DS199304: de Rijke, Maarten (1993) Extending Modal Logic. Doctoral thesis, University of Amsterdam.
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Abstract
This thesis is concerned with extensions of the standard modal language.
After the introduction in chapter 1, chapter 2 develops a general perspective
on modal logic according to which modal languages are primarily manysorted
descreption languages for relational structures, mainly concerned with the
finestructure of model theory. Moreover, the chapter presents a number of
central themes such as `expressivity', `combinations of modal logics',
`transfer of properties of modal logics to richer languages' and `connections
between modal logics'.
Chapters 3, 4 and 5 look into {\em specific} extended modal systems, e.g.
modal logics with a difference operator, a dynamic modal logic, and modal
systems that correspond to Peirce algebras. Some applications are sketched,
and the above themes are discussed for these systems. Furthermore, a method
for axiomatic completeness in systems with difference operators is presented
(chapter 3), and applied (chapters 4 and 5).
Chapters 6 and 7 are concerned with more {\em general themes} in extended
modal logic.
Chapter 6 develops the model theory of classes of basic modal logics with
the help of bisimulations. This results in general theorems about
definability and preservation. In addition, we give a characterization of
basic modal logic analogous to the wellknown Lindstr\"om theorem for
firstorder logic. Chapter 7 looks at extended modal formulas as classical
higherorder conditions on the underlying semantic structures. This chapter
formulates abstract and general algorithms that reduce higherorder
conditions corresponding to certain extended modal formulas to simpler
formulas.
Item Type:  Thesis (Doctoral) 

Report Nr:  DS199304 
Series Name:  ILLC Dissertation (DS) Series 
Year:  1993 
Subjects:  Language Logic 
Depositing User:  Dr Marco Vervoort 
Date Deposited:  14 Jun 2022 15:16 
Last Modified:  14 Jun 2022 15:16 
URI:  https://eprints.illc.uva.nl/id/eprint/1961 
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