- Type of paper
: Book
Title: Philosophy of Mathematics
- Authors:
- Šikić, Zvonimir (46613)
Publisher: školska knjiga
ISBN: 9530204202
Year: 1995
Number of pages: 81
- Type of paper
: Paper in book
Title: From Prolog Algebras Towards WAM - A Mathematical Study of
Implementation
- Authors:
- Boerger, Egon
- Rosenzweig, Dean (41536)
- Editors
- Boerger, Egon
- Kleine Buening, Hans
- Richter, Manfred
- Schoenfeld, Wilhelm
Publisher: Springer-Verlag
ISBN: 3-540-54487-9
Year: 1991
Pages: from 31 to 66
Number of references: 16
Language: engleski
Summary: This is the first part of a work presenting a natural
andtransparent albeit entirely mathematical description of Warren's
1983 abstract machine for executing Prolog. We derive thedescription from
Boerger's 1990 phenomenological description ofthe language, refining Prolog
algebras stepwise, provingconservation of correctness at each step.
Keywords: Prolog, Warren Abstract Machine, dynamic algebra, correctness proof, implementation, stepwise refinement
- Type of paper
: Paper in book
Title: WAM Algebras - A Mathematical Study of Implementation,
Part 2
- Authors:
- Boerger, Egon
- Rosenzweig, Dean (41536)
- Editors
- Voronkov, Andrei
Publisher: Springer-Verlag
ISBN: 3-540-55460-2
Year: 1992
Pages: from 35 to 54
Number of references: 7
Language: engleski
Summary: In direct sequel to ŠBoerger,Rosenzweig 91Ć term
representingalgebras are introduced,providing an evolving algebra account
ofWAM representation of terms and their unification. Prologalgebras of the
preceeding paper are adapted to termrepresentation, yielding, upon
optimization, a mathematicalreconstruction of the full WAM, and a proof of
its correctnesswrt to abstract Prolog algebras, given that the
compilersatisfies a set of (explicitly stated) sufficient conditions.
Keywords: Prolog, Warren Abstract Machine, correctness proof, evolving algebra, compiler correctness, term representation, unification
- Type of paper
: Paper in book
Title: The Mathematics of Set Predicates in Prolog
- Authors:
- Boerger, Egon
- Rosenzweig, Dean (41536)
- Editors
- Gottlob, Georg
- Leitsch, Alexander
- Mundici, Daniele
Publisher: Springer-Verlag
ISBN: 3-540-57184-1
Year: 1993
Pages: from 1 to 13
Number of references: 12
Language: engleski
Summary: We provide a logical specification of set predicates
findall andbagof of Prolog. The specification is given in proof
theoreticterms, and pertains to any SLD-resolution based language. Theorder
dependent aspects, relevant for languages embodying asequential proof
search strategy (possibly with side effects),can be added in an orthogonal
way. The specification also allowsus to prove that bagof cannot be defined
by SLD-resolution alone.We show the correctness, wrt our specification, of
Demoen'sdefinition of bagof for Prolog in Prolog. The specification ofbagof
allows us to throw some light on the logical problems withsetof.
Keywords: logical specification, set predicates, Prolog, findall, setof, bagof, SLD-resolution
Other: pozvano predavanje prvog autora na Third Kurt Goedel
Colloquium
- Type of paper
: Paper in book
Title: Communicating Evolving Algebras
- Authors:
- Glavan, Paola (170363)
- Rosenzweig, Dean (41536)
- Editors
- Boerger, Egon
- Martini, Simone
- Jaeger, Georg
- Kleine Buening, Hans
- Richter, Manfred
Publisher: Springer-Verlag
Year: 1993
Pages: from 186 to 215
Language: engleski
Summary: We develop the first steps of a theory of concurrency
within theframework of evolving algebras of Gurevich. As a basic tool
weintroduce a žmodal' logic of transition rules and runs, which is,in the
context of evolving algebras, just a definitionalextension of ordinary
first order logic. A notion of independenceof rules and runs enables us to
introduce a notion of (andnotation for) concurrent runs. The power of the
framework isdemonstrated by developing simple and transparent
evolvingalgebra models for the Chemica Abstract Machine of Berry andBoudol
and for the pi-calculus of Milner.
