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A Coalgebraic Approach to Linear-Time Logics [chapter]

Corina Cîrstea
2014 Lecture Notes in Computer Science  
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]

Baltasar Trancón y Widemann
2014 Lecture Notes in Computer Science  
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]

Baltasar Trancón y Widemann
2012 arXiv   pre-print
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

Ulrich Dorsch, Stefan Milius, Lutz Schröder, Michael Wagner
2019 International Conference on Concurrency Theory  
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

Corina Cirstea, Marc Herbstritt
2015 Conference on Algebra and Coalgebra in Computer Science  
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

Viliam Slodičák, Pavol Macko
2011 Journal of Information and Organizational Sciences  
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  
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

Corina Cirstea
2013 Electronic Proceedings in Theoretical Computer Science  
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

Ján PERHÁČ, Daniel MIHÁLYI
2015 Acta Electrotechnica et Informatica  
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  
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

Francesco Maria Ferrari
2018 Sofia  
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

Ján Perháč, Valerie Novitzká, William Steingartner, Zuzana Bilanová
2021 Mathematics  
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]

Corina Cirstea
2021 arXiv   pre-print
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

Ichiro Hasuo, Shunsuke Shimizu, Corina Cîrstea
2016 Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL 2016  
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

Ichiro Hasuo, Shunsuke Shimizu, Corina Cîrstea
2016 SIGPLAN notices  
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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