Seminar for Mathematical Logic


PROGRAM Program Seminara za logiku za mart 2006

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
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.

PETAK, 10. mart 2006.G. U 16.15 SATI
Dragan Doder(Masinski fakultet Univerziteta u Beogradu)
Mera u nestandardnoj analizi (Measure in non-standard analysis)

Ekspozitorno (pregledno) predavanje.

PETAK, 17. mart 2006.G. U 16.15 SATI
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 $CSP$.

PETAK, 24. mart 2006.G. U 16.15 SATI
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.

Petak 31. mart 2006.G. U 16.15 SATI
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.

U Beogradu, 01.03.2006.

Rukovodioci seminara:
Dr. Djordje Vukomanovic i Dr. Kosta Dosen.

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