MISANU

PROGRAM

Predavanja na Logičkom seminaru možete uživo pratiti preko linka
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Ukoliko želite i da učestvujete u diskusiji, to možete preko linka
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Neulogovani korisnici mogu pratiti prenos predavanja na ovom linku (ali ne mogu postavljati pitanja osim putem chata):
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Petak, 18.10.2024. u 14:15, Kneza Mihaila 36, sala 301f i Online
Stanislav Speranski, Steklov Mathematical Institute of RAS
CONCERNING DOŠEN'S LOGIC N AND SOME OF ITS EXTENSIONS
The idea of treating negation as a modality manifests itself in various logical systems, especially in Došen's propositional logic N, whose negation is weaker than that of Johansson's minimal logic. Among the interesting extensions of N are the propositional logics N* and Hype; the former was proposed by Cabalar, Odintsov and Pearce as a framework for studying foundations of well-founded semantics for logic programs with negation, while the latter has recently been advocated by Leitgeb as a basic system for dealing with hyperintensional contexts, but was first described by Moisil in 1942. We shall look at predicate versions of N and N*, and talk about a simple Routley-style semantics for Leitgeb's predicate version of Hype. The corresponding strong completeness results will be presented. Also, the disjunction property and the existential property will be discussed. In addition, we shall see what happens when we add the contraposition axiom to several important extensions of N.
Zajednički sastanak sa Odeljenjem za matematiku.

Ponedeljak, 21.10.2024. u 16:30, Kneza Mihaila 36, sala 301f i On-line
Stanislav Speranski, Steklov Mathematical Institute of RAS
QUANTIFYING OVER EVENTS IN PROBABILITY LOGIC: THE CASE OF ATOMLESS SPACES
We shall be concerned with the following result: all atomless probability spaces have the same ‘elementary’ theory; moreover, the corresponding theory — e.g., that of the Lebesgue measure on [0, 1] — is algorithmically decidable. Here the intended ‘elementary’ language, denoted by QPL, is two-sorted: it allows quantifying over events and over reals. The fragment of QPL that doesn't contain quantifiers over events may be viewed as a well-known ‘polynomial’ language of Fagin, Halpern and Megiddo. If time permits, we shall also discuss some more advanced results about QPL-theories, which can be obtained by using a related technique.
This talk is based on the article: An ‘elementary’ perspective on reasoning about probability spaces, Logic Journal of the IGPL, DOI. Preprint available at https://homepage.mi-ras.ru/~speranski/files/preprints/speranski-2024-igpl-a.pdf.

Utorak, 22.10.2024. u 16:30, Kneza Mihaila 36, sala 301f i On-line
Stanislav Speranski, Steklov Mathematical Institute of RAS
QUANTIFYING OVER EVENTS IN PROBABILITY LOGIC: THE CASE OF DISCRETE SPACES
Let QPL be the ‘elementary’ language of probability spaces [as in the previous talk] and QPL^e be its sublanguage obtained by excluding real-valued variables. Call a class of spaces ‘rich’ if it contains all infinite discrete spaces. We shall be concerned with the following result: for any rich class of spaces, its QPL^e-theory is at least as complex as complete second-order arithmetic — i.e., as the second-order theory of the natural numbers with addition and multiplication. Its original proof relied heavily on multiplication, and therefore on the polynomiality of the basic part. However, as we shall see, it remains true even if only linear combinations of a very special form are allowed. If time permits, some further applications of the underlying technique will also be discussed.
This talk is based on the article: Sharpening complexity results in quantified probability logic, Logic Journal of the IGPL, 2024, DOI. Preprint available at https://homepage.mi-ras.ru/~speranski/files/preprints/speranski-2024-igpl-b.pdf.

OBAVEŠTENJA:

Ukoliko zelite mesecne programe ovog Seminara u elektronskom obliku, obratite se: tane@mi.sanu.ac.rs. Programi svih seminara Matematickog instituta SANU nalaze se na sajtu: www.mi.sanu.ac.rs

Beograd,
Srdacan pozdrav,
Predrag Tanovic
rukovodilac seminara