Extracting spatial-temporal knowledge from data is useful in many applications. It is important that the obtained knowledge is human-interpretable and amenable to formal analysis. In this paper, we propose a method that trains neural networks to learn spatial-temporal properties in the form of weighted graph-based signal temporal logic (wGSTL) formulas. For learning wGSTL formulas, we introduce a flexible wGSTL formula structure in which the user's preference can be applied in the inferred wGSTL formulas. In the proposed framework, each neuron of the neural networks corresponds to a subformula in a flexible wGSTL formula structure. We initially train a neural network to learn the wGSTL operators and then train a second neural network to learn the parameters in a flexible wGSTL formula structure. We use a COVID-19 dataset and a rain prediction dataset to evaluate the performance of the proposed framework and algorithms. We compare the performance of the proposed framework with three baseline classification methods including K-nearest neighbors, decision trees, support vector machine, and artificial neural networks. The classification accuracy obtained by the proposed framework is comparable with the baseline classification methods.
The Logical Expressiveness of Temporal GNNs via Two-Dimensional Product Logics
RPTU Kaiserslautern-Landau（亚琛工业大学凯撒斯劳滕-兰道分校）；Queen Mary University of London（伦敦女王大学）；University of Łódź（卢宾大学）；Theoretical Computer Science / Formal Methods（理论计算机科学/形式方法）；University of Kassel（卡塞尔大学）
Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. Several classical probabilistic inference tasks (such as MAP and computing marginals) have not yet received a lot of attention for this formalism. The contribution of this paper is that we develop efficient inference algorithms for these tasks. This is based on a conversion of the probabilistic logic program and the query and evidence to a weighted CNF formula. This allows us to reduce the inference tasks to well-studied tasks such as weighted model counting. To solve such tasks, we emp…
Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. This paper investigates how classical inference and learning tasks known from the graphical model community can be tackled for probabilistic logic programs. Several such tasks such as computing the marginals given evidence and learning from (partial) interpretations have not really been addressed for probabilistic logic programs before. The first contribution of this paper is a suite of efficient algorithms for various inference tasks. It is based on a conversion of the program and the …
Weighted logic programming, a generalization of bottom-up logic programming, is a well-suited framework for specifying dynamic programming algorithms. In this setting, proofs correspond to the algorithm's output space, such as a path through a graph or a grammatical derivation, and are given a real-valued score (often interpreted as a probability) that depends on the real weights of the base axioms used in the proof. The desired output is a function over all possible proofs, such as a sum of scores or an optimal score. We describe the PRODUCT transformation, which can merge two weighted logic …
University of Nottingham（诺丁汉大学）；University of Utrecht（乌得勒支大学）
In this short note we address the issue of expressing norms (such as obligations and prohibitions) in temporal logic. In particular, we address the argument from [Governatori 2015] that norms cannot be expressed in Linear Time Temporal Logic (LTL).
King’s College London（伦敦国王学院）；University of Liverpool（利物浦大学）
In this paper, we construct and investigate a hierarchy of spatio-temporal formalisms that result from various combinations of propositional spatial and temporal logics such as the propositional temporal logic PTL, the spatial logics RCC-8, BRCC-8, S4u and their fragments. The obtained results give a clear picture of the trade-off between expressiveness and computational realisability within the hierarchy. We demonstrate how different combining principles as well as spatial and temporal primitives can produce NP-, PSPACE-, EXPSPACE-, 2EXPSPACE-complete, and even undecidable spatio-temporal log…
A class of interval-based temporal languages for uniformly representing and reasoning about actions and plans is presented. Actions are represented by describing what is true while the action itself is occurring, and plans are constructed by temporally relating actions and world states. The temporal languages are members of the family of Description Logics, which are characterized by high expressivity combined with good computational properties. The subsumption problem for a class of temporal Description Logics is investigated and sound and complete decision procedures are given. The basic lan…
There is uncertainty associated with the occurrence of many events in real life. In this paper we develop a temporal logic to deal with such uncertain events and outline a possible implementation in an extension of PROLOG. Events are represented as fuzzy sets with the membership function giving the possibility of occurrence of the event in a given interval of time. The developed temporal logic is simple but powerful. It can determine effectively the various temporal relations between uncertain events or their combinations. PROLOG provides a uniform substrate on which to effectively implement s…
University of Oxford（牛津大学）；Monash University（莫纳什大学）
In this paper, we study the problem of learning to satisfy temporal logic specifications with a group of agents in an unknown environment, which may exhibit probabilistic behaviour. From a learning perspective these specifications provide a rich formal language with which to capture tasks or objectives, while from a logic and automated verification perspective the introduction of learning capabilities allows for practical applications in large, stochastic, unknown environments. The existing work in this area is, however, limited. Of the frameworks that consider full linear temporal logic or ha…
Continuously learning new tasks using high-level ideas or knowledge is a key capability of humans. In this paper, we propose Lifelong reinforcement learning with Sequential linear temporal logic formulas and Reward Machines (LSRM), which enables an agent to leverage previously learned knowledge to fasten learning of logically specified tasks. For the sake of more flexible specification of tasks, we first introduce Sequential Linear Temporal Logic (SLTL), which is a supplement to the existing Linear Temporal Logic (LTL) formal language. We then utilize Reward Machines (RM) to exploit structural…
Institute for Research in Fundamental Sciences（基础科学研究所）；University of Tehran（德黑兰大学）；Sharif University of Technology（谢里夫理工大学）
In this note, a formal transition system model called LTPAL to extract knowledge in a classification process is suggested. The model combines the Public Announcement Logic (PAL) and the Linear Temporal Logic (LTL). In the model, first, we consider classifiers, which capture single-framed data. Next, we took classifiers for data-stream data input into consideration. Finally, we formalize natural language properties in LTPAL with a video-stream object detection sample.
