Computational complexity of hybrid interval temporal logics

Interval temporal logics are expressive formalisms for temporal representation and reasoning, which use time intervals as primitive temporal entities. They have been extensively studied for the past two decades and successfully applied in AI and computer science. Unfortunately, they lack the ability of expressing promptness conditions, as it happens with the commonly-used temporal logics, e.g., LTL: whenever we deal with a liveness request, such as “something good eventually happens”, there is no way to impose a bound on the delay with which it is fulfilled. In the last years, such an issue has been addressed in automata theory, game theory, and temporal logic. In this paper, we approach it in the interval temporal logic setting. First, we introduce PROMPT- PNL, a prompt extension of the well-studied interval temporal logic PNL, and we prove the undecidability of its satisfiability problem; then, we show how to recover decidability (NEXPTIME-completeness) by imposing a natural syntactic restriction on it.

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

The primary characteristic of interval temporal logic is that intervals, rather than points, are taken as the primitive ontological entities. Their computational behaviour is generally bad, and several restrictions have been considered in order to define 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 (\(\mathrm{HS} \)). We prove that one of them (denoted here by \(\mathrm{HS_7} \)) is still generally undecidable, while the other one (\(\mathrm{HS_3} \)) becomes, perhaps surprisingly, PSpace-complete, at least in the finite case.KeywordsInterval Temporal LogicCoarse IntervalsSatisfiability ProblemInterval Algebra (IA)Finite CaseThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Decision trees are simple, yet powerful, classification models used to classify categorical and numerical data, and, despite their simplicity, they are commonly used in operations research and management, as well as in knowledge mining. From a logical point of view, a decision tree can be seen as a structured set of logical rules written in propositional logic. Since knowledge mining is rapidly evolving towards temporal knowledge mining, and since in many cases temporal information is best described by interval temporal logics, propositional logic decision trees may evolve towards interval temporal logic decision trees. In this paper, we define the problem of interval temporal logic decision tree learning, and propose a solution that generalizes classical decision tree learning.

Interval temporal logics are based on interval structures over linearly (or partially) ordered domains, where time intervals, rather than time instants, are the primitive ontological entities. In this paper we introduce and study Right Propositional Neighborhood Logic over natural numbers with integer constraints for interval lengths, which is a propositional interval temporal logic featuring a modality for the `right neighborhood' relation between intervals and explicit integer constraints for interval lengths. We prove that it has the bounded model property with respect to ultimately periodic models and is therefore decidable. In addition, we provide an EXPSPACE procedure for satisfiability checking and we prove EXPSPACE-hardness by a reduction from the exponential corridor tiling problem.

Hybrid fragments of Halpern–Shoham logic and their expressive power

Logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems, spatial and constraint databases, and spatial reasoning in AI. In analogy with Halpern and Shoham's modal logic of time intervals based on the Allen relations, we introduce a family of modal logics equipped with eight modal operators that are interpreted by the Egenhofer-Franzosa (or RCC8) relations between regions in topological spaces such as the real plane. We investigate the expressive power and computational complexity of logics obtained in this way. It turns out that our modal logics have the same expressive power as the two-variable fragment of first-order logic, but are exponentially less succinct. The complexity ranges from (undecidable and) recursively enumerable to highly undecidable, where the recursively enumerable logics are obtained by considering substructures of structures induced by topological spaces. As our undecidability results also capture logics based on the real line, they improve upon undecidability results for interval temporal logics by Halpern and Shoham. We also analyze modal logics based on the five RCC5 relations, with similar results regarding the expressive power, but weaker results regarding the complexity.

During the last several years, we have explored temporal logic as a framework for specifying and reasoning about concurrent programs, distributed systems, and communications protocols. Previous papers[Schwartz/Melliar-Smith81, 82, Vogt82a,b] report on our efforts using temporal reasoning primitives to express very high-level abstract requirements that a program or system is to satisfy. Based on our experiences with those primitives, we have developed an interval logic more suitable for expressing higher-level temporal properties.

