# A quantitative extension of Interval Temporal Logic over infinite words

Model checking for Halpern and Shoham's interval temporal logic HS has been recently investigated in a systematic way, and it is known to be decidable under three distinct semantics (state-based, trace-based and tree-based semantics). Here, we focus on the trace-based semantics, where the main semantic entities are the infinite execution paths (traces) of the given Kripke structure, assuming in addition homogeneity in the propositional valuation. We introduce a quantitative extension of HS over traces, called Difference HS (DHS) allowing one to express timing constraints on the difference among interval lengths (durations). The quantitative extension of some modalities leads immediately to undecidability, so, we investigate the decidability border for the model checking and satisfiability problems by considering strict syntactical fragments of DHS. In particular, we identify the maximal decidable fragment DHSS of DHS proving in addition that the considered problems for the fragment are at least 2EXPSPACE-hard. Moreover, by exploiting new results on linear-time hybrid logics, we show that for an equally expressive fragment of DHSS, the problems are EXPSPACE-complete. Finally, we provide a characterization of HS over traces by means of the one-variable fragment of a novel hybrid logic.

• 14 publications
• 14 publications
09/21/2022

### Parametric Interval Temporal Logic over Infinite Words

Model checking for Halpern and Shoham's interval temporal logic HS has b...
07/06/2022

### Expressiveness and Decidability of Temporal Logics for Asynchronous Hyperproperties

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### Interval vs. Point Temporal Logic Model Checking: an Expressiveness Comparison

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### From Quantified CTL to QBF

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### A Constructive Equivalence between Computation Tree Logic and Failure Trace Testing

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03/06/2020

### Teaching Temporal Logics to Neural Networks

We show that a deep neural network can learn the semantics of linear-tim...
11/08/2019

### Revisiting Semantics of Interactions for Trace Validity Analysis

Interaction languages such as UML sequence diagrams are often associated...