Allen's Relations Research Articles

The addition of temporal neighborhood makes the logic of prefixes and sub-intervals EXPSPACE-complete

A classic result by Stockmeyer gives a non-elementary lower bound to the emptiness problem for star-free generalized regular expressions. This result is intimately connected to the satisfiability problem for interval temporal logic, notably for formulas that make use of the so-called chop operator. Such an operator can indeed be interpreted as the inverse of the concatenation operation on regular languages, and this correspondence enables reductions between non-emptiness of star-free generalized regular expressions and satisfiability of formulas of the interval temporal logic of chop under the homogeneity assumption. In this paper, we study the complexity of the satisfiability problem for suitable weakenings of the chop interval temporal logic, that can be equivalently viewed as fragments of Halpern and Shoham interval logic. We first consider the logic $\mathsf{BD}_{hom}$ featuring modalities $B$, for \emph{begins}, corresponding to the prefix relation on pairs of intervals, and $D$, for \emph{during}, corresponding to the infix relation. The homogeneous models of $\mathsf{BD}_{hom}$ naturally correspond to languages defined by restricted forms of regular expressions, that use union, complementation, and the inverses of the prefix and infix relations. Such a fragment has been recently shown to be PSPACE-complete . In this paper, we study the extension $\mathsf{BD}_{hom}$ with the temporal neighborhood modality $A$ (corresponding to the Allen relation \emph{Meets}), and prove that it increases both its expressiveness and complexity. In particular, we show that the resulting logic $\mathsf{BDA}_{hom}$ is EXPSPACE-complete.

Knowledge Representation and Reasoning for Complex Time Expression in Clinical Text

Abstract Temporal information is pervasive and crucial in medical records and other clinical text, as it formulates the development process of medical conditions and is vital for clinical decision making. However, providing a holistic knowledge representation and reasoning framework for various time expressions in the clinical text is challenging. In order to capture complex temporal semantics in clinical text, we propose a novel Clinical Time Ontology (CTO) as an extension from OWL framework. More specifically, we identified eight time-related problems in clinical text and created 11 core temporal classes to conceptualize the fuzzy time, cyclic time, irregular time, negations and other complex aspects of clinical time. Then, we extended Allen's and TEO's temporal relations and defined the relation concept description between complex and simple time. Simultaneously, we provided a formulaic and graphical presentation of complex time and complex time relationships. We carried out empirical study on the expressiveness and usability of CTO using real-world healthcare datasets. Finally, experiment results demonstrate that CTO could faithfully represent and reason over 93% of the temporal expressions, and it can cover a wider range of time-related classes in clinical domain.

Adding the Relation Meets to the Temporal Logic of Prefixes and Infixes makes it EXPSPACE-Complete

The choice of the right trade-off between expressiveness and complexity is the main issue in interval temporal logic. In their seminal paper, Halpern and Shoham showed that the satisfiability problem for HS (the temporal logic of Allen's relations) is highly undecidable over any reasonable class of linear orders. In order to recover decidability, one can restrict the set of temporal modalities and/or the class of models. In the following, we focus on the satisfiability problem for HS fragments under the homogeneity assumption, according to which any proposition letter holds over an interval if only if it holds at all its points. The problem for full HS with homogeneity has been shown to be non-elementarily decidable, but its only known lower bound is EXPSPACE (in fact, EXPSPACE-hardness has been shown for the logic of prefixes and suffixes BE, which is a very small fragment of it. The logic of prefixes and infixes BD has been recently shown to be PSPACE-complete. In this paper, we prove that the addition of the Allen relation Meets to BD makes it EXPSPACE-complete.

Cache-efficient sweeping-based interval joins for extended Allen relation predicates

We develop a family of efficient plane-sweeping interval join algorithms for evaluating a wide range of interval predicates such as Allen’s relationships and parameterized relationships. Our technique is based on a framework, components of which can be flexibly combined in different manners to support the required interval relation. In temporal databases, our algorithms can exploit a well-known and flexible access method, the Timeline Index, thus expanding the set of operations it supports even further. Additionally, employing a compact data structure, the gapless hash map, we utilize the CPU cache efficiently. In an experimental evaluation, we show that our approach is several times faster and scales better than state-of-the-art techniques, while being much better suited for real-time event processing.

