Taking It to the Limit: Approximate Reasoning for Markov Processes
We develop a fusion of logical and metrical principles for reasoning about Markov processes. More precisely, we lift metrics from processes to sets of processes satisfying a formula and explore how the satisfaction relation behaves as sequences of processes and sequences of formulas approach limits. A key new concept is dynamically-continuous metric bisimulation which is a property of (pseudo)metrics. We prove theorems about satisfaction in the limit, robustness theorems as well as giving a topological characterization of various classes of formulas. This work is aimed at providing approximate reasoning principles for Markov processes.
KeywordsMarkov Process Convergent Sequence Logical Formula Approximate Reasoning Markov Kernel
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- 1.Arveson, W.: An Invitation to C *-Algebra. Springer (1976)Google Scholar
- 3.Ballarini, P., Mardare, R., Mura, I.: Analysing Biochemical Oscillations through Probabilistic Model Checking. In: FBTC 2008. ENTCS, vol. 229(1), pp. 3–19 (2009)Google Scholar
- 4.Cardelli, L., Larsen, K.G., Mardare, R.: Continuous Markovian logic - from complete axiomatization to the metric space of formulas. In: CSL, pp. 144–158 (2011)Google Scholar
- 11.Dudley, R.M.: Real Analysis and Probability. Wadsworth and Brookes/Cole (1989)Google Scholar
- 14.Giacalone, A., Jou, C.-C., Smolka, S.A.: Algebraic Reasoning for Probabilistic Concurrent Systems. In: IFIP WG 2.2/2.3 Working Conference on Programming Concepts and Methods (1990)Google Scholar
- 17.Panangaden, P.: Labelled Markov Processes. Imperial College Press (2009)Google Scholar
- 20.Zhou, C.: A complete deductive system for probability logic with application to Harsanyi type spaces. PhD thesis, Indiana University (2007)Google Scholar