64,825 research outputs found
Specifying and Monitoring Properties of Stochastic Spatio-Temporal Systems in Signal Temporal Logic
We present an extension of the linear time, time-bounded, Signal Temporal Logic to describe spatio-temporal properties. We consider a discrete location/ patch-based representation of space, with a population of interacting agents evolving in each location and with agents migrating from one patch to another one. We provide both a boolean and a quantitative semantics to this logic. We then present monitoring algorithms to check the validity of a formula, or to compute its satisfaction (robustness) score, over a spatio-temporal trace, exploiting these routines to do statistical model checking of stochastic models. We illustrate the logic at work on an epidemic example, looking at the diffusion of a cholera infection among communities living along a river
Linear-Time Temporal Answer Set Programming
[Abstract]: In this survey, we present an overview on (Modal) Temporal Logic Programming in view of its application to Knowledge Representation and Declarative Problem Solving. The syntax of this extension of logic programs is the result of combining usual rules with temporal modal operators, as in Linear-time Temporal Logic (LTL). In the paper, we focus on the main recent results of the non-monotonic formalism called Temporal Equilibrium Logic (TEL) that is defined for the full syntax of LTL but involves a model selection criterion based on Equilibrium Logic, a well known logical characterization of Answer Set Programming (ASP). As a result, we obtain a proper extension of the stable models semantics for the general case of temporal formulas in the syntax of LTL. We recall the basic definitions for TEL and its monotonic basis, the temporal logic of Here-and-There (THT), and study the differences between finite and infinite trace length. We also provide further useful results, such as the translation into other formalisms like Quantified Equilibrium Logic and Second-order LTL, and some techniques for computing temporal stable models based on automata constructions. In the remainder of the paper, we focus on practical aspects, defining a syntactic fragment called (modal) temporal logic programs closer to ASP, and explaining how this has been exploited in the construction of the solver telingo, a temporal extension of the well-known ASP solver clingo that uses its incremental solving capabilities.Xunta de Galicia; ED431B 2019/03We are thankful to the anonymous reviewers for their thorough work and their useful
suggestions that have helped to improve the paper. A special thanks goes to Mirosaw
Truszczy´nski for his support in improving the quality of our paper. We are especially
grateful to David Pearce, whose help and collaboration on Equilibrium Logic was the
seed for a great part of the current paper. This work was partially supported by MICINN,
Spain, grant PID2020-116201GB-I00, Xunta de Galicia, Spain (GPC ED431B 2019/03),
R´egion Pays de la Loire, France, (projects EL4HC and etoiles montantes CTASP), European
Union COST action CA-17124, and DFG grants SCHA 550/11 and 15, Germany
A Quantitative Extension of Interval Temporal Logic over Infinite Words
Model checking (MC) for Halpern and Shoham’s interval temporal logic HS has been recently investigated in a systematic way, and it is known to be decidable under three distinct semantics (state-based, trace-based and tree-based semantics), all of them assuming homogeneity in the propositional valuation. Here, we focus on the trace-based semantics, where the main semantic entities are the infinite execution paths (traces) of the given Kripke structure. We introduce a quantitative extension of HS over traces, called Difference HS (DHS), allowing one to express timing constraints on the difference among interval lengths (durations). We show that MC and satisfiability of full DHS are in general undecidable, so, we investigate the decidability border for these problems by considering natural syntactical fragments of DHS. In particular, we identify a maximal decidable fragment DHSsimple of DHS proving in addition that the considered problems for this fragment are at least 2Expspace-hard. Moreover, by exploiting new results on linear-time hybrid logics, we show that for an equally expressive fragment of DHSsimple, the problems are Expspace-complete. Finally, we provide a characterization of HS over traces by means of the one-variable fragment of a novel hybrid logic
A decidable policy language for history-based transaction monitoring
Online trading invariably involves dealings between strangers, so it is
important for one party to be able to judge objectively the trustworthiness of
the other. In such a setting, the decision to trust a user may sensibly be
based on that user's past behaviour. We introduce a specification language
based on linear temporal logic for expressing a policy for categorising the
behaviour patterns of a user depending on its transaction history. We also
present an algorithm for checking whether the transaction history obeys the
stated policy. To be useful in a real setting, such a language should allow one
to express realistic policies which may involve parameter quantification and
quantitative or statistical patterns. We introduce several extensions of linear
temporal logic to cater for such needs: a restricted form of universal and
existential quantification; arbitrary computable functions and relations in the
term language; and a "counting" quantifier for counting how many times a
formula holds in the past. We then show that model checking a transaction
history against a policy, which we call the history-based transaction
monitoring problem, is PSPACE-complete in the size of the policy formula and
the length of the history. The problem becomes decidable in polynomial time
when the policies are fixed. We also consider the problem of transaction
monitoring in the case where not all the parameters of actions are observable.
We formulate two such "partial observability" monitoring problems, and show
their decidability under certain restrictions
A Temporal Logic for Hyperproperties
Hyperproperties, as introduced by Clarkson and Schneider, characterize the
correctness of a computer program as a condition on its set of computation
paths. Standard temporal logics can only refer to a single path at a time, and
therefore cannot express many hyperproperties of interest, including
noninterference and other important properties in security and coding theory.
In this paper, we investigate an extension of temporal logic with explicit path
variables. We show that the quantification over paths naturally subsumes other
extensions of temporal logic with operators for information flow and knowledge.
The model checking problem for temporal logic with path quantification is
decidable. For alternation depth 1, the complexity is PSPACE in the length of
the formula and NLOGSPACE in the size of the system, as for linear-time
temporal logic
LTLf and LDLf Monitoring: A Technical Report
Runtime monitoring is one of the central tasks to provide operational
decision support to running business processes, and check on-the-fly whether
they comply with constraints and rules. We study runtime monitoring of
properties expressed in LTL on finite traces (LTLf) and in its extension LDLf.
LDLf is a powerful logic that captures all monadic second order logic on finite
traces, which is obtained by combining regular expressions and LTLf, adopting
the syntax of propositional dynamic logic (PDL). Interestingly, in spite of its
greater expressivity, LDLf has exactly the same computational complexity of
LTLf. We show that LDLf is able to capture, in the logic itself, not only the
constraints to be monitored, but also the de-facto standard RV-LTL monitors.
This makes it possible to declaratively capture monitoring metaconstraints, and
check them by relying on usual logical services instead of ad-hoc algorithms.
This, in turn, enables to flexibly monitor constraints depending on the
monitoring state of other constraints, e.g., "compensation" constraints that
are only checked when others are detected to be violated. In addition, we
devise a direct translation of LDLf formulas into nondeterministic automata,
avoiding to detour to Buechi automata or alternating automata, and we use it to
implement a monitoring plug-in for the PROM suite
Computation Tree Logic with Deadlock Detection
We study the equivalence relation on states of labelled transition systems of
satisfying the same formulas in Computation Tree Logic without the next state
modality (CTL-X). This relation is obtained by De Nicola & Vaandrager by
translating labelled transition systems to Kripke structures, while lifting the
totality restriction on the latter. They characterised it as divergence
sensitive branching bisimulation equivalence.
We find that this equivalence fails to be a congruence for interleaving
parallel composition. The reason is that the proposed application of CTL-X to
non-total Kripke structures lacks the expressiveness to cope with deadlock
properties that are important in the context of parallel composition. We
propose an extension of CTL-X, or an alternative treatment of non-totality,
that fills this hiatus. The equivalence induced by our extension is
characterised as branching bisimulation equivalence with explicit divergence,
which is, moreover, shown to be the coarsest congruence contained in divergence
sensitive branching bisimulation equivalence
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