Decidability and complexity of the fragments of the modal logic of Allen's relations over the rationals

Interval temporal logics provide a natural framework for temporal reasoning about interval structures over linearly ordered domains, where intervals are taken as first-class citizens. Their expressive power and computational behavior mainly depend on two parameters: the set of modalities they feature and the linear orders over which they are interpreted. In this paper, we consider all fragments of Halpern and Shoham's interval temporal logic HS with a decidable satisfiability problem over the rationals, and we provide a complete classification of them in terms of their expressiveness and computational complexity by solving the last few open problems.

A Language for Online State Processing of Binary Sensors, Applied to Ambient Assisted Living

There is a large variety of binary sensors in use today, and useful context-aware services can be defined using such binary sensors. However, the currently available approaches for programming context-aware services do not conveniently support binary sensors. Indeed, no existing approach simultaneously supports a notion of state, central to binary sensors, offers a complete set of operators to compose states, allows to define reusable abstractions by means of such compositions, and implements efficient online processing of these operators. This paper proposes a new language for event processing specifically targeted to binary sensors. The central contributions of this language are a native notion of state and semi-causal operators for temporal state composition including: Allen's interval relations generalized for handling multiple intervals, and temporal filters for handling delays. Compared to other approaches such as CEP (complex event processing), our language provides less discontinued information, allows less restricted compositions, and supports reusable abstractions. We implemented an interpreter for our language and applied it to successfully rewrite a full set of real Ambient Assisted Living services. The performance of our prototype interpreter is shown to compete well with a commercial CEP engine when expressing the same services.

Effects of physical features on production of three macrofaunal species in different sandy beach zones in South America

Habitat Harshness Hypothesis (HHH) and Habitat Safety Hypothesis (HSH) successfully predict trends in diversity, abundance, individual growth, survival rate, and reproductive success of intertidal and supralittoral macrofauna species according to beach morphodynamic states. However, the effects of beach physical features on secondary production are still poorly known, especially concerning the response of species that inhabit different beach zones. Here we tested the hypothesis that production and P/B ratio of common species of lower and middle intertidal, the wedge clam Donax hanleyanus and the isopod Excirolana armata, respectively, follow HHH, increasing towards less severe dissipative/intermediate conditions. Conversely, the turnover rate (production-to-biomass ratio: P/B) of both species is expected to increase towards harsher reflective conditions according to Allen's relationship (instantaneous mortality rate Z = P/B). On the other hand, the production and P/B of the supralittoral isopod Excirolana braziliensis are expected to follow HSH, i.e. an opposite pattern to that of intertidal species, with higher production on reflective beaches and higher P/B on dissipative ones. To test these predictions, relationships of production and P/B with physical characteristics of beaches (grain size, beach slope, and width) were assessed using 34 estimates gathered from literature, obtained from 14 microtidal beaches located in the Southwestern Atlantic coasts. The results showed that D. hanleyanus production increased towards dissipative conditions following HHH, although P/B ratio followed the production trend. These results, however, agree with those previously observed in the mole crab Emerita brasiliensis, reinforcing these trends for inhabitants of the swash zone, the harshest beach zone. Similarly, E. armata production increased sharply towards dissipative conditions, finer sand and gentler slopes, an expected pattern for a middle intertidal, highly-substrate specific species. Production and P/B of the supralittoral species E. braziliensis followed HHH rather than HSH, with higher production in intermediate/dissipative conditions, and inversely, higher P/B and Z on reflective beaches. This study shows that the production of intertidal species both in the lower and in the middle intertidal increases from reflective to intermediate/dissipative conditions.

