A CDCL-style calculus for solving non-linear constraints

In this paper we propose a novel approach for checking satisfiability of non-linear constraints over the reals, called ksmt. The procedure is based on conflict resolution in CDCL style calculus, using a composition of symbolical and numerical methods. To deal with the non-linear components in case of conflicts we use numerically constructed restricted linearisations. This approach covers a large number of computable non-linear real functions such as polynomials, rational or trigonometrical functions and beyond. A prototypical implementation has been evaluated on several non-linear SMT-LIB examples and the results have been compared with state-of-the-art SMT solvers.Comment: 17 pages, 3 figures; accepted at FroCoS 2019; software available at <http://informatik.uni-trier.de/~brausse/ksmt/

From TimeML to TPL

This paper describes a subset of the temporal mark-up language TimeML, and explains its relation to various formalisms found in the literature on interval temporal logic. The subset of TimeML we describe can be viewed as an interval temporal logic with a tractable satisfiability problem, but very limited expressive power. Most crucially, that logic does not permit quantification over events. The contribution of this paper is to point out that, by choosing an appropriate interval temporal logic, it is possible to introduce quantification into representations of event-structure without sacrificing decidability

Logical and Algebraic Characterizations of Rational Transductions

Rational word languages can be defined by several equivalent means: finite state automata, rational expressions, finite congruences, or monadic second-order (MSO) logic. The robust subclass of aperiodic languages is defined by: counter-free automata, star-free expressions, aperiodic (finite) congruences, or first-order (FO) logic. In particular, their algebraic characterization by aperiodic congruences allows to decide whether a regular language is aperiodic. We lift this decidability result to rational transductions, i.e., word-to-word functions defined by finite state transducers. In this context, logical and algebraic characterizations have also been proposed. Our main result is that one can decide if a rational transduction (given as a transducer) is in a given decidable congruence class. We also establish a transfer result from logic-algebra equivalences over languages to equivalences over transductions. As a consequence, it is decidable if a rational transduction is first-order definable, and we show that this problem is PSPACE-complete

Qualitative Constraint Calculi: Heterogeneous Verification of Composition Tables

In the domain of qualitative constraint reasoning, a subfield of AI which has evolved in the past 25 years, a large number of calculi for efficient reasoning about spatial and temporal entities has been developed. Reasoning techniques developed for these constraint calculi typically rely on so-called composition tables of the calculus at hand, which allow for replacing semantic reasoning by symbolic operations. Often these composition tables are developed in a quite informal, pictorial manner and hence composition tables are prone to errors. In view of possible safety critical applications of qualitative calculi, however, it is desirable to formally verify these composition tables. In general, the verification of composition tables is a tedious task, in particular in cases where the semantics of the calculus depends on higher-order constructs such as sets. In this paper we address this problem by presenting a heterogeneous proof method that allows for combining a higher-order proof assistance system (such as Isabelle) with an automatic (first order) reasoner (such as SPASS or VAMPIRE). The benefit of this method is that the number of proof obligations that is to be proven interactively with a semi-automatic reasoner can be minimized to an acceptable level

The Introduction of Topology into Analytic Philosophy: Two Movements and a Coda

Both early analytic philosophy and the branch of mathematics now known as topology were gestated and born in the early part of the 20th century. It is not well recognized that there was early interaction between the communities practicing and developing these fields. We trace the history of how topological ideas entered into analytic philosophy through two migrations, an earlier one conceiving of topology geometrically and a later one conceiving of topology algebraically. This allows us to reassess the influence and significance of topological methods for philosophy, including the possible fruitfulness of a third conception of topology as a structure determining similarity

Service Contract Automation

Today’s transition from a product- to a service-oriented economy implies fundamental technical, organizational and economic challenges. The trend of compensating missing core competencies by requesting business services from external providers to be integrated in internal end-to-end processes has recently gained tremendous momentum. Nevertheless, service level agreements between the parties involved are still specified for each service entity that is part of composite business services which results in a managerial overhead generated from multiple contractual relations. The contribution of this paper is threefold: (i) We analyze the fundamental requirements in the context of describing services, quality and agreements as well as their aggregation in a generic manner. Based on the results, we (ii) provide a holistic framework that enables the automation of service contracts for composite business services. Facilitating semantic technologies we provide means for describing service quality from a technical and business-oriented perspective, adequate metrics as well as quality aggregation operations in the context of composite business services. Furthermore, we (iii) evaluate our framework based on an industrial application scenario

Chord Sequence patterns in OWL

This thesis addresses the representation of and reasoning on musical knowledge in the Semantic Web. The Semantic Web is an evolving extension of the World Wide Web that aims at describing information that is distributed on the web in a machine-processable form. Existing approaches to modelling musical knowledge in the context of the Semantic Web have focused on metadata. The description of musical content and reasoning as well as integration of content descriptions and metadata are yet open challenges. This thesis discusses the possibilities of representing musical knowledge in the Web Ontology Language (OWL) focusing on chord sequence representation and presents and evaluates a newly developed solution. The solution consists of two main components. Ontological modelling patterns for musical entities such as notes and chords are introduced in the (MEO) ontology. A sequence pattern language and ontology (SEQ) has been developed that can express patterns in a form resembling regular expressions. As MEO and SEQ patterns both rewrite to OWL they can be combined freely. Reasoning tasks such as instance classification, retrieval and pattern subsumption are then executable by standard Semantic Web reasoners. The expressiveness of SEQ has been studied, in particular in relation to grammars. The complexity of reasoning on SEQ patterns has been studied theoretically and empirically, and optimisation methods have been developed. There is still great potential for improvement if specific reasoning algorithms were developed to exploit the sequential structure, but the development of such algorithms is outside the scope of this thesis. MEO and SEQ have also been evaluated in several musicological scenarios. It is shown how patterns that are characteristic of musical styles can be expressed and chord sequence data can be classified, demonstrating the use of the language in web retrieval and as integration layer for different chord patterns and corpora. Furthermore, possibilities of using SEQ patterns for harmonic analysis are explored using grammars for harmony; both a hybrid system and a translation of limited context-free grammars into SEQ patterns have been developed. Finally, a distributed scenario is evaluated where SEQ and MEO are used in connection with DBpedia, following the Linked Data approach. The results show that applications are already possible and will benefit in the future from improved quality and compatibility of data sources as the Semantic Web evolves