scholarly journals Combining Spatial and Temporal Logics: Expressiveness vs. Complexity

2005 ◽  
Vol 23 ◽  
pp. 167-243 ◽  
Author(s):  
D. Gabelaia ◽  
R. Kontchakov ◽  
A. Kurucz ◽  
F. Wolter ◽  
M. Zakharyaschev
Keyword(s):  
Temporal Logic ◽  
Clear Picture ◽  
Temporal Logics ◽  
Trade Off ◽  
Spatio Temporal ◽  
Spatial Logics

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 logics out of components that are at most NP- or PSPACE-complete.

scholarly journals Ruina/basural: Lógicas temporales y espaciales de la ciudad de La Paz en Saenz y Viscarra

2021 ◽  
Vol 26 ◽  
pp. 158-180
Author(s):  
Irina Alexandra Feldman
Keyword(s):  
Temporal Logic ◽  
Linear Temporal Logic ◽  
Space Time ◽  
Victor Hugo ◽  
National Narrative ◽  
Temporal Logics ◽  
La Paz ◽  
Queer Space ◽  
Spatio Temporal ◽  
The City

This article analyzes spatio-temporal logics in the representation of the city of La Paz in Imágenes Paceñas by Jaime Saenz and the urban chronicles of Víctor Hugo Viscarra. Juxtaposing the concepts of chrononormativity and queer time, it explores how linear temporal logic remains insufficient for the understanding of the city and its inhabitants in the two narrative projects. The article postulates that the marginal spaces of architectural ruins and garbage dumps, and the marginalized people who inhabit queer space-time are key to “revealing the hidden city” and understanding its contradictory place in the national narrative and space.

scholarly journals Temporalising Separation Logic for Planning with Search Control Knowledge

2017 ◽  
Author(s):  
Xu Lu ◽  
Cong Tian ◽  
Zhenhua Duan
Keyword(s):  
Temporal Logic ◽  
Expressive Power ◽  
Separation Logic ◽  
Temporal Constraints ◽  
Ai Planning ◽  
Temporal Logics ◽  
Spatial Constraints ◽  
Spatio Temporal ◽  
Control Knowledge ◽  
Search Control

Temporal logics are widely adopted in Artificial Intelligence (AI) planning for specifying Search Control Knowledge (SCK). However, traditional temporal logics are limited in expressive power since they are unable to express spatial constraints which are as important as temporal ones in many planning domains. To this end, we propose a two-dimensional (spatial and temporal) logic namely PPTL^SL by temporalising separation logic with Propositional Projection Temporal Logic (PPTL). The new logic is well-suited for specifying SCK containing both spatial and temporal constraints which are useful in AI planning. We show that PPTL^SL is decidable and present a decision procedure. With this basis, a planner namely S-TSolver for computing plans based on the spatio-temporal SCK expressed in PPTL^SL formulas is developed. Evaluation on some selected benchmark domains shows the effectiveness of S-TSolver.

scholarly journals The temporal logic of coalgebras via Galois algebras

2002 ◽  
Vol 12 (6) ◽  
pp. 875-903 ◽  
Author(s):  
BART JACOBS
Keyword(s):  
State Space ◽  
Temporal Logic ◽  
Metric Spaces ◽  
Linear Temporal Logic ◽  
The State ◽  
Temporal Logics ◽  
Computation Tree Logic ◽  
Computation Tree ◽  
Polynomial Functors

This paper introduces a temporal logic for coalgebras. Nexttime and lasttime operators are defined for a coalgebra, acting on predicates on the state space. They give rise to what is called a Galois algebra. Galois algebras form models of temporal logics like Linear Temporal Logic (LTL) and Computation Tree Logic (CTL). The mapping from coalgebras to Galois algebras turns out to be functorial, yielding indexed categorical structures. This construction gives many examples, for coalgebras of polynomial functors on sets. More generally, it will be shown how ‘fuzzy’ predicates on metric spaces, and predicates on presheaves, yield indexed Galois algebras, in basically the same coalgebraic manner.

