Bilattice based Logical Reasoning for Automated Visual Surveillance and other Applications

The primary objective of an automated visual surveillance system is to observe and understand human behavior and report unusual or potentially dangerous activities/events in a timely manner. Automatically understanding human behavior from visual input, however, is a challenging task. The research presented in this thesis focuses on designing a reasoning framework that can combine, in a principled manner, high level contextual information with low level image processing primitives to interpret visual information. The primary motivation for this work has been to design a reasoning framework that draws heavily upon human like reasoning and reasons explicitly about visual as well as non-visual information to solve classification problems. Humans are adept at performing inference under uncertainty by combining evidence from multiple, noisy and often contradictory sources. This thesis describes a logical reasoning approach in which logical rules encode high level knowledge about the world and logical facts serve as input to the system from real world observations. The reasoning framework supports encoding of multiple rules for the same proposition, representing multiple lines of reasoning and also supports encoding of rules that infer explicit negation and thereby potentially contradictory information. Uncertainties are associated with both the logical rules that guide reasoning as well as with the input facts. This framework has been applied to visual surveillance problems such as human activity recognition, identity maintenance, and human detection. Finally, we have also applied it to the problem of collaborative filtering to predict movie ratings by explicitly reasoning about users preferences

Some classes of planar lattices and interval-valued fuzzy sets

U radu je ispitan sledeći problem: Pod kojim uslovima se može rekonstruisati  (sintetisati) intervalno-vrednosni rasplinuti skup iz  poznate familije nivo skupova. U tu svrhu su proučena svojstva mreža intervala za svaki od četiri izabrana mrežna  uređenja: poredak po komponentama, neprecizni poredak (skupovna inkluzija), strogi  i leksikografski poredak.  Definisane su i-između i ili-između ravne mreže   i ispitana njihova svojstva potrebna za rešavanje postavljenog problema sinteze za intervalno-vrednosne rasplinute skupove. Za i-između ravne mreže je dokazano da su, u svom konačnom slučaju, slim mreže i dualno, da su ili-između ravne mreže dualno-slim mreže. Data je karakterizacija kompletnih konačno prostornih i dualno konačno prostornih mreža.  Određena je klasa mreža koje se mogu injektivno preslikati u direktan proizvod n  kompletnih lanaca tako da su očuvani supremumi i dualno, određena je klasa mreža koje se mogu injektivno preslikati u direktan proizvod n lanaca tako da su očuvani infimumi.  U rešavanju problema sinteze posmatrana su dva tipa nivo skupova - gornji i donji nivo skupovi. Potreban i dovoljan uslov za sintezu intervalno-vrednosnog rasplinutog skupa iz poznate familije nivo skupova određen je za mrežu intervala koja je uređena poretkom po komponentama, za oba tipa posmatranih nivo skupova. Za mrežu intervala uređenu nepreciznim poretkom, problem je rešen za donje nivo skupove, dok su za gornje nivo skupove određeni dovoljni uslovi. Za mrežu intervala koja je uređena leksikografskim poretkom, takođe su dati dovoljni uslovi i to za oba tipa nivo skupova.  Za mrežu intervala uređenu strogim poretkom problem nije rešavan, jer izlazi izvan okvira ovog rada. Dobijeni rezultati su primenjeni za rešavanje sličnog problema sinteze za intervalno-vrednosne intuicionističke rasplinute skupove  za mrežu intervala uređenu poretkom po komponentama.  Rezultati ovog istraživanja su od teorijskog značaja u teoriji mreža i teoriji rasplinutih skupova, ali postoji mogućnost za primenu u matematičkoj morfologiji i obradi slika.In this thesis  the following problem was investigated: Under which conditions an interval-valued fuzzy set can be reconstructed from the given family of cut sets. We consider interval-valued fuzzy sets as  a special type of lattice-valued fuzzy sets and  we studied properties of lattices of intervals using four different lattice  order: componentwise ordering, imprecision ordering (inclusion of sets), strong and lexicographical ordering. We proposed new definitions  of meet-between planar and join - between planar lattices, we investigated their properties and used them for solving problem of synthesis  in  interval-valued fuzzy sets. It has been proven that finite meet- between planar lattices and slim lattices are equivalent, and dually:    finite join-  between planar lattices and dually slim lattices are equivalent. Complete finitely  spatial lattices and complete dually finitely spatial lattices are fully characterized  in this setting. Next, we characterized  lattices which can be order embedded into a Cartesian product of  n  complete chains such that all suprema are preserved under the embedding. And dually, we characterized lattices which can be order embedded into a Cartesian product of n complete chains such that all infima are preserved under the embedding. We considered two types of cut sets – upper cuts and lower cuts. Solution of the  problem of synthesis of interval-valued fuzzy sets are given for lattices of intervals under componentwise ordering for both types of cut sets. Solution of problem of synthesis of  interval-valued fuzzy sets  are  given for lower cuts for lattices of intervals under imprecision ordering.  Sufficient conditions are given for lattices of intervals under imprecision ordering and family of upper cuts. Sufficient conditions are also given for lattices of intervals under lexicographical ordering. The problem of synthesis of interval-valued fuzzy sets for lattices of  intervals under strong ordering is beyond the scope of this thesis. A similar problem of synthesis of  interval-valued intuitionistic fuzzy sets is solved for lattices of intervals under componentwise ordering. These results are  mostly of theoretical importance in lattice theory and fuzzy sets theory, but also they could  be applied in mathematical morphology and in  image processing

Proceedings of the 11th Workshop on Nonmonotonic Reasoning

These are the proceedings of the 11th Nonmonotonic Reasoning Workshop. The aim of this series is to bring together active researchers in the broad area of nonmonotonic reasoning, including belief revision, reasoning about actions, planning, logic programming, argumentation, causality, probabilistic and possibilistic approaches to KR, and other related topics. As part of the program of the 11th workshop, we have assessed the status of the field and discussed issues such as: Significant recent achievements in the theory and automation of NMR; Critical short and long term goals for NMR; Emerging new research directions in NMR; Practical applications of NMR; Significance of NMR to knowledge representation and AI in general

Preference modeling by rectangular bilattices

Many realistic decision aid problems are fraught with facets of ambiguity, uncertainty and conflict, which hamper the effectiveness of conventional and fuzzy preference modeling approaches, and command the use of more expressive representations. In the past, some authors have already identified Ginsberg’s/Fitting’s theory of bilattices as a naturally attractive candidate framework for representing uncertain and potentially conflicting preferences, yet none of the existing approaches addresses the real expressive power of bilattices, which lies hidden in their associated truth and knowledge orders. As a consequence, these approaches have to incorporate additional conventions and ‘tricks’ into their modus operandi, making the results unintuitive and/or tedious. By contrast, the aim of this paper is to demonstrate the potential of (rectangular) bilattices in encoding not just the problem statement, but also its generic solution strategy