On metric temporal description logics

We introduce metric temporal description logics (mTDLs) as combinations of the classical description logic ALC with (a) LTLbin, an extension of the temporal logic LTL with succinctly represented intervals, and (b) metric temporal logic MTL, extending LTLbin with capabilities to quantitatively reason about time delays. Our main contributions are algorithms and tight complexity bounds for the satisfiability problem in these mTDLs: For mTDLs based on (fragments of) LTLbin, we establish complexity bounds ranging from EXPTIME to 2EXPSPACE. For mTDLs based on (fragments of) MTL interpreted over the naturals, we establish complexity bounds ranging from EXPSPACE to 2EXPSPACE

Evolving Objects in Temporal Information Systems

This paper presents a semantic foundation of temporal conceptual models used to design temporal information systems. We consider a modelling language able to express both timestamping and evolution constraints. We conduct a deeper investigation of evolution constraints, eventually devising a model-theoretic semantics for a full-fledged model with both timestamping and evolution constraints. The proposed formalization is meant both to clarify the meaning of the various temporal constructors that appeared in the literature and to give a rigorous definition, in the context of temporal information systems, to notions like satisfiability, subsumption and logical implication. Furthermore, we show how to express temporal constraints using a subset of first-order temporal logic, i.e. DLRUS, the description logic DLR extended with the temporal operators Since and Until. We show how DLRUS is able to capture the various modelling constraints in a succinct way and to perform automated reasoning on temporal conceptual models

Ontology-mediated query answering over temporal data: a survey

We discuss the use of various temporal knowledge representation formalisms for ontology-mediated query answering over temporal data. In particular, we analyse ontology and query languages based on the linear temporal logic LTL, the multi-dimensional Halpern-Shoham interval temporal logic HSn, as well as the metric temporal logic MTL. Our main focus is on the data complexity of answering temporal ontology-mediated queries and their rewritability into standard first-order and datalog queries

Modeling Time in Computing: A Taxonomy and a Comparative Survey

The increasing relevance of areas such as real-time and embedded systems, pervasive computing, hybrid systems control, and biological and social systems modeling is bringing a growing attention to the temporal aspects of computing, not only in the computer science domain, but also in more traditional fields of engineering. This article surveys various approaches to the formal modeling and analysis of the temporal features of computer-based systems, with a level of detail that is suitable also for non-specialists. In doing so, it provides a unifying framework, rather than just a comprehensive list of formalisms. The paper first lays out some key dimensions along which the various formalisms can be evaluated and compared. Then, a significant sample of formalisms for time modeling in computing are presented and discussed according to these dimensions. The adopted perspective is, to some extent, historical, going from "traditional" models and formalisms to more modern ones.Comment: More typos fixe

Semantic validation in spatio-temporal schema integration

This thesis proposes to address the well-know database integration problem with a new method that combines functionality from database conceptual modeling techniques with functionality from logic-based reasoners. We elaborate on a hybrid - modeling+validation - integration approach for spatio-temporal information integration on the schema level. The modeling part of our methodology is supported by the spatio-temporal conceptual model MADS, whereas the validation part of the integration process is delegated to the description logics validation services. We therefore adhere to the principle that, rather than extending either formalism to try to cover all desirable functionality, a hybrid system, where the database component and the logic component would cooperate, each one performing the tasks for which it is best suited, is a viable solution for semantically rich information management. First, we develop a MADS-based flexible integration approach where the integrated schema designer has several viable ways to construct a final integrated schema. For different related schema elements we provide the designer with four general policies and with a set of structural solutions or structural patterns within each policy. To always guarantee an integrated solution, we provide for a preservation policy with multi-representation structural pattern. To state the inter-schema mappings, we elaborate on a correspondence language with explicit spatial and temporal operators. Thus, our correspondence language has three facets: structural, spatial, and temporal, allowing to relate the thematic representation as well as the spatial and temporal features. With the inter-schema mappings, the designer can state correspondences between related populations, and define the conditions that rule the matching at the instance level. These matching rules can then be used in query rewriting procedures or to match the instances within the data integration process. We associate a set of putative structural patterns to each type of population correspondence, providing a designer with a patterns' selection for flexible integrated schema construction. Second, we enhance our integration method by employing validation services of the description logic formalism. It is not guaranteed that the designer can state all the inter-schema mappings manually, and that they are all correct. We add the validation phase to ensure validity and completeness of the inter-schema mappings set. Inter-schema mappings cannot be validated autonomously, i.e., they are validated against the data model and the schemas they link. Thus, to implement our validation approach, we translate the data model, the source schemas and the inter-schema mappings into a description logic formalism, preserving the spatial and temporal semantics of the MADS data model. Thus, our modeling approach in description logic insures that the model designer will correctly define spatial and temporal schema elements and inter-schema mappings. The added value of the complete translation (i.e., including the data model and the source schemas) is that we validate not only the inter-schema mappings, but also the compliance of the source schemas to the data model, and infer implicit relationships within them. As the result of the validation procedure, the schema designer obtains the complete and valid set of inter-schema mappings and a set of valid (flexible) schematic patterns to apply to construct an integrated schema that meets application requirements. To further our work, we model a framework in which a schema designer is able to follow our integration method and realize the schema integration task in an assisted way. We design two models, UML and SEAM models, of a system that provides for integration functionalities. The models describe a framework where several tools are employed together, each involved in the service it is best suited for. We define the functionalities and the cooperation between the composing elements of the framework and detail the logics of the integration process in an UML activity diagram and in a SEAM operation model

