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Combining Event Calculus and Description Logic Reasoning via Logic Programming

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Frontiers of Combining Systems (FroCoS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12941))

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Abstract

The paper introduces a knowledge representation language that combines the event calculus with description logic in a logic programming framework. The purpose is to provide the user with an expressive language for modelling and analysing systems that evolve over time. The approach is exemplified with the logic programming language as implemented in the Fusemate system. The paper extends Fusemate’s rule language with a weakly DL-safe interface to the description logic \(\mathcal ALCIF\) and adapts the event calculus to this extended language. This way, time-stamped ABoxes can be manipulated as fluents in the event calculus. All that is done in the frame of Fusemate’s concept of stratification by time. The paper provides conditions for soundness and completeness where appropriate. Using an elaborated example it demonstrates the interplay of the event calculus, description logic and logic programming rules for computing possible models as plausible explanations of the current state of the modelled system.

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Notes

  1. 1.

    \(\mathcal ALCIF\) is the well-known description logic \(\mathcal ALC\) extended with inverse roles and functional roles. See [5] for background on description logics.

  2. 2.

    This definition of head is actually simplified as Fusemate offers an additional head operator for belief revision, see [11]. This is ignored here.

  3. 3.

    The variables \( var (t)\) in the special form have to be excluded from that because they are quantified within their “” body scope. To avoid name conflicts, we assume that \( var (t) \cap fvar (B') = \emptyset \) for all bodies \(B'\) such that \(B = B'\) or B occurs in \(B'\).

  4. 4.

    Body matcher are represented internally in the Scala runtime system without explicit grounding.

  5. 5.

    The concrete Fusemate syntax is but we stick with the better readable “:”-syntax. TBoxes have similar syntax and are typically bound to (Scala) variables like in the example. In concrete syntax, free constant, function and predicate symbols start with a capital letter, variables with a lower case letter. An underscore is an anonymous variable.

  6. 6.

    Access to I is unusual for logic programming systems. See [12] for a discussion of this features.

  7. 7.

    Actually, events can be inserted in retrospect using Fusemate’s revision operator, restarting the model computation from there. The paper [11] already has a “supply-chain” example for that.

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Acknowledgement

I am grateful to the reviewers for their constructive feedback.

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  1. Data61/CSIRO and The Australian National University, Canberra, Australia

    Peter Baumgartner

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  1. Peter Baumgartner
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Correspondence to Peter Baumgartner .

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  1. University of Liverpool, Liverpool, UK

    Boris Konev

  2. The University of Manchester, Manchester, UK

    Giles Reger

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Baumgartner, P. (2021). Combining Event Calculus and Description Logic Reasoning via Logic Programming. In: Konev, B., Reger, G. (eds) Frontiers of Combining Systems. FroCoS 2021. Lecture Notes in Computer Science(), vol 12941. Springer, Cham. https://doi.org/10.1007/978-3-030-86205-3_6

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