Keywords: evolving algebras, concurrency theory, independence, concurrent run, modal logic of rules and runs, chemical abstract machine, pi-calculus
- Type of paper
: Paper in book
Title:
- Authors:
- Boerger, Egon
- Rosenzweig, Dean (41536)
Publisher: North-Holland
ISBN: 0444820922
Year: 1995
Pages: from 21 to 90
Number of references: 19
Language: engleski
- Type of paper
: Paper in book
Title:
- Authors:
- Glavan, Paola (170363)
- Rosenzweig, Dean (41536)
- Editors
- Pehrson, Bjorn
- Simon, Imre
Publisher: North-Holland
ISBN: 0444819894
Year: 1994
Pages: from 416 to 422
Language: engleski
- Type of paper
: Paper in book
Title:
- Authors:
- Boerger, Egon
- Rosenzweig, Dean (41536)
- Gurevich, Yuri
- Editors
- Boerger, Egon
ISBN: 0198538545
Year: 1995
Pages: from 231 to 244
Language: engleski
- Type of paper
: Paper in journal
Title: A proof of the characterization theorem for consequence
relations
- Authors:
- Šikić, Zvonimir (46613)
Journal: Zeitschrifft fuer mathematische Logik und Grundlagen der
Mathematik
Number: 1
ISSN: 0044-3050
Volume: 37
Year: 1991
Pages: from 41 to 43
Number of references: 2
Language: engleski
Summary: Scott's characterization theorem for compact
consequencerelations is extended to general consequence relation
byShoesmith and Smiley, who proved that general consequencerelation is
characterized by Overlap, Dilution and Cut for sets.We prove that general
consequence relation is characterized bysimpler requirements: Overlap for
L, Dilution for L and Cut forsets for L.
Keywords: consequence relation, multiple consequence relation, Overlap, Dilution, Cut for sets, Overlap for L, Dilution for L, Cut for sets for L
- Type of paper
: Paper in journal
Title: On Devide's axiomatization of natural numbers
- Authors:
- Šikić, Zvonimir (46613)
Journal: Grazer Mathematische Berichte
Volume: 313
Year: 1991
Pages: from 57 to 64
Number of references: 6
Language: engleski
Summary: Devide proposed the simplest axiomatization of natural
numberswith the axioms S0 and D. We prove that axiom D is equivalent tothe
axiom of transfinite induction, i.e. it is equivalent to thestatement that
the successor function, viewed as a binaryrelation on N, is well founded.
It is also proved that immediatesuccessor axiomatization is based on
functionality, whereasgeneral successor axiomatization is based on
comparability.
Keywords: axiomatization of natural numbers, well founded relation, well-foundedness principle, transfinite induction, functionality axiom, comparability axiom
- Type of paper
: Paper in journal
Title: The diagonal argument - a study of cases
- Authors:
- Šikić, Zvonimir (46613)
Journal: International Studies in the Philosophy of Science
Volume: 6
Year: 1992
Pages: from 191 to 203
Number of references: 17
Language: engleski
Summary: The diagonal argument plays a prominent role in set theory
andlogicist account of mathematics, as well as in provingundecidability
results in computability theory and incompletenessresults in logic and
metamathematics. The simplicity and thecontinuity of inteconnections
between the areas is revealed bysimple and continuous transformations of
the diagonal argumentthrough all the areas. A very short and conceptually
simpleproof of Rice's theorem is given.
Keywords: diagonal argument, transfinite, increasible infinity, absolute infinity, Rice's theorem, computable function, halting problem, Russel's paradox, inconsistent class, truth predicate, provability predicate, undefinability of truth, incompleteness theorem
- Type of paper
: Paper in journal
Title: On predicative tautologies
- Authors:
- Kirin, Vladimir (20974)
Journal: Grazer Mathematische Berichte
Volume: 313
Year: 1991
Pages: from 19 to 28
Number of references: 2
Language: engleski
Summary: Whenever some formula of a given first order language is
apredicative tautology, at least one of its terminal subfomulasnecessarily
begins with a quantifier or is of the form =(tt).Therefore quantifiers
constitute essential parts of suchfomrulas.
