Seminar for
Mathematical Logic
PROGRAM
Sastanci Seminara za matematicku logiku Matematickog instituta
SANU odrzavace se i u akademskoj 2005/2006. godini po pravilu petkom od
16:15 sati u sali 2 na I spratu zgrade SANU, Beograd, Kneza Mihaila 35.
PETAK, 03. mart 2006.G. U 16.15 SATI
PETAK, 10. mart 2006.G. U 16.15 SATI
PETAK, 17. mart 2006.G. U 16.15 SATI
PETAK, 24. mart 2006.G. U 16.15 SATI
Petak 31. mart 2006.G. U 16.15 SATI
U Beogradu, 01.03.2006.
Rukovodioci seminara:
Azurirani programi svih seminara Matematickog instituta SANU mogu se naci
na adresi www.mi.sanu.ac.yu.
Program Seminara za logiku za mart 2006
Zoran Pucanovic (Gradjevinski fakultet Univerziteta u Beogradu)
Pojam jednoznacne faktorizacije u nekomutativnim domenima
(Concept of unique factorization in non-commutative domains)
Rezime: Razliciti pristupi definisanju pojma UFD (Unique Factorization
Domain). Primeri faktorijalnih prstena kosih polinoma.
Dragan Doder(Masinski fakultet Univerziteta u Beogradu)
Mera u nestandardnoj analizi (Measure in non-standard analysis)
Ekspozitorno (pregledno) predavanje.
Petar Markovic (Departman za matematiku i informatiku Prirodno-matematickog
fakulteta Univerziteta u Novom Sadu)
A polynomial-time algorithm for the Constraint Satisfaction Problem (CSP)
In this talk we'll give some of the details of the result by J.
Berman, P. Idziak, R. McKenzie, M. Valeriote and the speaker. We
proved that algebras with few subpowers have a tractable (poly-time
solvable $CSP$ As the totality of the results proved is to broad to
report in the detail in one lecture, we will concentrate on teh
actual algorithm and assume the algebraic results that make it work
to be correct. In this way, we hope to give an approximation of the
techniques and desired lemmas that would have to be used in order to
obtain future results about the tractability ofr the $CSP$.
Dragan Masulovic (Departman za matematiku i informatiku
Prirodno-matematickog fakulteta Univerziteta u Novom Sadu)
Kategorijska logika za invarijante ra\v cunskih procesa
(A categorical logic for invariants of computations)
In this talk we apply techniques of categorical logic to provide a
formal system suitable for reasoning about invariant properties of
computations. We consider computations modeled by coalgebras for a
functor endowed with the structure of a monad and propose a concept
of (external) invariants of such coalgebras. We show that the
category of invariants is actually a bifibration and a logic
associated to this bifibration is complete. We then characterize
models of this logic, which correspond to properties of computations
expressible in the language of invariants. In some cases invariants
uniquely determine the coalgebra although this is generally not the
case. We then show that there is a category $J_T$ of coalgebras
isomorphic to the category $Set_T$ of all coalgebras and with a
property that coalgebras in $J_T$ are uniquely determined predicates
("yes/no" invariants). Intuitively, this means that by following a
simple discipline it is possible to ensure that for every
computation there is a distinguishing invariant.
Zoran Markovic (Matematicki institut SANU, Beograd)
Intuicionisticka implikacija i uslovna verovatnoca
(Intuitionistic Implication and Conditional Probability)
It will be demonstrated that, in the context of probabilistic logic,
intuitionistic implication corresponds to conditional probability.
In fact, in a Kripke model for probabilistic logic (based on
classical propositional calculus), we may introduce a natural
partial order and define intuitionistic implication. It turns out
that the probability that A intuitionistically implies B is
equal to 1 iff the probability of B, given A, is equal to 1.
Dr. Djordje Vukomanovic i Dr. Kosta Dosen.