Model checking for fragments of the interval temporal logic HS at the low levels of the polynomial time hierarchy

Some temporal properties of reactive systems, such as actions with duration and temporal aggregations, which are inherently interval-based, can not be properly expressed by the standard, point-based temporal logics LTL, CTL and CTL⁎, as they give a state-by-state account of system evolution. Conversely, interval temporal logics—which feature intervals, instead of points, as their primitive entities—naturally express them.We study the model checking (MC) problem for Halpern and Shoham's modal logic of time intervals (HS), interpreted on Kripke structures, under the homogeneity assumption. HS is the best known interval-based temporal logic, which has one modality for each of the 13 ordering relations between pairs of intervals (Allen's relations), apart from equality. We focus on MC for some HS fragments featuring modalities for (a subset of) Allen's relations meet, met-by, started-by, and finished-by, showing that it is in PNP. Additionally, we provide some complexity lower bounds to the problem.

Which fragments of the interval temporal logic HS are tractable in model checking?

Since the 80s, model checking (MC) has been applied to the automatic verification of hardware/software systems. Point-based temporal logics, such as LTL, CTL, CTL⁎, and the like, are commonly used in MC as the specification language; however, there are some inherently interval-based properties of computations, e.g., temporal aggregations and durations, that cannot be properly dealt with by these logics, as they model a state-by-state evolution of systems.Recently, an MC framework for the verification of interval-based properties of computations, based on Halpern and Shoham's interval temporal logic (HS, for short) and its fragments, has been proposed and systematically investigated. In this paper, we focus on the boundaries that separate tractable and intractable HS fragments in MC. We first prove that MC for the logic BE of Allen's relations started-by and finished-by is provably intractable, being Expspace-hard. Such a lower bound immediately propagates to full HS. Then, in contrast, we show that other noteworthy HS fragments, i.e., the logic AA‾BB‾ (resp., AA‾EE‾) of Allen's relations meets, met-by, starts (resp., finishes), and started-by (resp., finished-by), are well-behaved, and turn out to have the same complexity as LTL (Pspace-complete). Halfway are the fragments AA‾BB‾E‾ and AA‾EB‾E‾, whose Expspace membership and Pspace hardness are already known. Here, we give an original proof of Expspace membership, that substantially simplifies the complexity of the constructions previously used for such a result. Contraction techniques—suitably tailored to each HS fragment—are at the heart of our results, enabling us to prove a pair of remarkable small-model properties.

Representing and querying now-relative relational medical data

Temporal information plays a crucial role in medicine. Patients' clinical records are intrinsically temporal. Thus, in Medical Informatics there is an increasing need to store, support and query temporal data (particularly in relational databases), in order, for instance, to supplement decision-support systems. In this paper, we show that current approaches to relational data have remarkable limitations in the treatment of "now-relative" data (i.e., data holding true at the current time). This can severely compromise their applicability in general, and specifically in the medical context, where "now-relative" data are essential to assess the current status of the patients. We propose a theoretically grounded and application-independent relational approach to cope with now-relative data (which can be paired, e.g., with different decision support systems) overcoming such limitations. We propose a new temporal relational representation, which is the first relational model coping with the temporal indeterminacy intrinsic in now-relative data. We also propose new temporal algebraic operators to query them, supporting the distinction between possible and necessary time, and Allen's temporal relations between data. We exemplify the impact of our approach, and study the theoretical and computational properties of the new representation and algebra.

Emergency Strategy Generation Method of Aircraft Disturbance based on Allen Relationship

Emergency Strategy Generation Method of Aircraft Disturbance based on Allen Relationship

Model checking for fragments of Halpern and Shoham's interval temporal logic based on track representatives

Model checking allows one to automatically verify a specification of the expected properties of a system against a formal model of its behavior (generally, a Kripke structure). Point-based temporal logics, such as LTL, CTL, and CTL⁎, that describe how the system evolves state-by-state, are commonly used as specification languages. They proved themselves quite successful in a variety of application domains. However, properties constraining the temporal ordering of temporally extended events as well as properties involving temporal aggregations, which are inherently interval-based, can not be properly dealt with by them. Interval temporal logics (ITLs), that take intervals as their primitive temporal entities, turn out to be well-suited for the specification and verification of interval properties of computations (we interpret all the tracks of a Kripke structure as computation intervals).In this paper, we study the model checking problem for some fragments of Halpern and Shoham's modal logic of time intervals (HS). HS features one modality for each possible ordering relation between pairs of intervals (the so-called Allen's relations). First, we describe an EXPSPACE model checking algorithm for the HS fragment of Allen's relations meets, met-by, starts, started-by, and finishes, which exploits the possibility of finding, for each track (of unbounded length), an equivalent bounded-length track representative. While checking a property, it only needs to consider tracks whose length does not exceed the given bound. Then, we prove the model checking problem for such a fragment to be PSPACE-hard. Finally, we identify other well-behaved HS fragments which are expressive enough to capture meaningful interval properties of systems, such as mutual exclusion, state reachability, and non-starvation, and whose computational complexity is less than or equal to that of LTL.