Pseudo-contractions as Gentle Repairs

Updating a knowledge base to remove an unwanted consequence is a challenging task. Some of the original sentences must be either deleted or weakened in such a way that the sentence to be removed is no longer entailed by the resulting set. On the other hand, it is desirable that the existing knowledge be preserved as much as possible, minimising the loss of information. Several approaches to this problem can be found in the literature. In particular, when the knowledge is represented by an ontology, two different families of frameworks have been developed in the literature in the past decades with numerous ideas in common but with little interaction between the communities: applications of AGM-like Belief Change and justification-based Ontology Repair. In this paper, we investigate the relationship between pseudo-contraction operations and gentle repairs. Both aim to avoid the complete deletion of sentences when replacing them with weaker versions is enough to prevent the entailment of the unwanted formula. We show the correspondence between concepts on both sides and investigate under which conditions they are equivalent. Furthermore, we propose a unified notation for the two approaches, which might contribute to the integration of the two areas

28th International Symposium on Temporal Representation and Reasoning (TIME 2021)

The 28th International Symposium on Temporal Representation and Reasoning (TIME 2021) was planned to take place in Klagenfurt, Austria, but had to move to an online conference due to the insecurities and restrictions caused by the pandemic. Since its frst edition in 1994, TIME Symposium is quite unique in the panorama of the scientifc conferences as its main goal is to bring together researchers from distinct research areas involving the management and representation of temporal data as well as the reasoning about temporal aspects of information. Moreover, TIME Symposium aims to bridge theoretical and applied research, as well as to serve as an interdisciplinary forum for exchange among researchers from the areas of artifcial intelligence, database management, logic and verifcation, and beyond

Interval-based temporal functional dependencies: specification and verification

In the temporal database literature, every fact stored in a database may beequipped with two temporal dimensions: the valid time, which describes the time whenthe fact is true in the modeled reality, and the transaction time, which describes the timewhen the fact is current in the database and can be retrieved. Temporal functional dependencies(TFDs) add valid time to classical functional dependencies (FDs) in order to expressdatabase integrity constraints over the flow of time. Currently, proposals dealing with TFDsadopt a point-based approach, where tuples hold at specific time points, to express integrityconstraints such as \u201cfor each month, the salary of an employee depends only on his role\u201d. Tothe best of our knowledge, there are no proposals dealing with interval-based temporal functionaldependencies (ITFDs), where the associated valid time is represented by an intervaland there is the need of representing both point-based and interval-based data dependencies.In this paper, we propose ITFDs based on Allen\u2019s interval relations and discuss theirexpressive power with respect to other TFDs proposed in the literature: ITFDs allow us toexpress interval-based data dependencies, which cannot be expressed through the existingpoint-based TFDs. ITFDs allow one to express constraints such as \u201cemployees starting towork the same day with the same role get the same salary\u201d or \u201cemployees with a given roleworking on a project cannot start to work with the same role on another project that willend before the first one\u201d. Furthermore, we propose new algorithms based on B-trees to efficientlyverify the satisfaction of ITFDs in a temporal database. These algorithms guaranteethat, starting from a relation satisfying a set of ITFDs, the updated relation still satisfies thegiven ITFDs

First-Order Rewritability and Complexity of Two-Dimensional Temporal Ontology-Mediated Queries

Aiming at ontology-based data access to temporal data, we design two-dimensional temporal ontology and query languages by combining logics from the (extended) DL-Lite family with linear temporal logic LTL over discrete time (Z,<). Our main concern is first-order rewritability of ontology-mediated queries (OMQs) that consist of a 2D ontology and a positive temporal instance query. Our target languages for FO-rewritings are two-sorted FO(<) - first-order logic with sorts for time instants ordered by the built-in precedence relation < and for the domain of individuals - its extension FOE with the standard congruence predicates t \equiv 0 mod n, for any fixed n > 1, and FO(RPR) that admits relational primitive recursion. In terms of circuit complexity, FOE- and FO(RPR)-rewritability guarantee answering OMQs in uniform AC0 and NC1, respectively. We proceed in three steps. First, we define a hierarchy of 2D DL-Lite/LTL ontology languages and investigate the FO-rewritability of OMQs with atomic queries by constructing projections onto 1D LTL OMQs and employing recent results on the FO-rewritability of propositional LTL OMQs. As the projections involve deciding consistency of ontologies and data, we also consider the consistency problem for our languages. While the undecidability of consistency for 2D ontology languages with expressive Boolean role inclusions might be expected, we also show that, rather surprisingly, the restriction to Krom and Horn role inclusions leads to decidability (and ExpSpace-completeness), even if one admits full Booleans on concepts. As a final step, we lift some of the rewritability results for atomic OMQs to OMQs with expressive positive temporal instance queries. The lifting results are based on an in-depth study of the canonical models and only concern Horn ontologies

Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions