Temporal expressions describing the so-called Allen’s relations between intervals are broadly exploited in Artificial Intelligence and engineering, for example, in a system specification. They may be formally rendered in terms of Halpern-Shoham logic. If these expressions are combined with some expressions describing differents obligations or permissions, then we need a kind of a deontic Halpern-Shoham logic to represent the combinations. If also obligations are gradable and they introduce a kind of a fuzziness, then a new multi-valued (fuzzy) deontic logic should be expected. According to it – a multi-valued deontic Halpern-Shoham logic is proposed in the paper. Its combined formulae are interpreted in the interval-based fibred semantics, which consitutes a modification of the pioneering ideas of Gabbay’s fibred semantics.
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