Interval-based Temporal Logic Research Articles

Satisfiability Checking of Clinical Practice Guidelines Using an Analyzer

: A clinical practice guideline consists of the best practices required for managing a particular disease. Designing a consistent guideline is difficult and error-prone; hence, checking the consistency of guidelines is crucial. Due to the complexity of guidelines, a formal language is an appropriate choice for modeling and analyzing a guideline. IMPNL has been introduced as a metric interval-based temporal logic to model such guidelines. Moreover, a sound and complete tableau-based algorithm has been designed for checking the satisfiability of an IMPNL formula. In this paper, we introduced a clinical practice guideline analyzer suitable for modeling and checking the consistency of a guideline. The analyzer can also determine points, in which inconsistencies occur, and help designers to quickly and easily fix a guideline. Moreover, physicians can use the output of the analyzer (the calendar model) to check whether a patient is coherently treated with a specific guideline.

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.

Model checking of pushdown systems for projection temporal logic

In this paper, we study the model checking problem of pushdown systems for projection temporal logic (PTL), an interval-based temporal logic that is as expressive as the full regular languages. For this, we provide an algorithm to decide whether a pushdown system, determined by a pushdown automaton, satisfies a desired logic property, by using relevant automata notations and operations. The algorithm terminates in exponential time for normal PTL properties, i.e. properties specified as normal PTL formulas. To show the lower bound of complexity of the model checking problem, we also construct a polynomial-time reduction from the acceptance problem of a linearly bounded alternating Turing machine. As a result, the model checking problem of pushdown systems for normal PTL properties is EXPTIME-complete.

Tractable Interval Temporal Propositional and Description Logics

We design a tractable Horn fragment of the Halpern-Shoham temporal logic and extend it to interval-based temporal description logics, instance checking in which is P-complete for both combined and data complexity.

John Buridan’s Sophismata and Interval Temporal Semantics

In this paper we look at the suitability of modern interval-based temporal logic for modeling John Buridan’s treatment of tensed sentences in his Sophismata. Building on the paper (Øhrstrøm 1984), we develop Buridan’s analysis of temporal logic, paying particular attention to his notions of negation and the absolute/relative nature of the future and the past.We introduce a number of standard modern propositional interval temporal logics (ITLs) to illustrate where Buridan’s interval-based temporal analysis differs from the standard modern approaches. We give formal proofs of some claims in (Øhrstrøm 1984), and sketch how the standard modern systems could be defined in terms of Buridan’s proposals, showing that his logic can be taken as more basic. In diesem Aufsatz betrachten wir das Geeignetsein einer modernen intervallbasierten temporalen Logik für die Modellierung von John Buridans Behandlung zeitabhängiger Sätze in seinen Sophismata. Aufbauend auf den Aufsatz (Øhrstrøm 1984) stellen wir Buridans Analyse der temporalen Logik dar, mit besonderer Berücksichtigung seiner Begriffe der Negation und der absoluten/relativen Natur der Zukunft und der Vergangenheit. Wir führen einige standardmäßige moderne intervallbasierte temporale Aussagenlogiken (ITLs) ein, um zu illustrieren, wo Buridans intervallbasierte temporale Analyse von den standardmäßigen modernen Zugangsweisen abweicht. Wir geben formale Beweise einiger Behauptungen in (Øhrstrøm 1984) an und skizzieren, wie die standardmäßigen modernen Systeme im Sinne der Vorschläge Buridans definiert werden könnten; wir zeigen damit, dass seine Logik als die grundlegendere aufgefasst werden kann.

An Optimal Decision Procedure for Right Propositional Neighborhood Logic

Propositional interval temporal logics are quite expressive temporal logics that allow one to naturally express statements that refer to time intervals. Unfortunately, most such logics turn out to be (highly) undecidable. In order to get decidability, severe syntactic or semantic restrictions have been imposed to interval-based temporal logics to reduce them to point-based ones. The problem of identifying expressive enough, yet decidable, new interval logics or fragments of existing ones that are genuinely interval-based is still largely unexplored. In this paper, we focus our attention on interval logics of temporal neighborhood. We address the decision problem for the future fragment of Neighborhood Logic (Right Propositional Neighborhood Logic, RPNL for short), and we positively solve it by showing that the satisfiability problem for RPNL over natural numbers is NEXPTIME-complete. Then, we develop a sound and complete tableau-based decision procedure, and we prove its optimality.

A practical pattern recovery approach based on both structural and behavioral analysis

While the merit of using design patterns is clear for forward engineering, we could also benefit from design pattern recovery in program understanding and reverse engineering. In this paper, we present a practical approach to enlarge the recoverable scope and improve precision ratio of pattern recovery. To specify both structural aspect and behavioral aspect of design patterns, we introduce traditional predicate logic combined with Allen's interval-based temporal logic as our theory foundation. The formal specifications could be conveniently converted into Prolog representations to support pattern recovery. To illustrate how to specify and recover design patterns in our approach, we take one example for each category of design patterns. Moreover, we give a taxonomy of design patterns based on the analysis in our approach to show its applicable scope. To validate our approach, we have developed a tool named PRAssistor and analyzed two well-known open source frameworks. The experiment results show that most of the patterns addressed in our taxonomy have been recovered. Besides larger recoverable scope, the recovery precision of our approach is much higher than others. Furthermore, we consider that our approach and tool could be promisingly extended to support “Debug at Design Level” and “Pattern-Driven Refactoring”.

