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 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 The Axiomatization of Propositional Linear Time Temporal Logic

2011 ◽  
Vol 19 (2) ◽  
pp. 113-119
Author(s):  
Mariusz Giero
Keyword(s):  
Temporal Logic ◽  
Linear Time ◽  
Formal System ◽  
Deduction Theorem ◽  
Linear Time Temporal Logic

The Axiomatization of Propositional Linear Time Temporal Logic The article introduces propositional linear time temporal logic as a formal system. Axioms and rules of derivation are defined. Soundness Theorem and Deduction Theorem are proved [9].

scholarly journals Tableau-Like Automata-Based Axiomatization for Propositional Linear Temporal Logic

10.29007/df56 ◽  
2018 ◽  
Author(s):  
Nikolay V. Shilov
Keyword(s):  
Model Checking ◽  
Temporal Logic ◽  
Decision Procedure ◽  
Computer Programs ◽  
Linear Temporal Logic ◽  
Local Model ◽  
Specification And Verification ◽  
Local Model Checking

Propositional Linear Temporal Logic (PLTL) is a very popular formalism for specification and verification of computer programs and systems. This extended abstract sketches a tableau-like axiomatization for PLTL based on automata-theoretic decision procedure coupled with tableau for local model checking of the propositional μ-Calculus.

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 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.

Modality and folk psychology

2019 ◽  
Vol 28 (1) ◽  
pp. 19-27
Author(s):  
Ja. O. Petik
Keyword(s):  
Modal Logic ◽  
Brain Activity ◽  
Formal System ◽  
Philosophy Of Logic ◽  
Psychological States ◽  
Formal Systems ◽  
Modern Psychology ◽  
Philosophical Interpretation ◽  
Important Direction

The connection of the modern psychology and formal systems remains an important direction of research. This paper is centered on philosophical problems surrounding relations between mental and logic. Main attention is given to philosophy of logic but certain ideas are introduced that can be incorporated into the practical philosophical logic. The definition and properties of basic modal logic and descending ones which are used in study of mental activity are in view. The defining role of philosophical interpretation of modality for the particular formal system used for research in the field of psychological states of agents is postulated. Different semantics of modal logic are studied. The hypothesis about the connection of research in cognitive psychology (semantics of brain activity) and formal systems connected to research of psychological states is stated.

An Automata-Theoretic Decision Procedure for Propositional Temporal Logic with Since and Until1

1992 ◽  
Vol 17 (3) ◽  
pp. 271-282
Author(s):  
Y.S. Ramakrishna ◽  
L.E. Moser ◽  
L.K. Dillon ◽  
P.M. Melliar-Smith ◽  
G. Kutty
Keyword(s):  
Temporal Logic ◽  
Decision Procedure ◽  
Linear Time ◽  
Computer Systems ◽  
Hierarchical Abstraction ◽  
Soundness And Completeness

We present an automata-theoretic decision procedure for Since/Until Temporal Logic (SUTL), a linear-time propositional temporal logic with strong non-strict since and until operators. The logic, which is intended for specifying and reasoning about computer systems, employs neither next nor previous operators. Such operators obstruct the use of hierarchical abstraction and refinement and make reasoning about concurrency difficult. A proof of the soundness and completeness of the decision procedure is given, and its complexity is analyzed.

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
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