 201