A Cookbook for Temporal Conceptual Data Modelling with Description Logics

Artale, Alessandro; Kontchakov, Roman; Ryzhikov, Vladislav; Zakharyaschev, Michael

doi:10.1145/2629565

Cited by 43 publications

(67 citation statements)

References 91 publications

(113 reference statements)

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“…Where only a universal (anywhere in time) modality is allowed their complexity is even lower (from NLogSpace to P). Temporal extensions of the description logic DL-Lite have been studied under similar sub-propositional restrictions, and similar improvements in the complexity of various problems have been found [AKRZ14]. Sub-propositional fragments of the undecidable interval temporal logic HS [HS91], have also been studied.…”

Section: Introductionmentioning

confidence: 80%

On the Expressive Power of Sub-Propositional Fragments of Modal Logic

Bresolin

Muñoz‐Velasco

Sciavicco

2016

Electron. Proc. Theor. Comput. Sci.

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Modal logic is a paradigm for several useful and applicable formal systems in computer science. It generally retains the low complexity of classical propositional logic, but notable exceptions exist in the domains of description, temporal, and spatial logic, where the most expressive formalisms have a very high complexity or are even undecidable. In search of computationally well-behaved fragments, clausal forms and other sub-propositional restrictions of temporal and description logics have been recently studied. This renewed interest on sub-propositional logics, which mainly focus on the complexity of the various fragments, raise natural questions on their the relative expressive power, which we try to answer here for the basic multi-modal logic K N . We consider the Horn and the Krom restrictions, as well as the combined restriction (known as the core fragment) of modal logic, and, orthogonally, the fragments that emerge by disallowing boxes or diamonds from positive literals. We study the problem in a very general setting, to ease transferring our results to other meaningful cases.

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Section: Introductionmentioning

confidence: 80%

On the Expressive Power of Sub-Propositional Fragments of Modal Logic

Bresolin

Muñoz‐Velasco

Sciavicco

2016

Electron. Proc. Theor. Comput. Sci.

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“…Choosing/designing the right languages. The languages and formalisms adopted in the various components of knowledge-enriched data management systems have to support different types of knowledge and data, e.g., mixing open and closed world assumption, and allowing for representing temporal, spatial, and other modalities of information [37,21,32,18,113]. It is well understood that the requirements in terms of expressive power for such languages would lead to formalisms that make the various inference tasks either undecidable or highly intractable.…”

Section: Development Of Reasoning-tuned Db Systems Such Systems Willmentioning

confidence: 99%

Research Directions for Principles of Data Management (Abridged)

Abiteboul¹,

Arenas²,

Barceló³

et al. 2017

SIGMOD Rec.

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Research directions for Principles of Data ManagementPDM played a foundational role in the relational database model, with the robust connection between algebraic and calculus-based query languages, the connection between integrity constraints and database design, key insights for the field of query optimization, and the fundamentals of consistent concurrent transactions. This early work included rich cross-fertilization between PDM and other disciplines in mathematics and computer science, including logic, complexity theory, and knowledge representation. Since the 1990s we have seen an overwhelming increase in both the production of data and the ability to store and access such data. This has led to a phenomenal metamorphosis in the ways that we manage and use data. During this time, we have gone (1) from stand-alone disk-based databases to data that is spread across and linked by the Web, (2) from rigidly structured towards loosely structured data, and (3) from relational data to many different data models (hierarchical, graph-structured, data points, NoSQL, text data, image data, etc.). Research on PDM has developed during that time, too, following, accompanying and influencing this process. It has intensified research on extensions of the relational model (data exchange, incomplete data, probabilistic data, . . . ), on other data models (hierachical, semi-structured, graph, text, . . . ), and on a variety of further data management areas, including knowledge representation and the semantic web, data privacy and security, and data-aware (business) processes. Along the way, the PDM community expanded its cross-fertilization with related areas, to include automata theory, web services, parallel computation, document processing, data structures, scientific workflow, business process management, data-centered dynamic systems, data mining, machine learning, information extraction, etc.Looking forward, three broad areas of data management stand out where principled, mathematical thinking can bring new approaches and much-needed clarity. The first relates to the full lifecycle of so-called "Big Data Analytics", that is, the application of statistical and machine learning techniques to make sense out of, and derive value from, massive volumes of data. The second stems from new forms of data creation and processing, especially as it arises in applications such as web-based commerce, social media applications, and dataaware workflow and business process management. The third, which is just beginning to emerge, is the development of new principles and approaches in support of ethical data management. We briefly illustrate some of the primary ways that these three areas can be supported by the seven PDM research themes that are explored in this report.The overall lifecycle of Big Data Analytics raises a wealth of challenge areas that PDM can help with. As documented in numerous sources, so-called "data wrangling" can form 50% to 80% of the labor costs in an analytics investigation. The challenges of data wrangling can be ...

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“…R 1 is a pseudo-equivalence, R 0 and R 1 commute} (2) (for more information on Sahlqvist formulas and canonicity, consult e.g. [4,6]).…”

Section: Propositional Bimodal Logicsmentioning

confidence: 99%

Undecidable Propositional Bimodal Logics and One-Variable First-Order Linear Temporal Logics with Counting

Hampson

Kurucz

2015

ACM Trans. Comput. Logic

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First-order temporal logics are notorious for their bad computational behaviour. It is known that even the two-variable monadic fragment is highly undecidable over various linear timelines, and over branching time even one-variable fragments might be undecidable. However, there have been several attempts on finding well-behaved fragments of first-order temporal logics and related temporal description logics, mostly either by restricting the available quantifier patterns, or considering sub-Boolean languages. Here we analyse seemingly 'mild' extensions of decidable one-variable fragments with counting capabilities, interpreted in models with constant, decreasing, and expanding first-order domains. We show that over most classes of linear orders these logics are (sometimes highly) undecidable, even without constant and function symbols, and with the sole temporal operator 'eventually'.We establish connections with bimodal logics over 2D product structures having linear and 'difference' (inequality) component relations, and prove our results in this bimodal setting. We show a general result saying that satisfiability over many classes of bimodal models with commuting 'unbounded' linear and difference relations is undecidable. As a by-product, we also obtain new examples of finitely axiomatisable but Kripke incomplete bimodal logics. Our results generalise similar lower bounds on bimodal logics over products of two linear relations, and our proof methods are quite different from the known proofs of these results. Unlike previous proofs that first 'diagonally encode' an infinite grid, and then use reductions of tiling or Turing machine problems, here we make direct use of the grid-like structure of product frames and obtain lower complexity bounds by reductions of counter (Minsky) machine problems. Representing counter machine runs apparently requires less control over neighbouring grid-points than tilings or Turing machine runs, and so this technique is possibly more versatile, even if one component of the underlying product structures is 'close to' being the universal relation.

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A Cookbook for Temporal Conceptual Data Modelling with Description Logics

Cited by 43 publications

References 91 publications

On the Expressive Power of Sub-Propositional Fragments of Modal Logic

On the Expressive Power of Sub-Propositional Fragments of Modal Logic

Research Directions for Principles of Data Management (Abridged)

Undecidable Propositional Bimodal Logics and One-Variable First-Order Linear Temporal Logics with Counting

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