5 research outputs found
Partially Punctual Metric Temporal Logic is Decidable
Metric Temporal Logic \mathsf{MTL}[\until_I,\since_I] is one of the most
studied real time logics. It exhibits considerable diversity in expressiveness
and decidability properties based on the permitted set of modalities and the
nature of time interval constraints . Henzinger et al., in their seminal
paper showed that the non-punctual fragment of called
is decidable. In this paper, we sharpen this decidability
result by showing that the partially punctual fragment of
(denoted ) is decidable over strictly monotonic finite point
wise time. In this fragment, we allow either punctual future modalities, or
punctual past modalities, but never both together. We give two satisfiability
preserving reductions from to the decidable logic
\mathsf{MTL}[\until_I]. The first reduction uses simple projections, while
the second reduction uses a novel technique of temporal projections with
oversampling. We study the trade-off between the two reductions: while the
second reduction allows the introduction of extra action points in the
underlying model, the equisatisfiable \mathsf{MTL}[\until_I] formula obtained
is exponentially succinct than the one obtained via the first reduction, where
no oversampling of the underlying model is needed. We also show that
is strictly more expressive than the fragments
\mathsf{MTL}[\until_I,\since] and \mathsf{MTL}[\until,\since_I]
Generalizing Non-Punctuality for Timed Temporal Logic with Freeze Quantifiers
Metric Temporal Logic (MTL) and Timed Propositional Temporal Logic (TPTL) are
prominent real-time extensions of Linear Temporal Logic (LTL). In general, the
satisfiability checking problem for these extensions is undecidable when both
the future U and the past S modalities are used. In a classical result, the
satisfiability checking for MITL[U,S], a non punctual fragment of MTL[U,S], is
shown to be decidable with EXPSPACE complete complexity. Given that this notion
of non punctuality does not recover decidability in the case of TPTL[U,S], we
propose a generalization of non punctuality called \emph{non adjacency} for
TPTL[U,S], and focus on its 1-variable fragment, 1-TPTL[U,S]. While non
adjacent 1-TPTL[U,S] appears to be be a very small fragment, it is strictly
more expressive than MITL. As our main result, we show that the satisfiability
checking problem for non adjacent 1-TPTL[U,S] is decidable with EXPSPACE
complete complexity
21st International Symposium on Temporal Representation and Reasoning, TIME 2014, Verona, Italy, September 8-10, 2014
The proceedings contain 18 papers. The topics discussed include: a tractable generalization of simple temporal networks and its relation to mean payoff games; sound and complete algorithms for checking the dynamic controllability of temporal networks with uncertainty, disjunction and observation; a formal account of planning with flexible timelines; metric propositional neighborhood logic with an equivalence relation; checking interval properties of computations; approximate interval-based temporal dependencies: the complexity landscape; a framework for managing temporal dimensions in archaeological data; lean index structures for snapshot access in transaction-time databases; high-level operations for creation and maintenance of temporal and conventional schema in the tauXSchema framework; summarizability in multiversion data warehouse; fairness with EXPTIME bundled CTL tableau; and partially punctual metric temporal logic is decidable