scholarly journals Upscaling with the dynamic two-layer classification concept (D2C): TreeMig-2L, an efficient implementation of the forest-landscape model TreeMig

2015 ◽  
Vol 8 (7) ◽  
pp. 5535-5575
Author(s):  
J. E. M. S. Nabel
Keyword(s):  
Vegetation Dynamics ◽  
Climatic Changes ◽  
Discrete Models ◽  
Similarity Criteria ◽  
Forest Landscape ◽  
Two Dimensional ◽  
Landscape Model ◽  
Trade Off ◽  
Forest Landscape Model ◽  
Spatio Temporal

Abstract. Models used to investigate impacts of climatic changes on spatio-temporal vegetation dynamics need to balance required accuracy with computational feasibility. To enhance the computational efficiency of these models, upscaling methods are required that maintain key fine-scale processes influencing vegetation dynamics. In this paper, an adjustable method – the dynamic two-layer classification concept (D2C) – for the upscaling of time- and space-discrete models is presented. D2C aims to separate potentially repetitive calculations from those specific to single grid cells. The underlying idea is to extract processes that do not require information about a grid cell's neighbourhood to a reduced-size non-spatial layer, which is dynamically coupled to the original two-dimensional layer. The size of the non-spatial layer is thereby adaptive and depends on dynamic classifications according to pre-specified similarity criteria. I present how D2C can be used in a model implementation on the example of TreeMig-2L, a new, efficient version of the intermediate-complexity forest-landscape model TreeMig. To discuss the trade-off between computational expenses and accuracy, as well as the applicability of D2C, I compare different model stages of TreeMig-2L via simulations of two different application scenarios. This comparison of different model stages demonstrates that applying D2C can strongly reduce computational expenses of processes calculated on the new non-spatial layer. D2C is thus a valuable upscaling method for models and applications in which processes requiring information about the neighbourhood constitute the minor share of the overall computational expenses.

scholarly journals Temporal Logics Over Finite Traces with Uncertainty

2020 ◽  
Vol 34 (06) ◽  
pp. 10218-10225 ◽  
Author(s):  
Fabrizio M Maggi ◽  
Marco Montali ◽  
Rafael Peñaloza
Keyword(s):  
Decision Making ◽  
Temporal Logic ◽  
Business Process ◽  
Dynamic Systems ◽  
Real Life ◽  
Temporal Logics ◽  
Business Process Modelling ◽  
Process Discovery ◽  
Event Log ◽  
Computational Properties

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.

scholarly journals Studying Emergent Behaviours in Morphogenesis Using Signal Spatio-Temporal Logic

2015 ◽  
pp. 156-172 ◽  
Author(s):  
Ezio Bartocci ◽  
Luca Bortolussi ◽  
Dimitrios Milios ◽  
Laura Nenzi ◽  
Guido Sanguinetti
Keyword(s):  
Temporal Logic ◽  
Spatio Temporal ◽  
Emergent Behaviours

A review of temporal logics

1989 ◽  
Vol 4 (2) ◽  
pp. 141-162 ◽  
Author(s):  
Derek Long
Keyword(s):  
Artificial Intelligence ◽  
Temporal Logic ◽  
Temporal Reasoning ◽  
Order Logic ◽  
First Order Logic ◽  
Temporal Logics ◽  
Detailed Review ◽  
First Order ◽  
Reasoning Tasks

AbstractA series of temporal reasoning tasks are identified which motivate the consideration and application of temporal logics in artificial intelligence. There follows a discussion of the broad issues involved in modelling time and constructing a temporal logic. The paper then presents a detailed review of the major approaches to temporal logics: first-order logic approaches, modal temporal logics and reified temporal logics. The review considers the most significant exemplars within the various approaches, including logics due to Russell, Hayes and McCarthy, Prior, McDermott, Allen, Kowalski and Sergot. The logics are compared and contrasted, particularly in their treatments of change and action, the roles they seek to fulfil and the underlying models of time on which they rest. The paper concludes with a brief consideration of the problem of granularity—a problem of considerable significance in temporal reasoning, which has yet to be satisfactorily treated in a temporal logic.

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