Information-Guided Temporal Logic Inference with Prior Knowledge (original) (raw)

Temporal logic inference for classification and prediction from data

Proceedings of the 17th international conference on Hybrid systems: computation and control - HSCC '14, 2014

This paper presents an inference algorithm that can discover temporal logic properties of a system from data. Our algorithm operates on finite time system trajectories that are labeled according to whether or not they demonstrate some desirable system properties (e.g. "the car successfully stops before hitting an obstruction"). A temporal logic formula that can discriminate between the desirable behaviors and the undesirable ones is constructed. The formulae also indicate possible causes for each set of behaviors (e.g. "If the speed of the car is greater than 15 m/s within 0.5s of brake application, the obstruction will be struck") which can be used to tune designs or to perform on-line monitoring to ensure the desired behavior. We introduce reactive parameter signal temporal logic (rPSTL), a fragment of parameter signal temporal logic (PSTL) that is expressive enough to capture causal, spatial, and temporal relationships in data. We define a partial order over the set of rPSTL formulae that is based on language inclusion. This order enables a directed search over this set, i.e. given a candidate rPSTL formula that does not adequately match the observed data, we can automatically construct a formula that will fit the data at least as well. Two case studies, one involving a cattle herding scenario and one involving a stochastic hybrid gene circuit model, are presented to illustrate our approach.

Parameterisation of Reasoning on Temporal Markov Logic Networks

arXiv (Cornell University), 2022

We aim at improving reasoning on inconsistent and uncertain data. We focus on knowledge-graph data, extended with time intervals to specify their validity, as regularly found in historical sciences. We propose principles on semantics for efficient Maximum A-Posteriori inference on the new Temporal Markov Logic Networks (TMLN) which extend the Markov Logic Networks (MLN) by uncertain temporal facts and rules. We examine total and partial temporal (in)consistency relations between sets of temporal formulae. Then we propose a new Temporal Parametric Semantics, which may combine several sub-functions, allowing to use different assessment strategies. Finally, we expose the constraints that semantics must respect to satisfy our principles.

Probabilistic Temporal Logic over Finite Traces

2019

Temporal logics over finite traces have recently gained attention due to their use in real-world applications, in particular in business process modelling and planning. In real life, processes contain some degree of uncertainty that is impossible to handle with classical logics. We propose a new probabilistic temporal logic over finite traces based on superposition semantics, where all possible evolutions are possible, until observed. We study the properties of the logic and provide automata-based mechanisms for deriving probabilistic inferences from its formulas. We ground the approach in the context of declarative process modelling, showing how the temporal patterns used in Declare can be lifted to our setting, and discussing how probabilistic inferences can be exploited to provide key offline and runtime reasoning tasks, and how to discover probabilistic Declare patterns from event data by minor adjustments to existing discovery algorithms.

NeoMaPy: A Parametric Framework for Reasoning with MAP Inference on Temporal Markov Logic Networks

Proceedings of the 32nd ACM International Conference on Information and Knowledge Management

Reasoning on inconsistent and uncertain data is challenging, especially for Knowledge-Graphs (KG) to abide temporal consistency. Our goal is to enhance inference with more general time interval semantics that specify their validity, as regularly found in historical sciences. We propose a new Temporal Markov Logic Networks (TMLN) model which extends the Markov Logic Networks (MLN) model with uncertain temporal facts and rules. Total and partial temporal (in)consistency relations between sets of temporal formulae are examined. We then propose a new Temporal Parametric Semantics (TPS) which allows combining several sub-functions leading to different assessment strategies. Finally, we present the NeoMaPy tool, to compute the MAP inference on MLNs and TMLNs with several TPS. We compare our performances with state-of-the-art inference tools and exhibit faster and higher quality results. CCS CONCEPTS • Computing methodologies → Semantic networks; Temporal reasoning.

Temporal reasoning with probabilities

2013

This paper explorett the use of probabilistic graphical modelling to represent and reason about temporal knowledge. The idea is that of representing concept~ and variables involved diagramatically, by means of a directed graph, called an influence diagram (ID), designed to capture probabilistic dependencies between those variables. Statistical models of progression in time, such as semi-Markov processes, can be translated into "pieces" of influence diagram, and then embedded into targe influence diagrams representing bodies of knowledge. In this way, we can include statistical modelling of time into expert systems. Stochastic simulation (Monte Carlo) approaches are proposed for probability propagation on the obtained diagrams. In particular, a combination of two techniques, known as "Gibbs salmpling' and 'forward sampling' , is discussed.

