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A Coalgebraic Approach to Linear-Time Logics
[chapter]
2014
Lecture Notes in Computer Science
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This yields logics for reasoning about quantitative aspects of linear-time behaviour. ...
In the case of non-deterministic branching, our logic supports reasoning about the possibility of exhibiting a given linear-time behaviour, and therefore resembles an existential version of the logic LTL ...
A similar approach is taken in [2] to define the extent to which a state in a coalgebra with branching can exhibit a given linear-time behaviour. ...
doi:10.1007/978-3-642-54830-7_28
fatcat:fqvo6h7m2ffhletcnnkz5u7wpi
Towards Systematic Construction of Temporal Logics for Dynamical Systems via Coalgebra
[chapter]
2014
Lecture Notes in Computer Science
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Here, a systematic approach to the construction of temporal logics for dynamical systems is proposed: Firstly, it is noted that dynamical systems can be seen as coalgebras in various ways. ...
Secondly, a straightforward standard construction of modal logics out of coalgebras, namely Moss's coalgebraic logic, is applied. ...
An orbital frame is called linear-time/invertible if and only if it corresponds to the orbit coalgebra of some linear-time/invertible dynamical system, respectively. ...
doi:10.1007/978-3-662-44124-4_12
fatcat:cubjy7rqe5dk3akiovnbyccmv4
Systematic Construction of Temporal Logics for Dynamical Systems via Coalgebra
[article]
2012
arXiv
pre-print
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Here, a systematic approach to the construction of temporal logics for dynamical systems is proposed: Firstly, it is noted that dynamical systems can be seen as coalgebras in various ways. ...
Secondly, a straightforward standard construction of modal logics out of coalgebras, namely Moss's coalgebraic logic, is applied. ...
The present article explores a systematic and fairly generic approach to the construction of temporal logics for dynamical systems, via the rather recent mathematical field of universal coalgebra which ...
arXiv:1212.1734v1
fatcat:yvtvvaxkrfbzjosqzjopixpg2q
Graded Monads and Graded Logics for the Linear Time - Branching Time Spectrum
2019
International Conference on Concurrency Theory
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In the case of labelled transition systems, these equivalences range from trace equivalence to (strong) bisimilarity, and are organized in what is known as the linear time -branching time spectrum. ...
We show in the present paper that this framework of graded semantics does subsume the most important equivalences from the linear time -branching time spectrum. ...
Example 6.5 (Expressive graded logics on the linear time -branching time spectrum). ...
doi:10.4230/lipics.concur.2019.36
dblp:conf/concur/DorschMS19
fatcat:eld6nrsmnrhqnluzpr6cxklmlm
Canonical Coalgebraic Linear Time Logics
2015
Conference on Algebra and Coalgebra in Computer Science
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We extend earlier work on linear time fixpoint logics for coalgebras with branching, by showing how propositional operators arising from the choice of branching monad can be canonically added to these ...
We also state conditions under which similar, non-canonical logics enjoy the same property -this applies both to the choice of a branching modality and to the choice of linear time modalities. ...
Coalgebraic Linear Time Logics via Dual Adjunctions This section rephrases the generalised predicate lifting approach to defining the semantics of coalgebraic linear time logics in terms of dual adjunctions ...
doi:10.4230/lipics.calco.2015.66
dblp:conf/calco/Cirstea15
fatcat:6swfor7dx5cxjjxbi2b4nmsyxe
The rôle of linear logic in coalgebraical approach of computing
2011
Journal of Information and Organizational Sciences
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Linear logic provides a logical perspective on computational issues such as control of resources and order of evaluation. ...
While classical logic treats the sentences that are always true or false, in linear logic it depends on an internal state of a dynamic system. ...
Then we are able to consider the program as a logical deduction within linear logical system. ...
doaj:75bab1b9dc2b46558af226dcb0ae2cd8
fatcat:3ftl4xi2evgwxfizt45gjduxyq
Page 4192 of Mathematical Reviews Vol. , Issue 2001F
[page]
2001
Mathematical Reviews
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Using a linear-time translation from branching-time temporal logic to alternating tree automata, model checking is translated into a l|-letter nonemptiness problem for word automata. ...
For the logic CTL, the resulting automata are weak, thus yielding an automaton-based linear-time model-checking algorithm for CTL. ...
From Branching to Linear Time, Coalgebraically
2013
Electronic Proceedings in Theoretical Computer Science
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account of the linear-time behaviour of a state in such a coalgebra. ...
