Allen's Interval Algebra Research Articles

On prime scenarios in qualitative spatial and temporal reasoning

The concept of prime implicant is a fundamental tool in Boolean algebra, which is used in Boolean circuit design and, recently, in explainable AI. This study investigates an analogous concept in qualitative spatial and temporal reasoning, called prime scenario. Specifically, we define a prime scenario of a qualitative constraint network (QCN) as a minimal set of decisions that can uniquely determine solutions of this QCN. We propose in this paper a collection of algorithms designed to address various problems related to prime scenarios, and also show how certain results can be useful for measuring the robustness of a QCN. In addition, we study the relationship between our notions in this paper and the notion of prime sub-QCN in the literature, and establish theoretical results in the process. Further, we devise a language based on the notion of prime scenario for knowledge compilation. Finally, an experimental evaluation is performed with instances of Allen's Interval Algebra and RCC8 to assess the efficiency of our algorithms and, hence, also the difficulty of the newly introduced problems here.

Bayesian chronology construction and substance time

Two views of archaeological time are distinguished; an event view that models stratigraphic relations, and a substance view that models genealogical relations among artifacts, including the three modes of change represented by branching, transformation, and reticulation. Chronology construction is more complex in substance time than it is in event time, which only concerns transformation. Allen's interval algebra can be used to specify the chronological relations associated with the modes of change, and these relations can be identified by post-processing the output from Bayesian chronological models. A worked example illustrates how identifying the chronological relations can aid construction of a phyletic seriation of beads recovered from Anglo-Saxon female graves. These results might encourage archaeologists to carry out chronology construction in substance time as an aid to historical inference.

Solving infinite-domain CSPs using the patchwork property

The constraint satisfaction problem (CSP) has important applications in computer science and AI. In particular, infinite-domain CSPs have been intensively used in subareas of AI such as spatio-temporal reasoning. Since constraint satisfaction is a computationally hard problem, much work has been devoted to identifying restricted problems that are efficiently solvable. One way of doing this is to restrict the interactions of variables and constraints, and a highly successful approach is to bound the treewidth of the underlying primal graph. Bodirsky & Dalmau (2013) [14] and Huang et al. (2013) [47] proved that CSP(Γ) can be solved in nf(w) time (where n is the size of the instance, w is the treewidth of the primal graph and f is a computable function) for certain classes of constraint languages Γ. We improve this bound to f(w)⋅nO(1), where the function f only depends on the language Γ, for CSPs whose basic relations have the patchwork property. Hence, such problems are fixed-parameter tractable and our algorithm is asymptotically faster than the previous ones. Additionally, our approach is not restricted to binary constraints, so it is applicable to a strictly larger class of problems than that of Huang et al. However, there exist natural problems that are covered by Bodirsky & Dalmau's algorithm but not by ours, and we begin investigating ways of generalising our results to larger families of languages. We also analyse our algorithm with respect to its running time and show that it is optimal (under the Exponential Time Hypothesis) for certain languages such as Allen's Interval Algebra.

Branching interval algebra: An almost complete picture

Branching Algebra is the natural branching-time generalization of Allen's Interval Algebra. As in the linear case, the consistency problem for Branching Algebra is NP-hard. Branching Algebra has many potential applications in different areas of Artificial Intelligence; therefore, being able to efficiently solve classical problems expressed in Branching Algebra is very important. This can be achieved in two steps: first, by identifying expressive enough, yet tractable fragments of the whole algebra, and, second, by using such fragments to boost the performances of a backtracking algorithm for the whole language. In this paper we study the properties of several such fragments, both from the algebraic and the computational point of view, and we give an almost complete picture of tractable and non-tractable fragments of the Branching Algebra.

Certain and Uncertain Temporal Data Representation and Reasoning in OWL 2

Temporal data given by Alzheimer's patients are mostly uncertain. Many approaches have been proposed to handle certain temporal data and lack uncertain ones. This paper proposes an approach to represent and reason about quantitative time intervals and points and qualitative relations between them. It is suitable to handle certain and uncertain temporal data. It includes three parts. (1) The authors extend the 4D-fluents approach with certain components to represent certain and uncertain temporal data. (2) They extend the Allen's interval algebra to reason about certain and uncertain time intervals. They adapt these relations to relate a time interval and a time point, and two time points. All relations can be used for temporal reasoning by means of transitivity tables. (3) They propose a certain ontology based on the extensions. A prototype is implemented and integrated into an ontology-based memory prosthesis for Alzheimer's patients to handle uncertain data inputs. The evaluation proves the usefulness of the approach as all the inferences are well established and the precision results are promising.

