An Algebra of Synchronous Scheduling Interfaces

In this paper we propose an algebra of synchronous scheduling interfaces which combines the expressiveness of Boolean algebra for logical and functional behaviour with the min-max-plus arithmetic for quantifying the non-functional aspects of synchronous interfaces. The interface theory arises from a realisability interpretation of intuitionistic modal logic (also known as Curry-Howard-Isomorphism or propositions-as-types principle). The resulting algebra of interface types aims to provide a general setting for specifying type-directed and compositional analyses of worst-case scheduling bounds. It covers synchronous control flow under concurrent, multi-processing or multi-threading execution and permits precise statements about exactness and coverage of the analyses supporting a variety of abstractions. The paper illustrates the expressiveness of the algebra by way of some examples taken from network flow problems, shortest-path, task scheduling and worst-case reaction times in synchronous programming.Comment: In Proceedings FIT 2010, arXiv:1101.426

Modular Logic Programming: Full Compositionality and Conflict Handling for Practical Reasoning

With the recent development of a new ubiquitous nature of data and the profusity of available knowledge, there is nowadays the need to reason from multiple sources of often incomplete and uncertain knowledge. Our goal was to provide a way to combine declarative knowledge bases – represented as logic programming modules under the answer set semantics – as well as the individual results one already inferred from them, without having to recalculate the results for their composition and without having to explicitly know the original logic programming encodings that produced such results. This posed us many challenges such as how to deal with fundamental problems of modular frameworks for logic programming, namely how to define a general compositional semantics that allows us to compose unrestricted modules. Building upon existing logic programming approaches, we devised a framework capable of composing generic logic programming modules while preserving the crucial property of compositionality, which informally means that the combination of models of individual modules are the models of the union of modules. We are also still able to reason in the presence of knowledge containing incoherencies, which is informally characterised by a logic program that does not have an answer set due to cyclic dependencies of an atom from its default negation. In this thesis we also discuss how the same approach can be extended to deal with probabilistic knowledge in a modular and compositional way. We depart from the Modular Logic Programming approach in Oikarinen & Janhunen (2008); Janhunen et al. (2009) which achieved a restricted form of compositionality of answer set programming modules. We aim at generalising this framework of modular logic programming and start by lifting restrictive conditions that were originally imposed, and use alternative ways of combining these (so called by us) Generalised Modular Logic Programs. We then deal with conflicts arising in generalised modular logic programming and provide modular justifications and debugging for the generalised modular logic programming setting, where justification models answer the question: Why is a given interpretation indeed an Answer Set? and Debugging models answer the question: Why is a given interpretation not an Answer Set? In summary, our research deals with the problematic of formally devising a generic modular logic programming framework, providing: operators for combining arbitrary modular logic programs together with a compositional semantics; We characterise conflicts that occur when composing access control policies, which are generalisable to our context of generalised modular logic programming, and ways of dealing with them syntactically: provided a unification for justification and debugging of logic programs; and semantically: provide a new semantics capable of dealing with incoherences. We also provide an extension of modular logic programming to a probabilistic setting. These goals are already covered with published work. A prototypical tool implementing the unification of justifications and debugging is available for download from http://cptkirk.sourceforge.net

Towards a Formal Theory of Interoperability

This dissertation proposes a formal theory of interoperability that explains 1) what interoperability is as opposed to how it works, 2) how to tell whether two or more systems can interoperate and 3) how to identify whether systems are interoperating or merely exchanging bits and bytes. The research provides a formal model of data in M&S that captures all possible representations of a real or imagined thing and distinguishes between existential dependencies and transformational dependencies. Existential dependencies capture the relationships within a model while transformational dependencies capture the relationships between interactions with a model. These definitions are used to formally specify interoperation, the ability to exchange information, as a necessary condition for interoperability. Theorems of interoperation that capture the nature and boundaries of the interoperation space and how to measure it are formulated. Interoperability is formally captured as a subset of the interoperation space for which transformational dependencies can be fulfilled. Theorems of interoperability that capture the interoperability space and how to measure it are presented. Using graph theory and complexity theory, the model of data is reformulated as a graph, and the complexity of interoperation and interoperability is shown to be at least NP-Complete. Model Based Data Engineering (MBDE) is formally defined using the model of data introduced earlier and transformed into a heuristic that supports interoperability. This heuristic is shown to be more powerful than current approaches in that it is consistent and can easily be verified

Consistent Query Answers in the Presence of Universal Constraints

The framework of consistent query answers and repairs has been introduced to alleviate the impact of inconsistent data on the answers to a query. A repair is a minimally different consistent instance and an answer is consistent if it is present in every repair. In this article we study the complexity of consistent query answers and repair checking in the presence of universal constraints. We propose an extended version of the conflict hypergraph which allows to capture all repairs w.r.t. a set of universal constraints. We show that repair checking is in PTIME for the class of full tuple-generating dependencies and denial constraints, and we present a polynomial repair algorithm. This algorithm is sound, i.e. always produces a repair, but also complete, i.e. every repair can be constructed. Next, we present a polynomial-time algorithm computing consistent answers to ground quantifier-free queries in the presence of denial constraints, join dependencies, and acyclic full-tuple generating dependencies. Finally, we show that extending the class of constraints leads to intractability. For arbitrary full tuple-generating dependencies consistent query answering becomes coNP-complete. For arbitrary universal constraints consistent query answering is \Pi_2^p-complete and repair checking coNP-complete.Comment: Submitted to Information System