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Generic Approach to Updating Uncertainty: Focus on Conditioning
Kuncová, Alexandra ; Peliš, Michal (advisor) ; Sedlár, Igor (referee)
First, we consider different kinds of representation of uncertainty and the meth- ods for updating each of them by conditioning. We focus on the generic frame- work of (conditional) plausibility spaces, since it generalises all the introduced representations. Further, we select three frameworks and list the properties that need to be added to a conditional plausibility space in order to recover each of these frameworks. The main goal of this work, however, is to show how public announcement on single-agent plausibility models, ranking structures, and pos- sibility structures realised by their corresponding update mechanisms, can be embedded into the framework of conditional plausibility spaces. At the very end we briefly illustrate a general update model using plausibility measures. Keywords: belief revision, dynamic logic, epistemic logic, plausibility space, pub- lic announcement, uncertainty, update.
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Generic Approach to Updating Uncertainty: Focus on Conditioning
Kuncová, Alexandra ; Peliš, Michal (advisor) ; Sedlár, Igor (referee)
First, we consider different kinds of representation of uncertainty and the meth- ods for updating each of them by conditioning. We focus on the generic frame- work of (conditional) plausibility spaces, since it generalises all the introduced representations. Further, we select three frameworks and list the properties that need to be added to a conditional plausibility space in order to recover each of these frameworks. The main goal of this work, however, is to show how public announcement on single-agent plausibility models, ranking structures, and pos- sibility structures realised by their corresponding update mechanisms, can be embedded into the framework of conditional plausibility spaces. At the very end we briefly illustrate a general update model using plausibility measures. Keywords: belief revision, dynamic logic, epistemic logic, plausibility space, pub- lic announcement, uncertainty, update.
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Introspection of Vague Knowledge in Fuzzy Logic
Běhounek, Libor
In classical epistemic logic, the principle of introspection for vague knowledge is precluded by Poincaré's paradox, which implies that the relation of indistinguishability cannot be transitive. The paper shows that the introspection principle for vague knowledge can be saved if T-transitive indistinguishability relations in fuzzy logic are used.
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Two Connections between Epistemic and Fuzzy Logics
Běhounek, Libor
Two possible connections between epistemic and fuzzy logics are studied. Epistemic fuzzy logic as a kind of modal logic studies the reasoning of agents about fuzzy propositions; problems of such a synthesis caused by the invalidity of the axiom K are hinted at. Another direction is to found epistemic on fuzzy logic; the paper sketches the way how representing feasible knowledge as a fuzzy modality eliminated the logical omniscience paradox.
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