On neighbourhood singleton-style consistencies for qualitative spatial and temporal reasoning

Given a qualitative constraint network (QCN), a singleton-style consistency focuses on each base relation (atom) of a constraint separately, rather than the entire constraint altogether. This local consistency is essential for tackling fundamental reasoning problems associated with QCNs, such as minimal labeling, but can suffer from redundant constraint checks, especially when checks occur far from where the pruning usually takes place. In this paper, we propose singleton-style consistencies that are applied just on the neighbourhood of a singleton-checked constraint instead of the whole network. We make a theoretical comparison with existing consistencies and consequently prove some properties of the new ones. Further, we propose algorithms to enforce our consistencies, as well as parsimonious variants thereof, that are more efficient in practice than the state of the art. An experimental evaluation with random and structured QCNs of Allen's Interval Algebra in the phase transition region demonstrates the potential of our approach.

Dealing with Precise and Imprecise Temporal Data in Crisp Ontology

This article proposes a crisp-based approach for representing and reasoning about concepts evolving in time and of their properties in terms of qualitative relations (e.g., “before”) in addition to quantitative ones, time intervals and points. It is not only suitable to handle precise time intervals and points, but also imprecise ones. It extends the 4D-fluents approach with crisp components to represent handed data. It also extends the Allen's interval algebra. This extension allows reasoning about imprecise time intervals. Compared to related work, it is based on crisp set theory. These relations preserve many properties of the original algebra. Their definitions are adapted to allow relating a time interval and a time point, and two time points. All relations can be used for temporal reasoning by means of transitivity tables. Finally, it proposes a crisp ontology that based on the extended Allen's algebra instantiates the 4D-fluents-based representation.

A Novel Dynamic Model Capturing Spatial and Temporal Patterns for Facial Expression Analysis.

Facial expression analysis could be greatly improved by incorporating spatial and temporal patterns present in facial behavior, but the patterns have not yet been utilized to their full advantage. We remedy this via a novel dynamic model-an interval temporal restricted Boltzmann machine (IT-RBM) - that is able to capture both universal spatial patterns and complicated temporal patterns in facial behavior for facial expression analysis. We regard a facial expression as a multifarious activity composed of sequential or overlapping primitive facial events. Allen's interval algebra is implemented to portray these complicated temporal patterns via a two-layer Bayesian network. The nodes in the upper-most layer are representative of the primitive facial events, and the nodes in the lower layer depict the temporal relationships between those events. Our model also captures inherent universal spatial patterns via a multi-value restricted Boltzmann machine in which the visible nodes are facial events, and the connections between hidden and visible nodes model intrinsic spatial patterns. Efficient learning and inference algorithms are proposed. Experiments on posed and spontaneous expression distinction and expression recognition demonstrate that our proposed IT-RBM achieves superior performance compared to state-of-the art research due to its ability to incorporate these facial behavior patterns.

Algebraic foundations for qualitative calculi and networks

Binary Constraint Problems have traditionally been considered as Network Satisfaction Problems over some relation algebra. A constraint network is satisfiable if its nodes can be mapped into some representation of the relation algebra in such a way that the constraints are preserved. A qualitative representation ϕ is like an ordinary representation, but instead of requiring that (a;b)ϕ is the composition aϕ∘bϕ of the relations aϕ and bϕ, as we do for ordinary representations, we only require that cϕ⊇aϕ∘bϕ⇔c≥a;b, for each c in the algebra. A constraint network is qualitatively satisfiable if its nodes can be mapped to elements of a qualitative representation, preserving the constraints. If a constraint network is satisfiable then it is clearly qualitatively satisfiable, but the converse can fail, as we show. However, for a wide range of relation algebras including the point algebra, the Allen Interval Algebra, RCC8 and many others, a network is satisfiable if and only if it is qualitatively satisfiable.Unlike ordinary composition, the weak composition arising from qualitative representations need not be associative, so we can generalise by considering network satisfaction problems over non-associative algebras. We prove that computationally, qualitative representations have many advantages over ordinary representations: whereas many finite relation algebras have only infinite representations, every finite qualitatively representable algebra has a finite qualitative representation; the representability problem for (the atom structures of) finite non-associative algebras is NP-complete; the network satisfaction problem over a finite qualitatively representable algebra is always in NP; the validity of equations over qualitative representations is co-NP-complete. On the other hand we prove that there is no finite axiomatisation of the class of qualitatively representable algebras.

On coarser interval temporal logics

The primary characteristic of interval temporal logic is that intervals, rather than points, are taken as the primitive ontological entities. Given their generally bad computational behavior of interval temporal logics, several techniques exist to produce decidable and computationally affordable temporal logics based on intervals. In this paper we take inspiration from Golumbic and Shamir's coarser interval algebras, which generalize the classical Allen's Interval Algebra, in order to define two previously unknown variants of Halpern and Shoham's logic (HS) based on coarser relations. We prove that, perhaps surprisingly, the satisfiability problem for the coarsest of the two variants, namely HS3, not only is decidable, but PSpace-complete in the finite/discrete case, and PSpace-hard in any other case; besides proving its complexity bounds, we implement a tableau-based satisfiability checker for it and test it against a systematically generated benchmark. Our results are strengthened by showing that not all coarser-than-Allen's relations are a guarantee of decidability, as we prove that the second variant, namely HS7, remains undecidable in all interesting cases.