Model Checking the Logic of Allen's Relations Meets and Started-by is P^NP-Complete

In the plethora of fragments of Halpern and Shoham's modal logic of time intervals (HS), the logic AB of Allen's relations Meets and Started-by is at a central position. Statements that may be true at certain intervals, but at no sub-interval of them, such as accomplishments, as well as metric constraints about the length of intervals, that force, for instance, an interval to be at least (resp., at most, exactly) k points long, can be expressed in AB. Moreover, over the linear order of the natural numbers N, it subsumes the (point-based) logic LTL, as it can easily encode the next and until modalities. Finally, it is expressive enough to capture the {\omega}-regular languages, that is, for each {\omega}-regular expression R there exists an AB formula {\phi} such that the language defined by R coincides with the set of models of {\phi} over N. It has been shown that the satisfiability problem for AB over N is EXPSPACE-complete. Here we prove that, under the homogeneity assumption, its model checking problem is {\Delta}^p_2 = P^NP-complete (for the sake of comparison, the model checking problem for full HS is EXPSPACE-hard, and the only known decision procedure is nonelementary). Moreover, we show that the modality for the Allen relation Met-by can be added to AB at no extra cost (AA'B is P^NP-complete as well).

Recognizing Complex Activities by a Probabilistic Interval-Based Model

A key challenge in complex activity recognition is the fact that a complex activity can often be performed in several different ways, with each consisting of its own configuration of atomic actions and their temporal dependencies. This leads us to define an atomic activity-based probabilistic framework that employs Allen's interval relations to represent local temporal dependencies. The framework introduces a latent variable from the Chinese Restaurant Process to explicitly characterize these unique internal configurations of a particular complex activity as a variable number of tables.It can be analytically shown that the resulting interval network satisfies the transitivity property, and as a result, all local temporal dependencies can be retained and are globally consistent.Empirical evaluations on benchmark datasets suggest our approach significantly outperforms the state-of-the-art methods.

Mining frequent arrangements and sequencing of events for diseases prognosis using reference event-based temporal relations

Mining temporal patterns has been an active research area in AI. Mining patterns of temporally correlated events called arrangements is required in many scientific domains, especially in the medical domain. Key events of the domain defined as reference events are used in describing the arrangements. In this work, mining events in arrangements (MENSA) algorithm is proposed to mine frequent arrangements and to generate sequential rules that can be used in early forecasting of probable diseases and symptoms and hence facilitate decision support related tasks. The MENSA algorithm has excellent scale-up property with respect to the size of the sequences. Temporal relations between events are defined using the contextual reference event-based temporal (REseT) relations. These relations can provide more useful knowledge about the order of events within an arrangement in comparison with Allen's relations and the effectiveness, applicability of these relations in prognosis is demonstrated using PREDICT algorithm with Percent_Similarity as the performance measure. The performance of the proposed algorithms is evaluated and they outperform other existing approaches when experimented on real finance dataset and synthetic medical dataset.

Mining frequent arrangements and sequencing of events for diseases prognosis using reference event-based temporal relations

Mining temporal patterns has been an active research area in AI. Mining patterns of temporally correlated events called arrangements is required in many scientific domains, especially in the medical domain. Key events of the domain defined as reference events are used in describing the arrangements. In this work, mining events in arrangements MENSA algorithm is proposed to mine frequent arrangements and to generate sequential rules that can be used in early forecasting of probable diseases and symptoms and hence facilitate decision support related tasks. The MENSA algorithm has excellent scale-up property with respect to the size of the sequences. Temporal relations between events are defined using the contextual reference event-based temporal REseT relations. These relations can provide more useful knowledge about the order of events within an arrangement in comparison with Allen's relations and the effectiveness, applicability of these relations in prognosis is demonstrated using PREDICT algorithm with Percent_Similarity as the performance measure. The performance of the proposed algorithms is evaluated and they outperform other existing approaches when experimented on real finance dataset and synthetic medical dataset.

