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Defeasible linear temporal logic

Defeasible linear temporal logic After the seminal work of Kraus, Lehmann and Magidor (formally known as the KLM approach) on conditionals and preferential models, many aspects of defeasibility in more complex formalisms have been studied in recent years. Examples of these aspects are the notion of typicality in description logic and defeasible necessity in modal logic. We discuss a new aspect of defeasibility that can be expressed in the case of temporal logic, which is the normality in an execution. In this contribution, we take Linear Temporal Logic ( ) as case study for this defeasible aspect. has found extensive applications in Computer Science and Artificial Intelligence, notably as a formal framework for representing and verifying computer systems that vary over time. However, some systems may presents exceptions at some innocuous time points where they can be tolerated, or conversely, exceptions at other crucial time points where they need to be addressed. In order to ensure the reliability of such systems, we study a preferential extension of , called defeasible linear temporal logic ( ). In the first part of this paper, we show how semantics of KLM's preferential models can be integrated with . We also discuss the addition of non-monotonic temporal operators as a way to formalise defeasible properties of these systems. The second part of this paper is a study of the satisfiability problem of sentences. Based on Sistla and Clarke's work on the complexity of the classical language, we show the bounded-model property of two fragments of language. Moreover, we provide a procedure to check the satisfiability of sentences in both of these fragments. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Non-Classical Logics Taylor & Francis

Defeasible linear temporal logic

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Publisher
Taylor & Francis
Copyright
© 2023 Informa UK Limited, trading as Taylor & Francis Group
ISSN
1958-5780
eISSN
1166-3081
DOI
10.1080/11663081.2023.2209494
Publisher site
See Article on Publisher Site

Abstract

After the seminal work of Kraus, Lehmann and Magidor (formally known as the KLM approach) on conditionals and preferential models, many aspects of defeasibility in more complex formalisms have been studied in recent years. Examples of these aspects are the notion of typicality in description logic and defeasible necessity in modal logic. We discuss a new aspect of defeasibility that can be expressed in the case of temporal logic, which is the normality in an execution. In this contribution, we take Linear Temporal Logic ( ) as case study for this defeasible aspect. has found extensive applications in Computer Science and Artificial Intelligence, notably as a formal framework for representing and verifying computer systems that vary over time. However, some systems may presents exceptions at some innocuous time points where they can be tolerated, or conversely, exceptions at other crucial time points where they need to be addressed. In order to ensure the reliability of such systems, we study a preferential extension of , called defeasible linear temporal logic ( ). In the first part of this paper, we show how semantics of KLM's preferential models can be integrated with . We also discuss the addition of non-monotonic temporal operators as a way to formalise defeasible properties of these systems. The second part of this paper is a study of the satisfiability problem of sentences. Based on Sistla and Clarke's work on the complexity of the classical language, we show the bounded-model property of two fragments of language. Moreover, we provide a procedure to check the satisfiability of sentences in both of these fragments.

Journal

Journal of Applied Non-Classical Logics – Taylor & Francis

Published: Jan 2, 2023

Keywords: Knowledge representation; non-monotonic reasoning; temporal logic

References

  • Conditional logics of normality: A modal approach
  • Preferential reasoning for modal logics
  • From KLM-style conditionals to defeasible modalities, and back
  • The complexity of propositional linear temporal logics in simple cases
  • Analytic tableaux calculi for KLM logics of nonmonotonic reasoning
  • ALC + T: A preferential extension of description logics
  • Nonmonotonic reasoning, preferential models and cumulative logics
  • Counterfactuals and comparative possibility
  • Possibilistic fuzzy linear temporal logic and its model checking
  • The complexity of propositional linear temporal logics