This paper is an appendix to the paper "Cut-free Calculi and Relational Semantics for Temporal STIT logics" by Berkel and Lyon, 2019. It provides the completeness proof for the basic STIT logic Ldm (relative to irreflexive, temporal Kripke STIT frames) as well as gives the derivation of the independence of agents axiom for the logic Xstit.
MIT Lincoln Laboratory（麻省理工学院林肯实验室）；Lehigh University（理海大学）
In this work, we focus on decomposing large multi-agent path planning problems with global temporal logic goals (common to all agents) into smaller sub-problems that can be solved and executed independently. Crucially, the sub-problems' solutions must jointly satisfy the common global mission specification. The agents' missions are given as Capability Temporal Logic (CaTL) formulas, a fragment of signal temporal logic, that can express properties over tasks involving multiple agent capabilities (sensors, e.g., camera, IR, and effectors, e.g., wheeled, flying, manipulators) under strict timing …
University of Corunna（科鲁尼亚大学）；IRIT - Université Paul Sabatier（IRIT - 保罗·萨巴蒂埃大学）
In this note we consider the problem of introducing variables in temporal logic programs under the formalism of "Temporal Equilibrium Logic" (TEL), an extension of Answer Set Programming (ASP) for dealing with linear-time modal operators. To this aim, we provide a definition of a first-order version of TEL that shares the syntax of first-order Linear-time Temporal Logic (LTL) but has a different semantics, selecting some LTL models we call "temporal stable models". Then, we consider a subclass of theories (called "splittable temporal logic programs") that are close to usual logic programs but …
Free University of Bozen-Bolzano（博尔扎诺自由大学）；Birkbeck, University of London（伦敦大学伯贝克学院）
We design temporal description logics suitable for reasoning about temporal conceptual data models and investigate their computational complexity. Our formalisms are based on DL-Lite logics with three types of concept inclusions (ranging from atomic concept inclusions and disjointness to the full Booleans), as well as cardinality constraints and role inclusions. In the temporal dimension, they capture future and past temporal operators on concepts, flexible and rigid roles, the operators `always' and `some time' on roles, data assertions for particular moments of time and global concept inclus…
Free University of Bozen-Bolzano（博尔扎诺自由大学）；University of Liverpool（利物浦大学）；Birkbeck, University of London（伦敦大学伯贝克学院）
Our aim is to investigate ontology-based data access over temporal data with validity time and ontologies capable of temporal conceptual modelling. To this end, we design a temporal description logic, TQL, that extends the standard ontology language OWL 2 QL, provides basic means for temporal conceptual modelling and ensures first-order rewritability of conjunctive queries for suitably defined data instances with validity time.
