Dissertation committee:
Δημητρακόπουλος Κωνσταντίνος Καθηγητής,(Επιβλέπων) Κούτρας Κωνσταντίνος Αναπληρωτής Καθηγητής, Ζάχος Ευστάθιος Καθηγητής, Κολέτσος Γεώργιος Καθηγητής
Summary:
The first chapter begins with a survey on the epistemic modal logics (EML) of
Lenzen and Stalnaker, continues with a presentation of the equivalent EML S4.2
and of the dominant definition of belief based on knowledge, and describes,
finally, the Kripke models of S4.2. In the second chapter, the KBp-structures
are being introduced in contrast to Stalnaker’s stable theories, it is proved
that negative introspection does not hold for them and that they are consistent
with S4.2. Next, characterization theorems of KBp-structures by S4.2 are
proved. In the third chapter, the bimodal logic KBE is defined, using a modal
language, which in addition to the operators K and B (representing knowledge
and belief, respectively) is endowed with an operator E, describing estimation.
Furthermore, weak ultrafilters are introduced, which are used for defining the
kbe-frames and models, which are Kripke-structures w.r.t. K, and modified
general Scott-Montague-structures w.r.t. E. Finally, there are proved some
characteristic properties of KBE and soundness / completeness of KBE w.r.t. the
kbe-frames. In the last chapter, it is attempted, using an EML, to capture the
epistemic change of an agent (i.e. what she knows / believes / estimates)
caused by new information received from different sources. So, the modal
language of KBE is expanded in order to contain two “copies” of its operators
(describing the situation before and after the information reception), and new
operators I, one for each information source. Then, the logic KBEI is defined
with the intention to describe this dynamic situation, and there are proved
some expected properties of it. Finally, the kbei-frames and models are
introduced, and soundness / completeness of KBEI w.r.t kbei-frames is proved.
Keywords:
Epistemic Modal Logic, Kripke Models, Negative Introspection, Stable Theories, Estimation
