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Modular Markovian Logic
"... We introduce Modular Markovian Logic (MML) for compositional continuoustime and continuousspace Markov processes. MML combines operators specific to stochastic logics with operators that reflect the modular structure of the semantics, similar to those used by spatial and separation logics. We pre ..."
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Cited by 9 (7 self)
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We introduce Modular Markovian Logic (MML) for compositional continuoustime and continuousspace Markov processes. MML combines operators specific to stochastic logics with operators that reflect the modular structure of the semantics, similar to those used by spatial and separation logics. We
Strong Completeness for Markovian Logics
"... Abstract. In this paper we present Hilbertstyle axiomatizations for three logics for reasoning about continuousspace Markov processes (MPs): (i) a logic for MPs defined for probability distributions on measurable state spaces, (ii) a logic for MPs defined for subprobability distributions and (iii ..."
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Cited by 2 (1 self)
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Abstract. In this paper we present Hilbertstyle axiomatizations for three logics for reasoning about continuousspace Markov processes (MPs): (i) a logic for MPs defined for probability distributions on measurable state spaces, (ii) a logic for MPs defined for subprobability distributions
Parameterized Metatheory for Continuous Markovian Logic
"... Abstract—This paper shows that a classic metalogical framework, including all Boolean operators, can be used to support the development of a metric behavioural theory for Markov processes. Previously, only intuitionistic frameworks or frameworks without negation and logical implication have been d ..."
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developed to fulfill this task. The focus of this paper is on continuous Markovian logic (CML), a logic that characterizes stochastic bisimulation of Markov processes with arbitrary measurable state space and continuoustime transitions. For a parameter ε> 0 interpreted as observational error, we
CONTINUOUS MARKOVIAN LOGICS AXIOMATIZATION AND QUANTIFIED METATHEORY
, 2011
"... Continuous Markovian Logic (CML) is a multimodal logic that expresses quantitative and qualitative properties of continuoustime labelled Markov processes with arbitrary (analytic) statespaces, henceforth called continuous Markov processes (CMPs). The modalities of CML evaluate the rates of the exp ..."
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Cited by 5 (4 self)
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Continuous Markovian Logic (CML) is a multimodal logic that expresses quantitative and qualitative properties of continuoustime labelled Markov processes with arbitrary (analytic) statespaces, henceforth called continuous Markov processes (CMPs). The modalities of CML evaluate the rates
Continuous Markovian Logic From Complete Axiomatization to the Metric Space of Formulas
"... In this paper we study the Continuous Markovian Logic (CML), a multimodal logic that expresses quantitative and qualitative properties of continuousspace and continuoustime labelled Markov processes(CMPs). The modalities of CML approximates the rates of the exponentially distributed random variabl ..."
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Cited by 7 (7 self)
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In this paper we study the Continuous Markovian Logic (CML), a multimodal logic that expresses quantitative and qualitative properties of continuousspace and continuoustime labelled Markov processes(CMPs). The modalities of CML approximates the rates of the exponentially distributed random
Markovian Logics: The Metric Space of Logical Formulas. The Bulletin of Symbolic Logic, the meeting report of Logic Colloquium 2011
"... A central questions in the field of probabilistic and Markovian systems is “when do two systems behave similarly up to some observational error?”. Probabilistic and stochastic bisimulations relates models with identical behaviours and are characterized by multimodal logics with operators indexed wit ..."
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Cited by 1 (1 self)
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A central questions in the field of probabilistic and Markovian systems is “when do two systems behave similarly up to some observational error?”. Probabilistic and stochastic bisimulations relates models with identical behaviours and are characterized by multimodal logics with operators indexed
Markovian Analysis of Large Finite State Machines
 IEEE Transactions on CAD
, 1996
"... Regarding finite state machines as Markov chains facilitates the application of probabilistic methods to very large logic synthesis and formal verification problems. In this paper we present symbolic algorithms to compute the steadystate probabilities for very large finite state machines (up to 10 ..."
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Cited by 77 (7 self)
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Regarding finite state machines as Markov chains facilitates the application of probabilistic methods to very large logic synthesis and formal verification problems. In this paper we present symbolic algorithms to compute the steadystate probabilities for very large finite state machines (up to 10
Modal Logic Characterization of Markovian Testing and Trace Equivalences
 in Proc. of the 1st Int. Workshop on Logic, Models and Computer Science (LMCS 2006), ENTCS
, 2006
"... Markovian testing and trace equivalences have been recently proposed as reasonable alternatives to Markovian bisimilarity, as both of them induce at the Markov chain level an aggregation strictly coarser than ordinary lumping that is still exact. In this paper we provide a modal logic characterizati ..."
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Cited by 2 (2 self)
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Markovian testing and trace equivalences have been recently proposed as reasonable alternatives to Markovian bisimilarity, as both of them induce at the Markov chain level an aggregation strictly coarser than ordinary lumping that is still exact. In this paper we provide a modal logic
On Markovian Fragments of COCOLOG for Logic Control Systems
, 1992
"... The COCOLOG (Conditional Observer and Controller Logic) system is a partially ordered family of first order logical theories expressed in the typed first order languages fL k ; k 0g describing the controlled evolution of the state of a given partially observered finite machine M. The initial theor ..."
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Cited by 5 (5 self)
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The COCOLOG (Conditional Observer and Controller Logic) system is a partially ordered family of first order logical theories expressed in the typed first order languages fL k ; k 0g describing the controlled evolution of the state of a given partially observered finite machine M. The initial
LOGIC CONTROL: MARKOVIAN FRAGMENTS, HIERARCHY AND HYBRID SYSTEMS
, 1995
"... In order to formulate the analysis and synthesis of hierarchical systems, a hierarchical structure based upon the notion of dynamical consistency is presented. The underlying motivation for this notion is that high level dynamics should be consistent with low level dynamics. The major part of this i ..."
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Cited by 4 (1 self)
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In order to formulate the analysis and synthesis of hierarchical systems, a hierarchical structure based upon the notion of dynamical consistency is presented. The underlying motivation for this notion is that high level dynamics should be consistent with low level dynamics. The major part of this investigation is carried out for the socalled inblock controllable partition lattices, which are the lattices of partitions for which each block element constitutes a controllable submachine. We show that most controllable finite state machines have at least one nontrivial inblock controllable partition machine. It is also shown that, subject to inblock controllability, the resulting partition machines are controllable if and only if the base machines are controllable. A consequence of this construction is that a statetostate reachability problem can be decomposed into reachability problems at different levels of abstraction. In terms of this theory, a hierarchical control system is a set of control systems associated with a chain from the top element to the bottom element of the inblock controllable partition lattice of a controlled machine. As an
Results 1  10
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