Interval temporal logic

Reasoning with Space and Time

Published in Konar Amit, Artificial Intelligence and Soft Computing, 2018

The usual definitions of ∧, →, ≡ and ∃ are maintained in interval temporal logic. The following transformations [3] are often useful to derive logical proofs in interval temporal logic. Holds (t1, t2, ϕ1 ∧ ϕ2) → Holds(t1, t2, ϕ1) ∧ holds(t1, t2, ϕ2).Holds(t1, t2, ¬ ϕ) → ¬ Holds(t1, t2, ϕ).

A separation theorem for discrete-time interval temporal logic

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Journal Information

Published in Journal of Applied Non-Classical Logics, 2022

Dimitar P. Guelev, Ben Moszkowski

In Interval Temporal Logic (, Cau et al., 2022; Halpern et al., 1983; Moszkowski, 1985, 1986), satisfaction of formulas is defined at intervals rather than time points, which are typical of other temporal logics. operators for sequentially combining formulas A;B (‘AchopB’) and (‘Achop-star’) are related to the concatenation and Kleene star operators for regular languages. -related logics include the logic of Halpern and Shoham (1986), Venema's (1991), which is based on chop too, real-time interval-based predicate logics for the modelling of hybrid systems such as the Duration Calculus (, Zhou and Hansen, 2004; Zhou et al., 1991), and interval-based modalities for Allen's interval relations (1983). Surveys can be found in Goranko et al. (2004) and Monica et al. (2011).

Interval temporal logic

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Reasoning with Space and Time

A separation theorem for discrete-time interval temporal logic