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Revising System Specifications in Temporal Logic

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Abstract

Although formal system verification has been around for many years, little attention was given to the case where the specification of the system has to be changed. This may occur due to a failure in capturing the clients’ requirements or due to some change in the domain (think for example of banking systems that have to adapt to different taxes being imposed). We are interested in having methods not only to verify properties, but also to suggest how the system model should be changed so that a property would be satisfied. For this purpose, we will use techniques from the area of Belief Revision, that deals with the problem of changing a knowledge base in view of new information. In the last thirty years, several authors have contributed with change operations and ways of characterizing them. However, most of the work concentrates on knowledge bases represented using classical propositional logic. In the last decade, there have been efforts to apply belief revision theory to description and modal logics. In this work, we analyze what is needed for a theory of belief revision which can be applied to the temporal logic, such as the Computation Tree Logic (CTL). In particular, we illustrate different alternatives for formalizing the concept of revision of CTL. Our interest in this particular logic comes both from practical issues, since it is used for software specification, as from theoretical issues, as it is a non-compact logic and most existing results rely on compactness. We focus here on the revision of CTL models and present a characterization result for the revision of partial models.

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Notes

  1. Actually, Alchourrón, Gärdenfors and Makinson proved the result for another operation, contraction, and then later proved the relation between contraction and revision, having this theorem as a corollary.

  2. A path \(\pi = [s_1, s_2,\ldots , s_{i-1}, s_i, s_{i+1},\ldots ]\) is a path in \( {\mathcal {M}}= {{\langle AP{}, S{}, s_0{}, R{}, L{} \rangle }}\) if and only if \( \forall s \in \pi , s \in S \) and \( (s_i, s_{i+1}) \in R \) for all \( i \ge 1 \).

  3. In fact, it is trivially satisfied by operations PU1–PU5. However (R*1)–(R*5) were intended to be applied for any set of primitive operations

  4. A KMTS is equivalent to a Kripke structure if its expansion generates a set with a single Kripke model. This occurs when in a KMTS there are no undeterminacies about labels or transitions.

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Funding

Paulo T. Guerra was funded by Grant #2010/15392-3, São Paulo Research Foundation (FAPESP). This work was developed under the Brazilian Research Council (CNPq) Grant #447178/2014-8.

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Authors and Affiliations

  1. Federal University of Ceará, Campus Quixadá, Quixadá, Brazil

    Paulo T. Guerra

  2. Institute of Mathematics and Statistics, University of São Paulo, São Paulo, Brazil

    Renata Wassermann

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  1. Paulo T. Guerra
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Correspondence to Paulo T. Guerra.

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Guerra, P.T., Wassermann, R. Revising System Specifications in Temporal Logic. J of Log Lang and Inf 31, 591–618 (2022). https://doi.org/10.1007/s10849-022-09376-9

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