Foundations for Reliable and Flexible Interactive Multimedia Scores

International audienceInteractive Scores (IS) is a formalism for composing and performing interactive multimedia scores with several applications in video games, live performance installations, and virtual museums. The composer defines the temporal organization of the score by asserting temporal relations (TRs) between temporal objects (TOs). At execution time, the performer may modify the start/stop times of the TOs by triggering interaction points and the system guarantees that all the TRs are satisfied. Implementations of IS and formal models of their behavior have already been proposed, but these do not provide usable means to reason about their properties. In this paper we introduce ReactiveIS, a programming language that fully captures the temporal structure of IS during both composition and execution. For that, we propose a semantics based on tree-like structures representing the execution state of the score at each point in time. The semantics captures the hierarchical aspects of IS and provides an intuitive representation of their execution. We also endow ReactiveIS with a logical semantics based on linear logic, thus widening the reasoning techniques available for IS. We show that ReactiveIS is general enough to capture the full behavior of IS and that it provides declarative ways to increase IS expressivity with, for instance, conditional statements and loops

Hybrid and Subexponential Linear Logics Technical Report

HyLL (Hybrid Linear Logic) and SELL (Subexponential Linear Logic) are logical frameworks that have been extensively used for specifying systems that exhibit modalities such as temporal or spatial ones. Both frameworks have linear logic (LL) as a common ground and they admit (cut-free) complete focused proof systems. The difference between the two logics relies on the way modalities are handled. In HyLL, truth judgments are labelled by worlds and hybrid connectives relate worlds with formulas. In SELL, the linear logic exponentials (!, ?) are decorated with labels representing locations, and an ordering on such labels defines the provability relation among resources in those locations. It is well known that SELL, as a logical framework, is strictly more expressive than LL. However, so far, it was not clear whether HyLL is more expressive than LL and/or SELL. In this paper, we show an encoding of the HyLL's logical rules into LL with the highest level of adequacy, hence showing that HyLL is as expressive as LL. We also propose an encoding of HyLL into SELL ⋓ (SELL plus quantification over locations) that gives better insights about the meaning of worlds in HyLL. We conclude our expressiveness study by showing that previous attempts of encoding Computational Tree Logic (CTL) operators into HyLL cannot be extended to consider the whole set of temporal connectives. We show that a system of LL with fixed points is indeed needed to faithfully encode the behavior of such temporal operators