Time-Based Web Service Composition

This article describes how incorporating temporal constraints in web service composition results in more complex models and makes the verification of temporal consistency during the modeling and execution crucial. This article proposes a model named H-Service-Net based on the time petri net model to control and manage temporal consistency; the model also supports time constraints and exception handling. First, this approach proposes a modular approach for modeling composition using Extend Time Unit System, Allen's interval algebra, and comparison operators in a time petri net model to consider all types of temporal constraints. Subsequently, this article presents algorithms on checking temporal consistency and mechanism for exception handling and validating the system in an implementation tool (H-Service-Editor) based on the proposed approach that uses BizTalk Server 2013 to evaluate the implementation of temporal constraints and timeout exception handling. Finally, an exhaustive performance experiment is presented to assess the scalability of the authors' approach.

Allen-like theory of time for tree-like structures

Allen's Interval Algebra is among the leading formalisms in the area of qualitative temporal reasoning. However, its applications are restricted to linear flows of time. While there is some recent work studying relations between intervals on branching structures, there is no rigorous study of the first-order theory of branching time. In this paper, we approach this problem under a general definition of time structures, namely, tree-like lattices. Allen's work proved that meets is expressively complete in the linear case. We also prove that, surprisingly, it remains complete for all unbounded tree-like lattices. This does not generalize to the case of all tree-like lattices, for which we prove that the smallest complete set of relations has cardinality three. We provide in this paper a sound and complete axiomatic system for both the unbounded and general case, in Allen's style, and we classify minimally complete and maximally incomplete sets of relations.

Network Flow Query Language—Design, Implementation, Performance, and Applications

Cisco’s NetFlow protocol and Internet engineering task force’s Internet protocol flow information export open standard are widely deployed protocols for collecting network flow statistics. Understanding intricate traffic patterns in these network statistics requires sophisticated flow analysis tools that can efficiently mine network flow records. We present a network flow query language (NFQL), which can be used to write expressive queries to process flow records, aggregate them into groups, apply absolute or relative filters, and invoke Allen interval algebra rules to merge group records. We demonstrate nfql , an implementation of the language that has comparable execution times to SiLK and flow-tools with absolute filters. However, it trades performance when grouping and merging flows in favor of more operational capabilities that help increase the expressiveness of NFQL. We present two applications to demonstrate richer capabilities of the language. We show queries to identify flow signatures of popular applications and behavioural signatures to identify SSH compromise detection attacks.

Ontology for temporal reasoning based on extended Allen's interval algebra

Aspects of time, change, evolution, temporal reasoning and decision-making remain in the focus of metadata and ontology engineering because many related challenges are yet to be fully addressed. In this paper, we present ontology ALLEN+ as a tool to reason with imperfect temporal information. We created a rule-set SWRL on top of OWL capable of temporal reasoning with partially incomplete and heterogeneous information. The ontology allows to have either quantitative, qualitative or hybrid information about temporal points and intervals, and the rules are capable of both ways transitions between different representations. We show how to use context of available imperfect temporal information to improve results of the composition operation of Allen's interval algebra, and we design rules for composition-in-context operation. We discover that additional context reduces the overall uncertainty of the composition and enables about 20% progress in overall quality of the composition and therefore in potential reasoning and decision-making.

Local-to-Global Consistency Implies Tractability of Abduction

Abduction is a form of nonmonotonic reasoning that looks for an explanation, built from a given set of hypotheses, for an observed manifestation according to some knowledge base. Following the concept behind the Schaefer's parametrization CSP(Gamma) of the Constraint Satisfaction Problem (CSP), we study here the complexity of the abduction problem Abduction(Gamma, Hyp, M) parametrized by certain (omega-categorical) infinite relational structures Gamma, Hyp, and M from which a knowledge base, hypotheses and a manifestation are built, respectively. We say that Gamma has local-to-global consistency if there is k such that establishing strong k-consistency on an instance of CSP(Gamma) yields a globally consistent (whose every solution may be obtained straightforwardly from partial solutions) set of constraints. In this case CSP(Gamma) is solvable in polynomial time. Our main contribution is an algorithm that under some natural conditions decides Abduction(Gamma, Hyp, M) in P when Gamma has local-to-global consistency. As we show in the number of examples, our approach offers an opportunity to consider abduction in the context of spatial and temporal reasoning (qualitative calculi such as Allen's interval algebra or RCC-5) and that our procedure solves some related abduction problems in polynomial time.

