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Specifying active databases as non-Markovian theories of actions

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Abstract

Over the last 15 years, database management systems (DBMSs) have been enhanced by the addition of rule-based programming to obtain active DBMSs. One of the greatest challenges in this area is to formally account for all the aspects of active behavior using a uniform formalism. In this paper, we formalize active relational databases within the framework of the situation calculus by uniformly accounting for them using theories embodying non-Markovian control in the situation calculus. We call these theories active relational theories and use them to capture the dynamics of active databases. Transaction processing and rule execution is modelled as a theorem proving task using active relational theories as background axioms. We show that the major components of an ADBMS, namely the rule sets and the execution models, may be given a clear semantics using active relational theories. More precisely: we represent the rule set as a program written in a suitable version of the situation calculus based language ConGolog; then we extend an existing situation calculus based framework for modelling advanced transaction models to one for modelling the execution models of active behaviors.

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Notes

  1. The terminology internal versus external action is also used in Lynch et al. (1994), though with a different meaning.

  2. Transactions may be concatenated to form a longer sequence of actions.

  3. We omit the foundational axioms, precondition axioms for external actions, and dependency axioms; they play no role in the sequel of this paper. Furthermore, we assume classical flat transactions as the underlying transaction mechanism (Kiringa 2001).

  4. The ConGolog programs we are referring to in this paper are called well formed. The formal definition of these programs is given in the longer version of this paper (Kiringa 2007).

  5. Readers from Knowledge Representation might get confused by the qualification “Knowledge” in the title of this section. It seems that a title like “Specifying Events” or “Specifying Active Relational Theories” would be a more appropriate title of the section. However, due to Paton (1999), “Knowledge model” is now prevalent in active databases to denote all aspects of active behavior related to events.

  6. For example, in Starburst (Widom and Ceri 1996), r will be considered in the future course of actions only from the time point where it last stopped being considered.

  7. They were first introduced in the HiPAC system (Hsu et al. 1988) and have since been widely used in most ADBMS proposals (Paton 1999). Our presentation is slightly more general than the original one, in which the relationships between coupling modes and execution models, and those between transactions and execution models were not conceptually separated.

  8. This constraint is in fact stricter than a similar constraint found in Hsu et al. (1988), where it is stated that “A cannot be executed before C is evaluated”. The formulation of Hsu et al. (1988), however, does not rule out simultaneous action executions and condition evaluations, a situation that obviously can lead to disastrous behaviors.

  9. Notice that this semantics means that transitions may in fact be big leaps involving many actions. This may prevent some desirable concurrency. We leave this problem out of the scope of this document.

  10. This sentence expresses the so-called confluence property of active rules. This property ensures that whenever a rule program reaches two final database states, then the two states are the same, independently of the order of the execution of non-prioritized rules.

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  1. School of Information Technology and Engineering Faculty of Engineering, University of Ottawa, Ottawa, Canada

    Iluju Kiringa

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  1. Iluju Kiringa
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Correspondence to Iluju Kiringa.

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An early version of this paper appeared in Kiringa and Reiter (2002), Kiringa (2002). Detailed technical specifications, as well as proofs of theorems are given in Kiringa (2007).

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Kiringa, I. Specifying active databases as non-Markovian theories of actions. J Intell Inf Syst 32, 105–138 (2009). https://doi.org/10.1007/s10844-007-0050-3

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