A decidable weakening of Compass Logic based on cone-shaped cardinal directions

We introduce a modal logic, called Cone Logic, whose formulas describe properties of points in the plane and spatial relationships between them. Points are labelled by proposition letters and spatial relations are induced by the four cone-shaped cardinal directions. Cone Logic can be seen as a weakening of Venema's Compass Logic. We prove that, unlike Compass Logic and other projection-based spatial logics, its satisfiability problem is decidable (precisely, PSPACE-complete). We also show that it is expressive enough to capture meaningful interval temporal logics - in particular, the interval temporal logic of Allen's relations "Begins", "During", and "Later", and their transposes.

Adding one or more equivalence relations to the interval temporal logic [formula omitted

Interval temporal logics provide a general framework for temporal representation and reasoning, where classical (point-based) linear temporal logics can be recovered as special cases. In this paper, we study the effects of the addition of one or more equivalence relations to one of the most representative interval temporal logics, namely, the logic ABB¯ of Allen's relations meets, begun by, and begins. We first prove that the satisfiability problem for the extension of ABB¯ with one equivalence relation remains decidable over finite linear orders, but it becomes nonprimitive recursive. Then, we show that decidability is lost over N. Finally, we show that the addition of two or more equivalence relations makes finite satisfiability for the resulting logic undecidable.1

A layout inference algorithm for Graphical User Interfaces

Context: Graphical User Interface (GUI) toolkits currently provide layout managers which lay out widgets in views according to certain constraints that characterise each type of layout manager. In some scenarios such as GUI migration and the automated generation of GUIs from wireframes, the layout of views is implicitly expressed through the use of coordinates. In these cases, it is desirable to represent the layout explicitly in terms of layout managers.Objective: To represent a coordinate-based GUI in terms of a set of layout managers, in order to provide different alternative solutions for a given view and select the best alternative.Method: The layout inference process consists of two phases. Firstly, the coordinate-based positioning system is changed to a relative positioning system based on directed graphs and Allen relations. Secondly, an exploratory algorithm based on pattern matching and graph rewriting is applied in order to obtain different layout solutions. The algorithm has been evaluated through a case study related to the automatic generation of fluid web interfaces from wireframes, involving 20 IT professionals.Results: The case study showed that the layout obtained is faithful to the original views in 97% of cases, and maintains its proportions when resized in 84% of views. The majority of the participants were satisfied with the results and found the approach useful.Conclusions: The layout manager representation obtained from the coordinate-based GUIs can be used to generate fluid layouts. The algorithm has two main features that overcome the limitations of the existing approaches: independence of specific layout managers and ability to generate several alternative solutions.

Mining approximate interval-based temporal dependencies

Temporal functional dependencies add valid time to classical functional dependencies in order to express data integrity constraints over the flow of time. If the temporal dimension adopted is an interval, we have to deal with interval-based temporal functional dependencies (ITFDs for short), which consider different interval relations between tuple valid times. The related approximate problem is when we want to check whether our data satisfy, without any constraint for the schema, a given ITFD under a given error threshold $$0 \leqslant \epsilon \leqslant 1$$0ź∈ź1. This can be rephrased as: given a relation instance r, is it possible to delete at most $$\epsilon \cdot |r|$$∈·|r| tuples from it in such a way that the resulting instance satisfies the given ITFD? This optimization problem, ITFD-Approx for short, may represent a way to discover (i.e., mine) important dependencies among attribute values in a database. In this paper we analyze the complexity of problem ITFD-Approx restricting ourselves to Allen's interval relations: we shall see how the complexity of such a problem may significantly change, depending on the considered interval relation.