Temporal reasoning with medical data—A review with emphasis on medical natural language processing

The propositional interval logic of temporal neighborhood (PNL for short) features two modalities that make it possible to access intervals adjacent to the right (modality xAy) and to the left (modality xAy) of the current interval. PNL stands at a central position in the realm of interval temporal logics, as it is expressive enough to encode meaningful temporal conditions and decidable (undecidability rules over interval temporal logics, while PNL is NEXPTIME-complete). Moreover, it is expressively complete with respect to FO2|<|. Various extensions of PNL have been studied in the literature, including metric, hybrid, and first-order ones. Here, we study the effects of the addition of an equivalence relation ~ to Metric PNL (MPNL~). We first show that finite satisfiability for PNL extended with ~ is still NEXPTIME-complete. Then, we prove that finite satisfiability for MPNL~ can be reduced to the decidable 0-0 reach ability problem for vector addition systems and vice versa (EXPSPACE-hardness immediately follows).

Developing software systems is a process of eliciting and evolving stakeholder requirements using informal, semiformal and formal representations of knowledge. Managing the transitions between these representations is a challenging task. On the one hand informal representations for capturing system requirements support straightforward involvement and interaction of even inexperienced stakeholders. On the other hand this approach may result in inconsistent, incomplete, and ambiguous specifications. Semiformal and formal representations overcome these problems but are less suited for stakeholder interaction. In this paper, we describe an experiment using the WinWin model for negotiating system requirements and the Unified Modelling Language. We discuss our experiences and draw conclusions useful in bridging informal and formal representations.

A new formal model for temporal representation and reasoning is proposed. The model is based on the modification of the Petri nets, called PNTT-Petri Nets with Time Tokens. The PNTT is the main building block of the KRPTT knowledge representation scheme. It integrates the theory of PNTT and Allen's interval-based temporal logic. The model is suitable for representing activities in temporally rich domains, reasoning as well as planning. The process of reasoning in the scheme is called time dependent event driven reasoning. It includes the ability to reason about the time relationship among actions and/or states, but it also includes the ability to determine the subsequent activities or states based on initial or current activities or states and temporal information associated with each activity or state. An example of the use of the model in temporally rich domain is given.

A scheme for fuzzy temporal knowledge representation and reasoning is proposed. The scheme is based on the modification of the Petri nets called fuzzy time Petri nets and fuzzy temporal relations. The reasoning process uses modified Petri nets theory, possibility theory and a fuzzified version of Allen's (1983) temporal relations. The temporal linguistic expressions are modelled by primitives derived from the knowledge representation scheme. By combining and connecting these primitives the complex forms of situations from fuzzy temporal rich domains are modelled. An example of the use of the proposed scheme is given.

Computational complexity of linear constraints over the integers

We present the Angerona framework for the implementation of knowledge-based agents with a strong focus on flexibility, extensibility, and compatibility with diverse knowledge representation formalisms. As the basis for this framework we propose and formalize a general concept of compound agents in which we consider agents to consist of hierarchies of interacting epistemic and functional components. Each epistemic component is instantiated by a knowledge representation formalism. Different knowledge representation formalisms can be used within one agent and different agents in the same system can be based on different agent architectures and can use different knowledge representation formalisms. Partially instantiations define sub-frameworks for, e. g., the development of BDI agents and variants thereof. The Angerona framework realizes this concept by means of a flexible JAVA plug-in architecture for the epistemic and the functional components of an agent. The epistemic plug-ins are based on the Tweety library for knowledge representation, which provides various ready-for-use implementations and knowledge representation formalisms and a framework for the implementation of additional ones. Angerona already contains several partial and complete instantiations that implement several approaches. Angerona also features an environment plug-in for communicating agents and a flexible GUI to monitor the multiagent system and the inner workings of the agents, particularly the inspection of the dynamics of their epistemic states. Angerona and Tweety are ready to use, well documented, and open source.KeywordsKnowledge RepresentationMultiagent SystemEpistemic StateBelief BaseBelief ChangeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.