SVIBOR - Project code: 1-01-090


Strossmayerov trg 4, HR - 10000 ZAGREB
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Project code: 1-01-090

Logical foundations of mathematics and computer science

Main researcher: ŠIKIĆ, ZVONIMIR (46613)

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

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.


  1. Name of institution: Dipartimento di Informatica, Universita di Pisa
    Type of institution: University/Faculty
    City: 51060 - Pisa, Italija

  2. Name of institution: Dept. Electrical Engineering and Computer Science, University of Michigan
    Type of institution: University/Faculty
    City: MI - Ann Arbor, SAD

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Last update: 04/11/94