A Temporal Datalog Primer: Talk Abstract Livia Blasi1,2 1 Banca d’Italia, Italy 2 TU Wien, Austria 1. Talk Abstract case, we assume the time unit is in months. Thus, Rule 1 tells the company to buy π‘ π‘‘π‘Žπ‘Ÿπ‘‘π‘’π‘ if it has shown an In this talk1 we present a review of the literature on tem- πΈπ‘ π‘‘π‘–π‘šπ‘Žπ‘‘π‘’π‘‘π‘‰ π‘Žπ‘™π‘’π‘’πΌπ‘›π‘π‘Ÿπ‘’π‘Žπ‘ π‘’ continually in the interval poral reasoning, with particular focus on DatalogMTL, that goes from 0 to 3 months in the past. an extension of the Datalog language with Metric Tem- We present now another example in the same scenario poral Logic operators. We show how temporal reasoning that uses the diamond minus operator and recursion. can prove to be a crucial tool for financial data dealing with time. Financial and economics applications have temporal [0,2] InvestInSector(π‘ π‘’π‘π‘‘π‘œπ‘Ÿ, π‘–π‘›π‘£π‘’π‘ π‘‘π‘šπ‘’π‘›π‘‘), data deeply ingrained in their nature, and nowadays it is [0,1] ReturnFromInvestment(π‘ π‘’π‘π‘‘π‘œπ‘Ÿ, π‘Ÿπ‘’π‘‘π‘’π‘Ÿπ‘›) more important than ever to be able to reason over such data. For example, we may be interested in understanding π‘Ÿπ‘’π‘‘π‘’π‘Ÿπ‘› > π‘–π‘›π‘£π‘’π‘ π‘‘π‘šπ‘’π‘›π‘‘, the trend of the price of the stock for a certain company, β†’ SuccessfulInvestment(π‘ π‘’π‘π‘‘π‘œπ‘Ÿ, π‘–π‘›π‘£π‘’π‘ π‘‘π‘šπ‘’π‘›π‘‘) (2) or in being able to derive conclusions about the likeliness SuccessfulInvestment(π‘ π‘’π‘π‘‘π‘œπ‘Ÿ, π‘–π‘›π‘£π‘’π‘ π‘‘π‘šπ‘’π‘›π‘‘), of change of ownership of a company depending on how many of their shares have been bought over time by a π‘›π‘’π‘€πΌπ‘›π‘£π‘’π‘ π‘‘π‘’π‘šπ‘’π‘›π‘‘ = π‘–π‘›π‘£π‘’π‘ π‘‘π‘šπ‘’π‘›π‘‘ * 𝛽 shareholder. β†’ InvestInSector(π‘ π‘’π‘π‘‘π‘œπ‘Ÿ, π‘›π‘’π‘€πΌπ‘›π‘£π‘’π‘ π‘‘π‘šπ‘’π‘›π‘‘) (3) Temporal reasoning is one of the key approaches that allow for such and similar reasoning tasks, as it allows to The diamond minus 𝜚 operator assesses whether a fact consider complex data structures (e.g. Knowledge Graphs has been valid at least once in the past relative interval 𝜚. or KGs) not just as a snapshot fixed in time (as it would In this case we will consider the time unit being in years. be for non temporal automated reasoning), but in the Rule 2 states that if an investment in π‘ π‘’π‘π‘‘π‘œπ‘Ÿ in the last evolution of the entities represented in the data, so as 2 years had a π‘Ÿπ‘’π‘‘π‘’π‘Ÿπ‘›, in the last year, greater than the to provide a much needed additional dimension to the original π‘–π‘›π‘£π‘’π‘ π‘‘π‘šπ‘’π‘›π‘‘, then it is considered a SuccessfulIn- scope of the domain at hand. vestment. In Rule 3, then, for each SuccessfulInvestment In particular, we are interested in temporal operators we compute a π‘›π‘’π‘€πΌπ‘›π‘£π‘’π‘ π‘‘π‘šπ‘’π‘›π‘‘ that will be used to in- that allow to reason on the validity of data for specific vest in the same sector. periods of time in the past or in the future w.r.t. the Languages. While proposals of a temporal reasoning current moment. language and in extension to Datalog have been pre- In order to show how some of these operators work sented already starting from the 1980s, it is only thanks and their usefulness in reasoning, we present, as an ex- to a recent resurgence of interest in temporal logic, and ample, the scenario of a company concerned with future in particular in extending Datalog with Metric Tempo- acquisitions and investments. ral Logic (MTL), that led to several studies on various fragments of the proposed language DatalogMTL. These studies attest to the feasibility and the potential of its ⊟[0,3] EstimatedValueIncrease(π‘ π‘‘π‘Žπ‘Ÿπ‘‘π‘’π‘), possible applications, and in recent years we have seen β†’ Buy(π‘ π‘‘π‘Žπ‘Ÿπ‘‘π‘’π‘) (1) many of them [1, 2, 3, 4, 5, 6, 7, 8, 9]. However, even The box minus ⊟𝜚 operator assesses whether a fact considering a limited volume of published literature, it is always valid in the past relative interval 𝜚. In this is a challenge to understand the expressive power of the involved languages, especially in the context of current ones, and even more than that what is the path to take $ liviablasi@gmail.com (L. Blasi) this research into the future.  