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 An axiomatization of full Computation Tree Logic

2001 ◽  
Vol 66 (3) ◽  
pp. 1011-1057 ◽  
Author(s):  
M. Reynolds
Keyword(s):  
Temporal Logic ◽  
Open Problem ◽  
Branching Time ◽  
Computation Tree Logic ◽  
Computation Tree ◽  
Complete Axiomatization

AbstractWe give a sound and complete axiomatization for the full computation tree logic. CTL*, of R-generable models. This solves a long standing open problem in branching time temporal logic.

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 Best-First Heuristic Search for Multicore Machines

2010 ◽  
Vol 39 ◽  
pp. 689-743 ◽  
Author(s):  
E. Burns ◽  
S. Lemons ◽  
W. Ruml ◽  
R. Zhou
Keyword(s):  
State Space ◽  
Shared Memory ◽  
Temporal Logic ◽  
Heuristic Search ◽  
Multicore Processors ◽  
The State ◽  
New Method ◽  
Parallel Search ◽  
Empirical Comparison ◽  
Best First Search

To harness modern multicore processors, it is imperative to develop parallel versions of fundamental algorithms. In this paper, we compare different approaches to parallel best-first search in a shared-memory setting. We present a new method, PBNF, that uses abstraction to partition the state space and to detect duplicate states without requiring frequent locking. PBNF allows speculative expansions when necessary to keep threads busy. We identify and fix potential livelock conditions in our approach, proving its correctness using temporal logic. Our approach is general, allowing it to extend easily to suboptimal and anytime heuristic search. In an empirical comparison on STRIPS planning, grid pathfinding, and sliding tile puzzle problems using 8-core machines, we show that A*, weighted A* and Anytime weighted A* implemented using PBNF yield faster search than improved versions of previous parallel search proposals.

Logical foundations of hierarchical model checking

2018 ◽  
Vol 52 (4) ◽  
pp. 539-563 ◽  
Author(s):  
Norihiro Kamide
Keyword(s):  
Model Checking ◽  
Temporal Logic ◽  
Hierarchical Model ◽  
Design Methodology ◽  
Linear Time ◽  
Hierarchical Systems ◽  
Content Type ◽  
Computation Tree Logic ◽  
Computation Tree ◽  
Linear Time Temporal Logic

Purpose The purpose of this paper is to develop new simple logics and translations for hierarchical model checking. Hierarchical model checking is a model-checking paradigm that can appropriately verify systems with hierarchical information and structures. Design/methodology/approach In this study, logics and translations for hierarchical model checking are developed based on linear-time temporal logic (LTL), computation-tree logic (CTL) and full computation-tree logic (CTL*). A sequential linear-time temporal logic (sLTL), a sequential computation-tree logic (sCTL), and a sequential full computation-tree logic (sCTL*), which can suitably represent hierarchical information and structures, are developed by extending LTL, CTL and CTL*, respectively. Translations from sLTL, sCTL and sCTL* into LTL, CTL and CTL*, respectively, are defined, and theorems for embedding sLTL, sCTL and sCTL* into LTL, CTL and CTL*, respectively, are proved using these translations. Findings These embedding theorems allow us to reuse the standard LTL-, CTL-, and CTL*-based model-checking algorithms to verify hierarchical systems that are modeled and specified by sLTL, sCTL and sCTL*. Originality/value The new logics sLTL, sCTL and sCTL* and their translations are developed, and some illustrative examples of hierarchical model checking are presented based on these logics and translations.