Keywords: quantifier, formula, first order language, terminal subformula, predicative tautology
- Type of paper
: Paper in journal
Title: On 2-(85.28.98) design
- Authors:
- Horvatić-Baldasar, Ksenija (16123)
- Matulić-Bedenić, Ida (29864)
Journal: Punime matematike
Number: 4
Year: 1991
Pages: from 56 to 60
Number of references: 1
Language: engleski
Summary: In this paper we are proving the following
Theorem. There does not exist a symmetrical block design2-(85.28.9) on
which operates the automorphism group Z14 = Z7xZ2
Keywords: block design, automorphism group
- Type of paper
: Paper in journal
Title: The classification of projective planes of order 13 which
possess an involution
- Authors:
- Matulić-Bedenić, Ida (29864)
Journal: Rad HAZU
Number: 456
ISSN: 0351-8639
Volume: 10
Year: 1991
Pages: from 9 to 13
Number of references: 2
Language: engleski
Summary: In this paper is proved the following
Theorem. If a projective plane of order n=13 possesses aninvolutory
collineation, then it is isomorphic to theDesarguesian plane.
Keywords: Semi-biplane, collineation, Desarguesian plane
- Type of paper
: Paper in journal
Title: On a distinction between pure and applied mathematics
- Authors:
- Šikić, Zvonimir (46613)
Journal: Encyclopaedia Moderna
Number: 1
ISSN: 0013-7138
Volume: 13
Year: 1992
Pages: from 74 to 78
Language: engleski
- Type of paper
: Paper in journal
Title:
- Authors:
- Šikić, Zvonimir (46613)
Journal: Grazer Mathematische Berichte
Number: 323
Year: 1994
Pages: from 69 to 78
Language: engleski
- Type of paper
: Paper in journal
Title:
- Authors:
- Horvatić-Baldasar, Ksenija (16123)
- Matulić-Bedenić, Ida (29864)
Journal: Rad HAZU
Number: 12
ISSN: 0351-8639
Volume: 470
Year: 1995
Pages: from 7 to 12
Language: engleski
- Type of paper
: M.A.
Title: Semantic analysis of concurrent logic programming
languages
Faculty: Prirodoslovno matemati;ki fakultet, Matemati;ki odjel Svau;iliŠte u Zagrebu
Date of defense: 01/25/93
Number of pages: 72
Summary: The fomralism of evolving algebras of Gurevich is
preciselydescribed, and the modal logic of rules and sequential runs
isdeveloped. The notion of independence enables a theory ofconcurrency to
be developed within the framework of evolvingalgebras. The modal logic is
extended to concurrent runs. Theresults obtained are a proper
generalization of the existingconcrete studies (of Occam, Parlog and
Concurrent Prolog), andare intended as a foundation for a general theory of
concurrencywithin the framework of evolving algebras.
Keywords: evolving algebra, independence, concurrent run, modal logic of rules and runs
- Type of paper
: M.A.
Title: Models of the lambda-calculus
Faculty: Prirodoslovno matemati;ki fakultet, Matemati;ki odjel Svau;iliŠte u Zagrebu
Date of defense: 04/26/93
Language: hrvatski
Number of pages: 117
Summary: Lambda-calculus is defined together with some properties
neededfor analysis of the models. Some properties of complete partialorders
are given. The notion of reduction of terms is analysedand results applied
to beta-reduction. Boehm trees are defined,and topology is introduced on
them. The general notion of alambda-model is defined. The categorical
approach to the notionof lambda-model is described. The following models
areconstructed and described: Engeler's, Plotkin's, Scott's and
theBoehm-tree model. Local and global structure of models isanalysed.
Keywords: lambda calculus, lambda calculus model, Boehm tree, lambda-model
- Type of paper
: Mentorship
Title: Semantic analysis of concurrent logic programming
languages
Faculty: Prirodoslovno matemati;ki fakultet, Matemati;ki odjel Svau;iliŠte u Zagrebu
Number of pages: 72
Author: Glavan mr. Paola
Degree level: M.A.
- Type of paper
: Mentorship
Title: Models of the lambda-calculus
Faculty: Prirodoslovno matemati;ki fakultet, Matemati;ki odjel Svau;iliŠte u Zagrebu
Date of defense: 04/26/93
Number of pages: 117
Author: Urbiha mr Igor
Degree level: M.A.
