In the wake of the recent resurgence of the Datalog language of databases, together with its extensions for ontological reasoning settings, this work aims to bridge the gap between the theoretical studies of DatalogMTL (Datalog extended with metric temporal logic) and the development of production-ready reasoning systems. In particular, we lay out the functional and architectural desiderata of a modern reasoner and propose our system, Temporal Vadalog. Leveraging the vast amount of experience from the database community, we go beyond the typical chase-based implementations of reasoners, and propose a set of novel techniques and a system that adopts a modern data pipeline architecture. We discuss crucial architectural choices, such as how to guarantee termination when infinitely many time intervals are possibly generated, how to merge intervals, and how to sustain a limited memory footprint. We discuss advanced features of the system, such as the support for time series, and present an extensive experimental evaluation. This paper is a substantially extended version of “The Temporal Vadalog System” as presented at RuleML+RR ’22.

The representation of a temporal problem in answer set programming (ASP) usually boils down to using copies of variables and constraints, one for each time stamp, no matter whether it is directly encoded or expressed via an action or temporal language. The multiplication of variables and constraints is commonly done during grounding, and the solver is completely ignorant about the temporal relationship among the different instances. On the other hand, a key factor in the performance of today’s ASP solvers is conflict-driven constraint learning. Our question in this paper is whether a constraint learned for particular time steps can be generalized and reused at other time steps, and ultimately whether this enhances the overall solver performance on temporal problems. Knowing well the domain of time, we study conditions under which learned dynamic constraints can be generalized. Notably, we identify a property of temporal representations that enables the generalization of learned constraints across all time steps. It turns out that most ASP planning encodings either satisfy this property or can be easily adapted to do so. In addition, we propose a general translation that transforms programs to fulfill this property. Finally, we empirically evaluate the impact of adding the generalized constraints to an ASP solver.

DatalogMTL is an extension of Datalog with metric temporal operators that has found an increasing number of applications in recent years. Reasoning in DatalogMTL is, however, of high computational complexity, which makes reasoning in modern data-intensive applications challenging. In this paper we present a practical reasoning algorithm for the full DatalogMTL language, which we have implemented in a system called MeTeoR. Our approach effectively combines an optimised (but generally non-terminating) materialisation (a.k.a. forward chaining) procedure, which provides scalable behaviour, with an automata-based component that guarantees termination and completeness. To ensure favourable scalability of the materialisation component, we propose a novel seminaïve materialisation procedure for DatalogMTL enjoying the non-repetition property, which ensures that each rule instance will be applied at most once throughout its entire execution. Moreover, our materialisation procedure is enhanced with additional optimisations which further reduce the number of redundant computations performed during materialisation by disregarding rules as soon as it is certain that they cannot derive new facts in subsequent materialisation steps. Our extensive evaluation supports the practicality of our approach.

We introduce negation under the stable model semantics in DatalogMTL – a temporal extension of Datalog with metric temporal operators. As a result, we obtain a rule language which combines the power of answer set programming with the temporal dimension provided by metric operators. We show that, in this setting, reasoning becomes undecidable over the rational timeline, and decidable in ${{\rm E}{\small\rm XP}{\rm S}{\small\rm PACE}}$ in data complexity over the integer timeline. We also show that, if we restrict our attention to forward-propagating programs, reasoning over the integer timeline becomes ${{\rm PS}{\small\rm PACE}}$-complete in data complexity, and hence, no harder than over positive programs; however, reasoning over the rational timeline in this fragment remains undecidable.

We outline a dual systems approach to temporal cognition, which distinguishes between two cognitive systems for dealing with how things unfold over time – a temporal updating system and a temporal reasoning system – of which the former is both phylogenetically and ontogenetically more primitive than the latter, and which are at work alongside each other in adult human cognition. We describe the main features of each of the two systems, the types of behavior the more primitive temporal updating system can support, and the respects in which it is more limited than the temporal reasoning system. We then use the distinction between the two systems to interpret findings in comparative and developmental psychology, arguing that animals operate only with a temporal updating system and that children start out doing so too, before gradually becoming capable of thinking and reasoning about time. After this, we turn to adult human cognition and suggest that our account can also shed light on a specific feature of humans’ everyday thinking about time that has been the subject of debate in the philosophy of time, which consists in a tendency to think about the nature of time itself in a way that appears ultimately self-contradictory. We conclude by considering the topic of intertemporal choice, and argue that drawing the distinction between temporal updating and temporal reasoning is also useful in the context of characterizing two distinct mechanisms for delaying gratification.

Representing defeasibility is an important issue in common sense reasoning. In reasoning about action and change, this issue becomes more difficult because domain and action related defeasible information may conflict with general inertia rules. Furthermore, different types of defeasible information may also interfere with each other during the reasoning. In this paper, we develop a prioritized logic programming approach to handle defeasibilities in reasoning about action. In particular, we propose three action languages ${\cal AT}^{0}$, ${\cal AT}^{1}$, and ${\cal AT}^{2}$ which handle three types of defeasibilities in action domains named defeasible constraints, defeasible observations and actions with defeasible and abnormal effects respectively. Each language with a higher superscript can be viewed as an extension of the language with a lower superscript. These action languages inherit the simple syntax of ${\cal A}$ language but their semantics is developed in terms of transition systems where transition functions are defined based on prioritized logic programs. By illustrating various examples, we show that our approach eventually provides a powerful mechanism to handle various defeasibilities in temporal prediction and postdiction. We also investigate semantic properties of these three action languages and characterize classes of action domains that present more desirable solutions in reasoning about action within the underlying action languages.

In this paper we present a specialized system for temporal reasoning representing possibly uncertain qualitative and quantitative constraints relative to temporal intervals in a homogeneous framework. The underlying logic is that of Allen, which we have extended to include quantitative temporal information. Intervals are still assumed as primitive entities while, to represent metric information, time points are introduced only at the algorithmic level. We illustrate the properties of the temporal representation, the algorithms used for constraint propagation, and their complexity. We show how the system can be used to schedule manufacturing operations in a small factory.

Computer-aided process planning has been recognized as an important tool for coordinating the different operations involved in making the product. While temporal knowledge is central to the design of efficient and reliable process plans, little attention is given to the integration of process planning and temporal processing and reasoning. To fill the void, we propose in this paper a practical approach, which is inspired by the framework of Temporal Constraint Satisfaction Problem (TCSP), to integrate process planning and temporal reasoning. We show that a TCSP formulation is a subset of a formulation using a reified temporal logic, and discuss the advantages of using such a restricted model. To reflect more realistic process planning encountered in real manufacturing environments, we present a model, called n-TCSP, which is a generalization of the TCSP framework. We envision the proposed temporal reasoning framework as one of the modules in the evolving new intelligent computer-aided process planning.