0000-0003-0701-1688 (L. Blasi) Β© 2022 Copyright for this paper by its authors. Use permitted under Creative In particular, we are interested in understanding what Commons License Attribution 4.0 International (CC BY 4.0). CEUR CEUR Workshop Proceedings (CEUR-WS.org) Workshop Proceedings http://ceur-ws.org ISSN 1613-0073 it means to reason in a certain DatalogMTL fragment, 1 The views and opinions expressed in this paper are those of the and what kind of applications can make use of such a authors and do not necessarily reflect the official policy or position reasoning space. of Banca d’Italia. While several surveys have been conducted on tem- [7] P. A. Walega, B. C. Grau, M. Kaminski, E. V. poral logic and reasoning over time [10], in fact, to our Kostylev, Tractable fragments of datalog with met- knowledge most of them are now either outdated [11] or ric temporal operators, in: IJCAI, ijcai.org, 2020, pp. are not focused on covering the topic in terms of practi- 1919–1925. cal applications, hence ignoring the latest finds on Data- [8] P. A. Walega, D. J. T. Cucala, E. V. Kostylev, B. C. logMTL and the dense timeline [12, 13, 14, 15]. Grau, Datalogmtl with negation under stable mod- Contribution. In this talk, we present the following els semantics, in: KR, 2021, pp. 609–618. contributions: [9] P. A. Walega, M. Zawidzki, B. C. Grau, Finitely ma- terialisable datalog programs with metric temporal β€’ We present a short introduction on temporal rea- operators, in: KR, 2021, pp. 619–628. soning, with a focus on DatalogMTL, which ex- [10] J. Chomicki, Temporal query languages: A survey, tends the Datalog language with Metric Temporal in: D. M. Gabbay, H. J. Ohlbach (Eds.), Temporal Logic operators, and which has been deemed to Logic, Springer Berlin Heidelberg, Berlin, Heidel- be very promising in terms of practical applica- berg, 1994, pp. 506–534. tions. [11] G. Gottlob, E. GrΓ€del, H. Veith, Linear Time Data- β€’ We present some of the recent results of the re- log and Branching Time Logic, Kluwer Academic search on DatalogMTL in terms of complexity Publishers, USA, 2000, p. 443–467. and integration with other Datalog languages. [12] S. Konur, A survey on temporal logics for specify- β€’ We propose a number of scenarios in financial ing and verifying real-time systems, Frontiers of applications which deal with temporal data, and Computer Science 7 (2013) 370. we show how problems can be solved through [13] S. Konur, A survey on temporal logics, CoRR the use of temporal reasoning. abs/1005.3199 (2010). arXiv:1005.3199. [14] A. Artale, R. Kontchakov, A. Kovtunova, β€’ We list some desiderata for future development of V. Ryzhikov, F. Wolter, M. Zakharyaschev, temporal Datalog that would allow us to integrate Ontology-mediated query answering over powerful temporal reasoning into the Vadalog temporal data: a survey, 2017. system [16] a reasoning system for Knowledge [15] V. Goranko, A. Rumberg, Temporal Logic, in: E. N. Graphs. Zalta (Ed.), The Stanford Encyclopedia of Philoso- phy, Fall 2021 ed., Metaphysics Research Lab, Stan- ford University, 2021. URL: https://plato.stanford. 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