PhD Thesis

PhD Thesis

I was a PhD student at RISC Linz under the supervision of Professor Jochen Pfalzgraf.
In my PhD thesis I studied applications of fibered structures in computer science, more precisely to automated theorem proving in certain classes of finitely-valued logics, and to modeling interacting systems. The main topics of the thesis are the following:

  • Fibered structures in universal algebra
  • Sheaf representation theorems in universal algebra and applications
  • Priestley-type representations for distributive lattices with operators and applications to automated theorem proving in certain classes of finitely-valued logics.
  • A sheaf-theoretical approach to modeling interacting systems.

    • The first direction of work is concerned with finding decompositions of given structures in terms of simpler structures; the second with "putting together" (interconnecting) different structures and studying the properties of the result of this interconnection.

    For more details have a look at the abstract of my thesis. For further details please refer to the introduction of my thesis; for a summary of the results, check the conclusion. A gzipped postcript file of the last version of the thesis can be found at here ; for a hardcopy or questions feel free to mail me at sofronie@mpi-sb.mpg.de.

    Other activities at RISC-Linz

    During of my PhD study I was a member of the Working Group in Computational Category Theory. I also collaborated on several research projects: PARAGRAPH (1993 - 1994), MEDLAR II project (ESPRIT Basic Research Project 6471) (1994 - 1996), and a project on multi-agent systems sponsored by ProFactor Steyr, Austria (1996 - 1997). I also participate in the COST action 15 on many-valued logics. Besides this, I was a member of the organisation committee for AISMC-3, held in Steyr, Austria, September 23-25, 1996.

    Master thesis and specialization thesis

    I studied computer science at the Faculty of Mathematics (Department of Computer Science) of the University of Bucharest. The topic of my Master's thesis, which I finished in 1987, was the study of critical-pair/completion algorithms for automated theorem proving. I continued the study at the University Bucharest with a further specialization year in computer science and algebra. The study was concluded with a specialization thesis on modal logic. Both theses are written in Romanian; for the abstracts in English click here.