By moving away from a boolean universe of truth values, our approach can measure the extent to which a state in a system with branching is able to exhibit a particular linear-time behaviour. ...
a path-based semantics akin to those of standard linear-time logics. ...
doi:10.4204/eptcs.126.2
fatcat:qcjyc5vvnfgzfpybpc2j67euim
INTRUSION DETECTION SYSTEM BEHAVIOR AS RESOURCE-ORIENTED FORMULA
2015
Acta Electrotechnica et Informatica
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For description of the IDS via logical systems, the Coalgebraic Modal Linear logic for IDS has been introduced, by which the behavioral effects of the IDS has been expressed by formula after simulated ...
One of the possibilities how to increase network security is the deployment of the Intrusion Detection System in computer network -IDS. ...
It means, that in the future we would like to extend our approach by expanding Coalgebraic Modal Linear Logic for IDS with time-spatial calculus from Girard's Ludics theory. ...
doi:10.15546/aeei-2015-0022
fatcat:qzreaa6gznbo3en7hcvqz6sfny
Page 8462 of Mathematical Reviews Vol. , Issue 2004k
[page]
2004
Mathematical Reviews
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This approach generalizes atomic propositions and modal operators from Kripke models to arbitrary coalgebras. ...
The attention of other approaches was restricted to a syntactically defined class of endofunctors. ...
Towards a dual ontology: duality, a case study
2018
Sofia
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Formally, this is due to their non-linear mathematical behaviour.This make a question about the ontology of such systems, given thatthe actual most widespread ontologies conceive existent entities just ...
Actually, providing a contribution to thisvery shift is what this paper want to be focused on. ...
able to treat at that time were the linear ones. ...
doi:10.47456/sofia.v7i1.19403
fatcat:5opze73ornhs7fnwu7ajaehgh4
Formal Model of IDS Based on BDI Logic
2021
Mathematics
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In our paper, we present a logical model of an active IDS based on category theory, coalgebras, linear logic, and Belief–Desire–Intention (BDI) logic. ...
Such an IDS can not only detect intrusions but also autonomously react to them according to a defined security policy. We demonstrate our approach on a motivating example with real network intrusions. ...
For that, we use a linear logic [14] , a coalgebraic logic [15] , and a BDI logic [16] . ...
doi:10.3390/math9182290
fatcat:jb76oivtxje5pprydamvkyrw6a
Linear Time Logics – A Coalgebraic Perspective
[article]
2021
arXiv
pre-print
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We describe a general approach to deriving linear-time logics for a wide variety of state-based, quantitative systems, by modelling the latter as coalgebras whose type incorporates both branching and linear ...
semantics for them: a step-wise semantics akin to that of standard coalgebraic logics, and a path-based semantics akin to that of standard linear-time logics. ...
Thanks are due to Clemens Kupke for prompting me towards a study of logical distance as opposed to simply logical equivalence (the outcome of which is Section 7), and to Clemens Kupke and Toby Wilkinson ...
arXiv:1612.07844v3
fatcat:wwwzzrw7jzbb5dvyg5zyyij2xq
Lattice-theoretic progress measures and coalgebraic model checking
2016
Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL 2016
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The framework's theoretical robustness is witnessed by a smooth transfer from the branching-time setting to the linear-time one. ...
We then apply our theory of progress measures to a general model-checking framework, where systems are categorically presented as coalgebras. ...
I.H. and S.S. are supported by Grants-in-Aid No. 24680001 & 15KT0012, JSPS; C.C. was supported by a Royal Society International Exchanges Grant (IE131642). ...
doi:10.1145/2837614.2837673
dblp:conf/popl/HasuoSC16
fatcat:lmj4qiwlnndvlh5sws243ikj4e
Lattice-theoretic progress measures and coalgebraic model checking
2016
SIGPLAN notices
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The framework's theoretical robustness is witnessed by a smooth transfer from the branching-time setting to the linear-time one. ...
We then apply our theory of progress measures to a general model-checking framework, where systems are categorically presented as coalgebras. ...
I.H. and S.S. are supported by Grants-in-Aid No. 24680001 & 15KT0012, JSPS; C.C. was supported by a Royal Society International Exchanges Grant (IE131642). ...
doi:10.1145/2914770.2837673
fatcat:k5va5skyjvbcpcaocwqqy5tx5y
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