Method for Combining Paraconsistency and Probability in Temporal Reasoning

2016 ◽  
Vol 20 (5) ◽  
pp. 813-827 ◽  
Author(s):  
Norihiro Kamide ◽  
◽  
Daiki Koizumi ◽  
Keyword(s):  
Model Checking ◽  
Temporal Reasoning ◽  
Concurrent Systems ◽  
Embedding Theorem ◽  
Temporal Logics ◽  
Probabilistic Computation ◽  
Computation Tree Logic ◽  
Computation Tree

Computation tree logic (CTL) is known to be one of the most useful temporal logics for verifying concurrent systems by model checking technologies. However, CTL is not sufficient for handling inconsistency-tolerant and probabilistic accounts of concurrent systems. In this paper, a paraconsistent (or inconsistency-tolerant) probabilistic computation tree logic (PpCTL) is derived from an existing probabilistic computation tree logic (pCTL) by adding a paraconsistent negation connective. A theorem for embedding PpCTL into pCTL is proven, thereby indicating that we can reuse existing pCTL-based model checking algorithms. A relative decidability theorem for PpCTL, wherein the decidability of pCTL implies that of PpCTL, is proven using this embedding theorem. Some illustrative examples involving the use of PpCTL are also presented.

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].

Ergodic decompositions associated with regular Markov operators on Polish spaces

2010 ◽  
Vol 31 (2) ◽  
pp. 571-597 ◽  
Author(s):  
DANIËL T. H. WORM ◽  
SANDER C. HILLE
Keyword(s):  
State Space ◽  
Metric Spaces ◽  
Transition Probabilities ◽  
Polish Space ◽  
Invariant Probability Measure ◽  
The State ◽  
Probability Measures ◽  
Ergodic Decomposition ◽  
Polish Spaces ◽  
Appl Math

AbstractFor any regular Markov operator on the space of finite Borel measures on a Polish space we give a Yosida-type decomposition of the state space, which yields a parametrization of the ergodic probability measures associated with this operator in terms of particular subsets of the state space. We use this parametrization to prove an integral decomposition of every invariant probability measure in terms of the ergodic probability measures and give an ergodic decomposition of the state space. This extends results by Yosida [Functional Analysis. Springer, Berlin, 1980, Ch. XIII.4], Hernández-Lerma and Lasserre [Ergodic theorems and ergodic decomposition for Markov chains. Acta Appl. Math.54 (1998), 99–119] and Zaharopol [An ergodic decomposition defined by transition probabilities. Acta Appl. Math.104 (2008), 47–81], who considered the setting of locally compact separable metric spaces. Our extension to Polish spaces solves an open problem posed by Zaharopol (loc. cit.) in a satisfactory manner.

Bisimulation proof methods in a path-based specification language for polynomial coalgebras

2014 ◽  
Vol 25 (4) ◽  
pp. 765-804
Author(s):  
XIAO-CONG ZHOU ◽  
YONG-JI LI ◽  
WEN-JUN LI ◽  
HAI-YAN QIAO ◽  
ZHONG-MEI SHU
Keyword(s):  
State Space ◽  
Specification Language ◽  
Transition System ◽  
The State ◽  
Specification Languages ◽  
Transition Systems ◽  
Algebraic Specifications ◽  
Polynomial Functors ◽  
Proof Techniques ◽  
Proof Methods

What reasoning rules can be used for the deduction of bisimulation formulas in coalgebraic specifications is problematic because those rules used in algebraic specifications possibly cannot be applied to bisimulation formulas. Although some categorical bisimulation proof methods for coalgebras have been proposed, they are not based on specification languages of coalgebras so that they cannot be used as reasoning rules. In this paper, a specification language based on paths of polynomial functors is proposed to specify polynomial coalgebras. Paths of polynomial functors give detailed observations and transitions on the state space of coalgebras so that the techniques used in transition system specifications can be applied to such a path-based language. In particular, because bisimulations can be characterized by paths, the notions of progressions, respectful functions and faithful contexts can be defined based on paths, and then bisimulation up-to proof techniques, including bisimulation up-to bisimilarities and up-to contexts for transition systems can be transformed into reasoning rules in the language. Several examples illustrate how to reason syntactically about bisimulations in the language by using the rules induced by the bisimulation proof techniques.

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.

Sign in / Sign up

Export Citation Format

Share Document