Satisfiability of CTL* with constraints

We show that satisfiability for CTL* with equality-, order-, and modulo-constraints over Z is decidable. Previously, decidability was only known for certain fragments of CTL*, e.g., the existential and positive fragments and EF.Comment: To appear at Concur 201

A Temporal Web Ontology Language

The Web Ontology Language (OWL) is the most expressive standard language for modeling ontologies on the Semantic Web. In this paper, we present a temporal extension of the very expressive fragment SHIN(D) of the OWL-DL language resulting in the tOWL language. Through a layered approach we introduce 3 extensions: i) Concrete Domains, that allows the representation of restrictions using concrete domain binary predicates, ii) Temporal Representation, that introduces timepoints, relations between timepoints, intervals, and Allen’s 13 interval relations into the language, and iii) TimeSlices/Fluents, that implements a perdurantist view on individuals and allows for the representation of complex temporal aspects, such as process state transitions. We illustrate the expressiveness of the newly introduced language by providing a TBox representation of Leveraged Buy Out (LBO) processes in financial applications and an ABox representation of one specific LBO

Decentralized case-based reasoning and Semantic Web technologies applied to decision support in oncology

International audienceThis article presents the Kasimir system dedicated to decision knowledge management in oncology and which is built on top of Semantic Web technologies, taking benefit from standard knowledge representation formalisms and open reasoning tools. The representation of medical decision protocols, in particular for breast cancer treatment, is based on concepts and instances implemented within the description logic OWL DL. The knowledge units related to a protocol can then be applied for solving specific medical problems, using instance or concept classification. However, the straight application of a protocol is not always satisfactory, e.g., because of contraindications, necessitating an adaptation of the protocol. This is why the principles and methods of case-based reasoning in the framework of description logics have been used. In addition, the domain of oncology is complex and involves several specialties, e.g. surgery and chemotherapy. This complexity can be better undertaken with a viewpoint-based representation of protocols and viewpoint-based reasoning, for either application or adaptation of the protocols. Accordingly, a distributed description logic has been used for representing a viewpoint-based protocol. The application and the adaptation of the viewpoint-based protocol to medical cases is carried out using global instance classification and decentralized case-based reasoning

A Tableau Algorithm for Description Logics with Concrete Domains and General TBoxes

Abstract. To use description logics (DLs) in an application, it is crucial to identify a DL that is sufficiently expressive to represent the relevant notions of the application domain, but for which reasoning is still decidable. Two means of expressivity that are required by many modern applications of DLs are concrete domains and general TBoxes. The former are used for defining concepts based on concrete qualities of their instances such as the weight, age, duration, and spatial extension. The purpose of the latter is to capture background knowledge by stating that the extension of a concept is included in the extension of another concept. Unfortunately, it is wellknown that combining concrete domains with general TBoxes often leads to DLs for which reasoning is undecidable. In this paper, we identify a general property of concrete domains that is sufficient for proving decidability of DLs with both concrete domains and general TBoxes. We exhibit some useful concrete domains, most notably a spatial one based on the RCC-8 relations, which have this property. Then, we present a tableau algorithm for reasoning in DLs equipped with concret

On the Satisfiability of Temporal Logics with Concrete Domains

Temporal logics are a very popular family of logical languages, used to specify properties of abstracted systems. In the last few years, many extensions of temporal logics have been proposed, in order to address the need to express more than just abstract properties. In our work we study temporal logics extended by local constraints, which allow to express quantitative properties on data values from an arbitrary relational structure called the concrete domain. An example of concrete domain can be (Z, <, =), where the integers are considered as a relational structure over the binary order relation and the equality relation. Formulas of temporal logics with constraints are evaluated on data-words or data-trees, in which each node or position is labeled by a vector of data from the concrete domain. We call the constraints local because they can only compare values at a fixed distance inside such models. Several positive results regarding the satisfiability of LTL (linear temporal logic) with constraints over the integers have been established in the past years, while the corresponding results for branching time logics were only partial. In this work we prove that satisfiability of CTL* (computation tree logic) with constraints over the integers is decidable and also lift this result to ECTL*, a proper extension of CTL*. We also consider other classes of concrete domains, particularly ones that are \"tree-like\". We consider semi-linear orders, ordinal trees and trees of a fixed height, and prove decidability in this framework as well. At the same time we prove that our method cannot be applied in the case of the infinite binary tree or the infinitely branching infinite tree. We also look into extending the expressiveness of our logic adding non-local constraints, and find that this leads to undecidability of the satisfiability problem, even on very simple domains like (Z, <, =). We then find a way to restrict the power of the non-local constraints to regain decidability