A New Pattern-Based Flexible Approach for Maintaining a Constrained Workflow

The context of any workflow has functional and non functional characteristics. Functional characteristics give rise to Workflow Patterns (WPs) in a workflow. Changes may occur to the relationships amongst patterns in a workflow after the initial enactment. Run-time changes could occur due to roles executing the patterns. Design-time changes could occur due to changing user specifications and subsequent decisions being taken by the workflow composer. An approach of accommodating and propagating such changes is required. These changes are to be accommodated in a manner that the relationships amongst the existing patterns remain consistent. This paper formalizes an approach that facilitates composition and accommodation of changes into a composed workflow maintaining consistency. We make use of tools and algorithms from Formal Concept Analysis (FCA) to organize WPs as a lattice. Graph searching techniques are exploited for composition of the workflow graph. For accommodating changes into the composed workflow, we consider the WPs as Reference Intervals from Allen's Interval Algebra (IA) framework. Change accommodation in our approach is achieved by three functionalities - a transform function that traces a Reference Interval Hierarchy (RIH) from the workflow graph; a constraint propagation function that accommodates raised changes into the RIH; an inverse transform function that updates the corresponding workflow graph with the changes in the RIH.

Combining Activity DSM with Temporal Logic for Collaborative Planning and Scheduling

This work presents an approach that implements enhanced scheduling algorithms to plan and schedule interventions in scientific facilities emitting various types of ionizing radiation such as the ones present at CERN in Geneva, (Switzerland) or at GSI in Darmstadt (Germany). To deal with the collaborative process of activity creation and submission used in those organizations, we propose a framework to set the appropriate sequence or skeleton for the activities. This framework combines Allen's Interval Algebra and DSM (Design Structure Matrix). It enables the sequence of activities to be automatically computed while gathering and taking into account the needs of users and testing their compatibility. It also deals with technical-type or resource-type constraints between activities as well as incompatible submissions. The work described in this paper includes details of the collaborative submission process and introduces suggestions for compromising as well as temporal calculations with the introduction of parameterized DSMs rather than binary ones.

Multimodal digital semiotics: the interaction of language with other resources

AbstractA “multimodal digital semiotics” approach, involving the development and use of interactive digital media technology, mathematical techniques of analysis and scientific visualization for modeling and analyzing multimodal phenomena, is demonstrated through the analysis of an interview between a climate scientist and a climate denialist on Fox News. Prototype software for multimodal analysis and network visualizations are used in combination with Allen's interval algebra to model multimodal semantic data and identify significant patterns based on temporal relationships between different semiotic choices. The resulting semantic patterns reveal combinations of semiotic choices that were drawn upon by the different speakers during the interview, accounting for how the climate denialist emerges as the dominant and convincing interviewee. Such an approach combines the objectivity of mathematical modeling and scientific visualization with the interpretive power of Halliday's systemic theory.

A constraint-based approach for proactive, context-aware human support

In this article we address the problem of realizing a service-providing reasoning infrastructure for pro-active human assistance in intelligent environments. We propose SAM, an architecture which leverages temporal knowledge represented as relations in Allen's interval algebra and constraint-based temporal planning techniques. SAM provides two key capabilities for contextualized service provision: human activity recognition and planning for controlling pervasive actuation devices. While drawing inspiration from several state-of-the-art approaches, SAM provides a unique feature which has thus far not been addressed in the literature, namely the seamless integration of these two key capabilities. It does so by leveraging a constraint-based reasoning paradigm whereby both requirements for recognition and for planning/execution are represented as constraints and reasoned upon continuously. This work is partially supported by NovaMedTech project “Angen” (EU regional funds) and by the Swedish Knowledge Foundation (KK Stiftelsen).

Probabilistic temporal multimedia data mining

Existing sequence pattern mining techniques assume that the obtained events from event detectors are accurate. However, in reality, event detectors label the events from different modalities with a certain probability over a time-interval. In this article, we consider for the first time Probabilistic Temporal Multimedia (PTM) Event data to discover accurate sequence patterns. PTM event data considers the start time, end time, event label and associated probability for the sequence pattern discovery. As the existing sequence pattern mining techniques cannot work on such realistic data, we have developed a novel framework for performing sequence pattern mining on probabilistic temporal multimedia event data. We perform probability fusion to resolve the redundancy among detected events from different modalities, considering their cross-modal correlation. We propose a novel sequence pattern mining algorithm called Probabilistic Interval based Event Miner (PIE-Miner) for discovering frequent sequence patterns from interval based events. PIE-Miner has a new support counting mechanism developed for PTM data. Existing sequence pattern mining algorithms have event label level support counting mechanism, whereas we have developed event cluster level support counting mechanism. We discover the complete set of all possible temporal relationships based on Allen's interval algebra. The experimental results showed that the discovered sequence patterns are more useful than the patterns discovered with state-of-the-art sequence pattern mining algorithms.