scholarly journals Bayesian Inference of Linear Temporal Logic Specifications for Contrastive Explanations

2019 ◽  
Author(s):  
Joseph Kim ◽  
Christian Muise ◽  
Ankit Shah ◽  
Shubham Agarwal ◽  
Julie Shah
Keyword(s):  
Bayesian Inference ◽  
Temporal Logic ◽  
Probabilistic Model ◽  
Noisy Data ◽  
Linear Temporal Logic ◽  
System Behavior ◽  
Temporal Logics ◽  
Input Dataset ◽  
Bayesian Probabilistic Model ◽  
The Given

Temporal logics are useful for providing concise descriptions of system behavior, and have been successfully used as a language for goal definitions in task planning. Prior works on inferring temporal logic specifications have focused on "summarizing" the input dataset - i.e., finding specifications that are satisfied by all plan traces belonging to the given set. In this paper, we examine the problem of inferring specifications that describe temporal differences between two sets of plan traces. We formalize the concept of providing such contrastive explanations, then present BayesLTL - a Bayesian probabilistic model for inferring contrastive explanations as linear temporal logic (LTL) specifications. We demonstrate the robustness and scalability of our model for inferring accurate specifications from noisy data and across various benchmark planning domains.

Logical consecutions in discrete linear temporal logic

2005 ◽  
Vol 70 (4) ◽  
pp. 1137-1149 ◽  
Author(s):  
V. V. Rybakov
Keyword(s):  
Temporal Logic ◽  
Propositional Logic ◽  
Inference Rule ◽  
Logical Consequence ◽  
Linear Temporal Logic ◽  
Inference Rules ◽  
Temporal Logics ◽  
Temporal Inference ◽  
Semantic Techniques ◽  
The Given

AbstractWe investigate logical consequence in temporal logics in terms of logical consecutions, i.e., inference rules. First, we discuss the question: what does it mean for a logical consecution to be ‘correct’ in a propositional logic. We consider both valid and admissible consecutions in linear temporal logics and discuss the distinction between these two notions. The linear temporal logic LDTL, consisting of all formulas valid in the frame 〈L ≤, ≥〉 of all integer numbers, is the prime object of our investigation. We describe consecutions admissible in LDTL in a semantic way—via consecutions valid in special temporal Kripke/Hintikka models. Then we state that any temporal inference rule has a reduced normal form which is given in terms of uniform formulas of temporal degree 1. Using these facts and enhanced semantic techniques we construct an algorithm, which recognizes consecutions admissible in LDTL. Also, we note that using the same technique it follows that the linear temporal logic L(N) of all natural numbers is also decidable w.r.t. inference rules. So, we prove that both logics LDTL and L(N) are decidable w.r.t. admissible consecutions. In particular, as a consequence, they both are decidable (known fact), and the given deciding algorithms are explicit.

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 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 Propositional Linear Temporal Logic with Initial Validity Semantics

2015 ◽  
Vol 23 (4) ◽  
pp. 379-386
Author(s):  
Mariusz Giero
Keyword(s):  
Temporal Logic ◽  
Formal System ◽  
Computer Programs ◽  
Linear Temporal Logic ◽  
Deduction Theorem ◽  
Temporal Logics ◽  
Initial State ◽  
Formal Systems ◽  
Soundness And Completeness ◽  
The One

Summary In the article [10] a formal system for Propositional Linear Temporal Logic (in short LTLB) with normal semantics is introduced. The language of this logic consists of “until” operator in a very strict version. The very strict “until” operator enables to express all other temporal operators. In this article we construct a formal system for LTLB with the initial semantics [12]. Initial semantics means that we define the validity of the formula in a model as satisfaction in the initial state of model while normal semantics means that we define the validity as satisfaction in all states of model. We prove the Deduction Theorem, and the soundness and completeness of the introduced formal system. We also prove some theorems to compare both formal systems, i.e., the one introduced in the article [10] and the one introduced in this article. Formal systems for temporal logics are applied in the verification of computer programs. In order to carry out the verification one has to derive an appropriate formula within a selected formal system. The formal systems introduced in [10] and in this article can be used to carry out such verifications in Mizar [4].

scholarly journals Divergent stutter bisimulation abstraction for controller synthesis with linear temporal logic specifications

Automatica ◽  
2021 ◽  
Vol 130 ◽  
pp. 109723
Author(s):  
Sahar Mohajerani ◽  
Robi Malik ◽  
Andrew Wintenberg ◽  
Stéphane Lafortune ◽  
Necmiye Ozay
Keyword(s):  
Temporal Logic ◽  
Linear Temporal Logic ◽  
Controller Synthesis

scholarly journals A Unified Translation of Linear Temporal Logic to ω-Automata

2020 ◽  
Vol 67 (6) ◽  
pp. 1-61
Author(s):  
Javier Esparza ◽  
Jan Křetínský ◽  
Salomon Sickert
Keyword(s):  
Temporal Logic ◽  
Linear Temporal Logic

Extending Linear Temporal Logic with Clocks to Object-Z

2014 ◽  
Vol 513-517 ◽  
pp. 927-930
Author(s):  
Zhi Cheng Wen ◽  
Zhi Gang Chen
Keyword(s):  
Real Time ◽  
Temporal Logic ◽  
Formal Specification ◽  
Large Scale ◽  
Linear Temporal Logic ◽  
Specification Language ◽  
Continuous Variables ◽  
Real Time System ◽  
Software Specification ◽  
Formal Specification Language

Object-Z, an extension to formal specification language Z, is good for describing large scale Object-Oriented software specification. While Object-Z has found application in a number of areas, its utility is limited by its inability to specify continuous variables and real-time constraints. Linear temporal logic can describe real-time system, but it can not deal with time variables well and also can not describe formal specification modularly. This paper extends linear temporal logic with clocks (LTLC) and presents an approach to adding linear temporal logic with clocks to Object-Z. Extended Object-Z with LTLC, a modular formal specification language, is a minimum extension of the syntax and semantics of Object-Z. The main advantage of this extension lies in that it is convenient to describe and verify the complex real-time software specification.

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