Deriving Explanations From Partial Temporal Information

2008

The representation and manipulation of natural human understanding of temporal phenomena is a fundamental field of study in Computer Science, which aims both to emulate human thinking, and to use the methods of human intelligence to underpin engineering solutions. In particular, in the domain of Artificial Intelligence, temporal knowledge may be uncertain and incomplete due to the unavailability of complete and absolute temporal information. This paper introduces an inferential framework for deriving logical explanations from partial temporal information. Based on a graphical representation which allows expression of both absolute and relative temporal knowledge in incomplete forms, the system can deliver a verdict to the question if a given set of statements is temporally consistent or not, and provide understandable logical explanation of analysis by simplified contradiction and rule based reasoning.

Temporal Reasoning and Bayesian Networks

Computational Intelligence, 2000

This work examines important issues in probabilistic temporal representation and reasoning using Bayesian networks (also known as belief networks). The representation proposed here utilizes temporal (or dynamic) probabilities to represent facts, events, and the effects of events. The architecture of a belief network may change with time to indicate a different causal context. Probability variations with time capture temporal properties such as persistence and causation. They also capture event interaction, and when the interaction between events follows known models such as the competing risks model, the additive model, or the dominating event model, the net effect of many interacting events on the temporal probabilities can be calculated efficiently. This representation of reasoning also exploits the notion of temporal degeneration of relevance due to information obsolescence to improve the efficiency.

Uncertainty-Aware Signal Temporal Logic Inference

2021

Temporal logic inference is the process of extracting formal descriptions of system behaviors from data in the form of temporal logic formulas. The existing temporal logic inference methods mostly neglect uncertainties in the data, which results in limited applicability of such methods in real-world deployments. In this paper, we first investigate the uncertainties associated with trajectories of a system and represent such uncertainties in the form of interval trajectories. We then propose two uncertaintyaware signal temporal logic (STL) inference approaches to classify the undesired behaviors and desired behaviors of a system. Instead of classifying finitely many trajectories, we classify infinitely many trajectories within the interval trajectories. In the first approach, we incorporate robust semantics of STL formulas with respect to an interval trajectory to quantify the margin at which an STL formula is satisfied or violated by the interval trajectory. The second approach reli...

Temporal Logics Over Finite Traces with Uncertainty

Proceedings of the AAAI Conference on Artificial Intelligence

Temporal logics over finite traces have recently seen wide application in a number of areas, from business process modelling, monitoring, and mining to planning and decision making. However, real-life dynamic systems contain a degree of uncertainty which cannot be handled with classical logics. We thus propose a new probabilistic temporal logic over finite traces using superposition semantics, where all possible evolutions are possible, until observed. We study the properties of the logic and provide automata-based mechanisms for deriving probabilistic inferences from its formulas. We then study a fragment of the logic with better computational properties. Notably, formulas in this fragment can be discovered from event log data using off-the-shelf existing declarative process discovery techniques.

Annotated probabilistic temporal logic

ACM Transactions on …, 2011

The semantics of most logics of time and probability is given via a probability distribution over "threads" where a thread is a structure specifying what will be true at different points in time (in the future). When assessing the probabilities of statements such as "Event a will occur within 5 units of time of event b", there are many different semantics possible, even when assessing the truth of this statement within a single thread. We introduce the syntax of annotated probabilistic temporal (APT) logic programs and axiomatically introduce the key notion of a frequency function (for the first time) to capture different types of intra-thread reasoning, and then provide a semantics for intra-thread and inter-thread reasoning in APT logic programs parameterized by such frequency functions. We develop a comprehensive set of complexity results for consistency checking and entailment in APT logic programs, together with sound and complete algorithms to check consistency and entailment. The basic algorithms use linear programming, but we then show how to substantially (and correctly) reduce the sizes of these linear programs to yield better computational properties. We describe a real world application we are developing using APT logic programs.