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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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Comparison of logical and psychological perspectives on the concept of number.
Kuncová, Alexandra ; Punčochář, Vít (advisor) ; Kůrka, Petr (referee)
This paper is divided into three main parts. In the first part, we propose a logical approach to the concept of number based on Frege's Foundations of Arithmetic. Besides the main attempt to define and classify number per se, we also discuss Husserl's struggle with psychologism, Frege's logicism, and the construction of the series of natural numbers. In the second part, we look at a psychological approach to the concept of number through theories and experiments of cogni- tive science. We focus on infants' understanding of numbers and amounts, their counting abilities and later conventional skills. In the third part, we summarise differences as well as similarities of these two approaches. Keywords: cognitive science, concept, Frege, Husserl, identity, logicism, num- ber, one-to-one correspondence, Piaget, psychologism. "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." (Albert Einstein, Geometry and Experience, 1921)
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