Logical foundations of mathematics and computer science
Main researcher
: ŠIKIĆ, ZVONIMIR (46613) Assistants
KIRIN, VLADIMIR (20974)
KRNIĆ, LUKA (23806)
ROSENZWEIG, DEAN (41536)
DEVIDE, VLADIMIR (9581)
HORVATIĆ-BALDASAR, KSENIJA (16123)
MATULIĆ-BEDENIĆ, IDA (29864)
GLAVAN, PAOLA (170363)
ČULINA, BORIS (187035)
Type of research: basic Duration from: 04/30/91. to 04/30/94. Papers on project (total): 23
Papers on project quoted in Current Contents: 6
Institution name: Fakultet strojarsva i brodogradnje, Zagreb (120) Department/Institute: Institute of mechanical construction Chair of mathematics and descriptive geometry Address: Dj. Salaja 5 City: 10000 - Zagreb, Croatia
Communication
E-mail: dean@srce.hr
Summary: Mathematical logic as foundation of mathematics and
computer science. Syntactical properties of fomulas as determinants of
their semantic properties. Axiomatization of arithmetics within the
framework of axiomatization of well-founded structures. Characterization of
multiplary logical consequence relations. Analysis of implementational
procedures by means of evolving algebras of Gurevich. Analysis of parallel
computational processes.
Keywords: evolving algebra, Warren's Abstract Machine, correctness of implementation, theory of concurrent processes, Chemical Abstract Machine, pi-calculus, well founded relation, transfinite induction, multiple consequence relation, overlap, dilution, cut, diagonal argument, computable function, Rice's theorem, inconsistent class, predicative tautology, terminal subformula
Research goals: Investigation of the formal logical structure of
arithmetics has, as direct goal, to embed Devide's axiomatization of
arithmetics into the more general framework of axiomatization of well
founded structures. Investigation of multiplary logical consequence
relation aims at a simpler derivation of Scott's characterization under
weaker condition. Investigation of algebraic operational semantics has as
goal to extend the methodology of evolving algebras of Gurevich to
implementation methods. For the case of Prolog a notion of WAM algebra will
be developed, and correctness will bre proved by establishing a
correspondence with Prolog algebras. One of general aims of the project is
introducing young researchers to the field of mathematical logic, in order
to master logical foundation of mathematics and computing science, so that
this important field develops also in Croatia. In particular directions of
research a contribution is expected in the form of 5-10 papers published in
international mathematical journals. Young researchers are expected to
specialize in the filed, what shoudl result in completion of their masters'
thesis.
COOPERATION - INSTITUTIONS
Name of institution
: Dipartimento di Informatica, Universita di
Pisa Type of institution: University/Faculty City: 51060 - Pisa, Italija
Name of institution
: Dept. Electrical Engineering and Computer
Science, University of Michigan Type of institution: University/Faculty City: MI - Ann Arbor, SAD Other information about the project.