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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
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
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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φ ∈ L) is approximated by a function d: P×L → [0, 1] such that d(P, φ) = 0 iff P
φ. d induces a distance D on processes by D(P, P ′) = sup{d(P, φ)−d(P ′, φ), φ ∈ L} and similarly, a pseudometric δ on formulas by δ(φ, ψ) = sup{d(P, φ)−d(P,ψ), P ∈ P. In the context of complete axiomatizations
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
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
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
A PROOF OF COMPLETENESS FOR CONTINUOUS FIRSTORDER LOGIC
, 2009
"... Continuous firstorder logic has found interest among model theorists who wish to extend the classical analysis of “algebraic” structures (such as fields, group, and graphs) to various natural classes of complete metric structures (such as probability algebras, Hilbert spaces, and Banach spaces). W ..."
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Cited by 8 (1 self)
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Continuous firstorder logic has found interest among model theorists who wish to extend the classical analysis of “algebraic” structures (such as fields, group, and graphs) to various natural classes of complete metric structures (such as probability algebras, Hilbert spaces, and Banach spaces
Logical axiomatizations of spacetime. Samples from the literature
 In: NonEuclidean Geometries (J'anos Bolyai Memorial Volume
, 2005
"... Abstract We study relativity theory as a theory in the sense of mathematical logic. We use firstorder logic (FOL) as a framework to do so. We aim at an “analysis of the logical structure of relativity theories”. First we build up (the kinematics of) special relativity in FOL, then analyze it, and t ..."
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Cited by 25 (14 self)
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related in a broader sense. In the perspective of the present work, axiomatization is not a final goal. Axiomatization is only a first step, a tool. The goal is something like a conceptual analysis of relativity in the framework of logic. In section 1 we recall a complete FOLaxiomatization Specrel
Localic completion of generalized metric spaces I
, 2005
"... Abstract. Following Lawvere, a generalized metric space (gms) is a set X equipped with a metric map from X 2 to the interval of upper reals (approximated from above but not from below) from 0 to ∞ inclusive, and satisfying the zero selfdistance law and the triangle inequality. We describe a complet ..."
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Cited by 9 (0 self)
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Abstract. Following Lawvere, a generalized metric space (gms) is a set X equipped with a metric map from X 2 to the interval of upper reals (approximated from above but not from below) from 0 to ∞ inclusive, and satisfying the zero selfdistance law and the triangle inequality. We describe a
Robustness of Temporal Logic Specifications for ContinuousTime Signals
, 2009
"... In this paper, we consider the robust interpretation of Metric Temporal Logic (MTL) formulas over signals that take values in metric spaces. For such signals, which are generated by systems whose states are equipped with nontrivial metrics, for example continuous or hybrid, robustness is not only na ..."
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Cited by 42 (18 self)
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In this paper, we consider the robust interpretation of Metric Temporal Logic (MTL) formulas over signals that take values in metric spaces. For such signals, which are generated by systems whose states are equipped with nontrivial metrics, for example continuous or hybrid, robustness is not only
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