A Hierarchical Completeness Proof for Propositional Interval Temporal Logic with Finite Time

We present a completeness proof for Propositional Interval Temporal Logic (PITL) with finite time which avoids certain difficulties of conventional methods. It is more gradated than previous efforts since we progressively reduce reasoning within the original logic to simpler reasoning in sublogics. Furthermore, our approach benefits from being less constructive since it is able to invoke certain theorems about regular languages over finite words without the need to explicitly describe the associated intricate proofs. A modified version of regular expressions called Fusion Expressions is used as part of an intermediate logic called Fusion Logic. Both have the same expressiveness as PITL but are lower-level notations which play an important role in the hierarchical structure of the overall completeness proof. In particular, showing completeness for PITL is reduced to showing completeness for Fusion Logic. This in turn is shown to hold relative to completeness for conventional linear-time temporal logic with finite time. Logics based on regular languages over finite words and !-words offer a promising but elusive framework for formal specification and verification. A number of such logics and decision procedures have been proposed. In addition, various researchers have obtained complete axiom systems by embedding and expressing the decision procedures directly within the logics. The work described here contributes to this topic by showing how to exploit some interesting links between regular languages and interval-based temporal logics.

A Correspondence between Temporal Description Logics

In this paper, we investigate the relationship between two decidable interval-based temporal description logics that have been proposed in the literature, T L-ALCF and ALCF(A). Although many aspects of these two logics are quite similar, the two logics suggest two rather different paradigms for representing temporal conceptual knowledge. In this paper, we exhibit a reduction from T L-ALCF concepts to ALCF(A) concepts that serves two purposes: first, it nicely illustrates the relationship between the two knowledge representation paradigms; and second, it provides a tight PSPACE upper bound for T L-ALCF concept satisfiabiliy, whose complexity was previously unknown.

定性的時間情報を用いた処理の順序の設計手法 事象駆動型制御プログラム設計への応用

This paper proposes a method on fundamental process design with timing constraints. In the fundamental design phase, a designer is required to make a timing-chart from qualitative information concerned with timing constraints such as requirements and causality of processes. The purpose of this method is to present a way of deriving a solution regarding process timing from qualitative information. According to the method, a designer is able to formulate requirements and constraint conditions of process timing by the use of interval-based temporal logic. Then the method gives an algorithm to search timing solution. The algorithm, simultaneously, indicates additional constraint conditions concerned with length of interval in case of need. To verify the method, a support tool of software program is developed and the effectiveness is confirmed by the results of process timing design of event-driven type software of an asynchronous data transmission equipment.

Managing tasks using an interval-based temporal logic

We develop here a logic % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9qq-f0-yqaqVeLsFr0-vr% 0-vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaatuuDJXwAK1% uy0HwmaeHbfv3ySLgzG0uy0Hgip5wzaGqbcKqzagGae8NeHW0aaSba% aKazbauabaqcLbyacaWG0baajqwaafqabaaaaa!4823!\[\mathcal{L}_t \] for reasoning about time. The main intended application is the task management of a medical decision support system. The language of the logic is propositional extended with interval concepts. A brief description is given of the implementation of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9qq-f0-yqaqVeLsFr0-vr% 0-vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaatuuDJXwAK1% uy0HwmaeHbfv3ySLgzG0uy0Hgip5wzaGqbcKqzagGae8NeHW0aaSba% aKazbauabaqcLbyacaWG0baajqwaafqabaaaaa!4823!\[\mathcal{L}_t \] in Prolog. The implementation is motivated by the management of cancer treatment and illustrated in terms of a small example.

An imperative language for task-level planning: Definition in temporal logic

The problem of the execution of plans of actions by a robot inspired the conception of various representations. Some of them concern the problems of control theory and geometry involved in the execution of each task of a robot. We are interested in the task-level sequencing of such actions, from the point of view of planning in artificial intelligence and languages for the synchronisation of tasks. Planning formalisms are often based on predicate logic and sometimes temporal logic. Robot programming languages, at the task-level, have classical control structures derived from computer programming languages, as well as ones more specifically related to real-time execution. We propose a logical and temporal model of plans of actions augmented by an imperative control structure. We therefore define, on the basis of an interval-based temporal logic, a set of imperative control primitives that define the temporal arrangement of the actions. After that, primitives for the reaction to evolutions in the environment are defined in the same formalism, in order to respond to constraints concerning interaction and adaptation to the external world. The application of the model in a simulation system is described, as well as its use in execution monitoring systems.

Maintaining knowledge about temporal intervals

An interval-based temporal logic is introduced, together with a computationally effective reasoning algorithm based on constraint propagation. This system is notable in offering a delicate balance between