This paper argues that a combined treatment of probabilities, time and actions is essential for an appropriate logical account of the notion of probability; and, based on this intuition, describes an expressive probabilistic temporal logic for reasoning about actions with uncertain outcomes. The logic is modal and higher-order: modalities annotated by actions are used to express possibility and necessity of propositions in the next states resulting from the actions, and a higher-order function is needed to express the probability operator. The proposed logic is shown to be an adequate extensio…
University of Tartu（塔尔图大学）；Free University of Bozen-Bolzano（博尔扎诺自由大学）；University of Milano-Bicocca（米兰比可卡大学）
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 stu…
We present a multi-modal action logic with first-order modalities, which contain terms which can be unified with the terms inside the subsequent formulas and which can be quantified. This makes it possible to handle simultaneously time and states. We discuss applications of this language to action theory where it is possible to express many temporal aspects of actions, as for example, beginning, end, time points, delayed preconditions and results, duration and many others. We present tableaux rules for a decidable fragment of this logic.
Léonard de Vinci Pôle Universitaire, Research Center（列奥纳多·达·芬奇大学中心研究中心）；Conservatoire National des Arts et Métiers（法国国立工艺学院）
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-functi…
We present cut-free labelled sequent calculi for a central formalism in logics of agency: STIT logics with temporal operators. These include sequent systems for Ldm, Tstit and Xstit. All calculi presented possess essential structural properties such as contraction- and cut-admissibility. The labelled calculi G3Ldm and G3TSTIT are shown sound and complete relative to irreflexive temporal frames. Additionally, we extend current results by showing that also XSTIT can be characterized through relational frames, omitting the use of BT+AC frames.
University of Corunna（拉科鲁尼亚大学）；University of Potsdam（波茨坦大学）
We present an overview on Temporal Logic Programming under the perspective of its application for Knowledge Representation and declarative problem solving. Such programs are the result of combining usual rules with temporal modal operators, as in Linear-time Temporal Logic (LTL). We focus on recent results of the non-monotonic formalism called Temporal Equilibrium Logic (TEL) that is defined for the full syntax of LTL, but performs a model selection criterion based on Equilibrium Logic, a well known logical characterization of Answer Set Programming (ASP). We obtain a proper extension of the s…
We present Dynamic Epistemic Temporal Logic, a framework for reasoning about operations on multi-agent Kripke models that contain a designated temporal relation. These operations are natural extensions of the well-known "action models" from Dynamic Epistemic Logic. Our "temporal action models" may be used to define a number of informational actions that can modify the "objective" temporal structure of a model along with the agents' basic and higher-order knowledge and beliefs about this structure, including their beliefs about the time. In essence, this approach provides one way to extend the …
In this paper, we consider a temporal logic planning problem in which the objective is to find an infinite trajectory that satisfies an optimal selection from a set of soft specifications expressed in linear temporal logic (LTL) while nevertheless satisfying a hard specification expressed in LTL. Our previous work considered a similar problem in which linear dynamic logic for finite traces (LDLf), rather than LTL, was used to express the soft constraints. In that work, LDLf was used to impose constraints on finite prefixes of the infinite trajectory. By using LTL, one is able not only to impos…
In artificial intelligence, multi agent systems constitute an interesting typology of society modeling, and have in this regard vast fields of application, which extend to the human sciences. Logic is often used to model such kind of systems as it is easier to verify than other approaches, and provides explainability and potential validation. In this paper we define a time module suitable to add time to many logic representations of agents.
We consider intuitionistic variants of linear temporal logic with `next', `until' and `release' based on expanding posets: partial orders equipped with an order-preserving transition function. This class of structures gives rise to a logic which we denote $\iltl$, and by imposing additional constraints we obtain the logics $\itlb$ of persistent posets and $\itlht$ of here-and-there temporal logic, both of which have been considered in the literature. We prove that $\iltl$ has the effective finite model property and hence is decidable, while $\itlb$ does not have the finite model property. We a…
In this paper, we define a novel census signal temporal logic (CensusSTL) that focuses on the number of agents in different subsets of a group that complete a certain task specified by the signal temporal logic (STL). CensusSTL consists of an "inner logic" STL formula and an "outer logic" STL formula. We present a new inference algorithm to infer CensusSTL formulae from the trajectory data of a group of agents. We first identify the "inner logic" STL formula and then infer the subgroups based on whether the agents' behaviors satisfy the "inner logic" formula at each time point. We use two diff…
Birkbeck, University of London（伦敦大学伯贝克学院）；University of Oxford（牛津大学）；University of Warsaw（华沙大学）
We investigate the data complexity of answering queries mediated by metric temporal logic ontologies under the event-based semantics assuming that data instances are finite timed words timestamped with binary fractions. We identify classes of ontology-mediated queries answering which can be done in AC0, NC1, L, NL, P, and coNP for data complexity, provide their rewritings to first-order logic and its extensions with primitive recursion, transitive closure or datalog, and establish lower complexity bounds.
