Interval-Related Interpolation in Interval Temporal Logics

@article{Guelev2001IntervalRelatedII,
  title={Interval-Related Interpolation in Interval Temporal Logics},
  author={Dimitar P. Guelev},
  journal={Log. J. IGPL},
  year={2001},
  volume={9},
  pages={677-685}
}
This paper presents a new kind of interpolation theorems about Neighbourhood Logic (NL, [10]) and Interval Temporal Logic (ITL, [8, 4]). Unlike Craig interpolation, which holds for these logics too, the new theorems treat the existence of interpolants which specify properties of selected intervals in the models of NL and ITL. 
4 Citations
Logical Interpolation and Projection onto State in the Duration Calculus
TLDR
A way to understand interpolation in the context of formal verification is proposed and it is shown that both Craig and projection-related interpolation hold about the ⌈P⌉-subset of DC without such restrictions. Expand
Probabilistic Neighbourhood Logic
TLDR
This paper presents a probabilistic extension of Neighbourhood Logic (NL), motivated by the need to supply the Probabilistic Duration Calculus (PDC, [10,4]) with a proof system. Expand
Probabilistic Interval Temporal Logic and Duration Calculus with Infinite Intervals: Complete Proof Systems
TLDR
The paper presents probabilistic extensions of interval temporal logic (ITL) and duration calculus (DC) with infinite intervals and complete Hilbert-style proof for them and results are a strong completeness theorem and a relative completeness the- orem for the system of Probabilistic DC with respect to real-time semantics. Expand
Interpolation and Related Results on the
the governments of the People's Republic of China and Portugal through a contribution to the UNU Endownment Fund. As well as providing two-thirds of the endownment fund, the Macau authorities alsoExpand

References

SHOWING 1-10 OF 21 REFERENCES
Completeness of Neighbourhood Logic
This paper presents a completeness result for a first-order interval temporal logic, called Neighbourhood Logic (NL) which has two neighbourhood modalities. NL can support the specification ofExpand
An Adequate First Order Interval Logic
TLDR
Left and right neighbourhoods are introduced as primitive interval modalities to define other unary and binary modalities of intervals in a first order logic with interval length. Expand
Probabilistic Neighbourhood Logic
TLDR
This paper presents a probabilistic extension of Neighbourhood Logic (NL), motivated by the need to supply the Probabilistic Duration Calculus (PDC, [10,4]) with a proof system. Expand
A Temporal Logic for Multilevel Reasoning about Hardware
TLDR
Interval temporal logic offers a natural basis for the specification of devices and digital signals and is suitable for hardware description languages based on formalisms suited to temporal reasoning. Expand
Notes on Neighbourhood Logic
UNU/IIST UNU/IIST enables developing countries to attain self-reliance in software technology by: (i) their own development of high integrity computing systems, (ii) highest level postgraduateExpand
Neighbourhood Logics: NL and NL2
  • Research Report 120, UNU/IIST,
  • 1997
Received July
  • Received July
  • 2001
Probabilistic Neighbourhood Logic In: Formal Techniques for Real Time and Fault Tolerant Systems An extended version is available as
  • LNCS 1926
  • 2000
Probabilistic Neighbourhood Logic In: Formal Techniques for Real Time and Fault Tolerant Systems An extended version is available as
  • LNCS 1926
  • 2000
Probabilistic Neighbourhood Logic. In: Formal Techniques for Real Time and Fault Tolerant Systems, Mathai Joseph (ed.), LNCS 1926
  • 2000
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