Related papers: IKP and Friends
We sample some Poincare-Birkhoff-Witt theorems appearing in mathematics. Along the way, we compare modern techniques used to establish such results, for example, the Composition-Diamond Lemma, Groebner basis theory, and the homological…
This course introduces the fruitful links between model theory and a combinatoric of sets given by independence relations. An independence relation on a set is a ternary relation between subsets. Chapter 1 should be considered as an…
We study dependence and independence concepts found in quantum physics, especially those related to hidden variables and non-locality, through the lens of team semantics and probabilistic team semantics, adapting a relational framework…
This report consists of two parts. The first part is a brief exposition of classical descriptive set theory. This part introduces some fundamental concepts, motivations and results from the classical theory and ends with a section on the…
The standard semantics of multi-agent epistemic logic S5 is based on Kripke models whose accessibility relations are reflexive, symmetric and transitive. This one dimensional structure contains implicit higher-dimensional information beyond…
The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebraic. The second leading idea is to provide a unified picture…
It is shown that separation conditions (separation curves) are fundamental objects of separability theory. They are used for the classification of certain clases of separable systems, for the proof of bi-Hamiltonian property and finally…
We introduce the notion of BMT independence, allowing us to take arbitrary mixtures of boolean, monotone, and tensor independence and generalizing the notion of BM independence of Wysoczanski. Pair-wise independence relations are encoded…
In fuzzy theory of sets and groups, the use of $\alpha$--levels is a standard to translate problems from the fuzzy to the crisp framework. Using strong $\alpha$--levels, it is possible to establish a one to one correspondence which makes…
We give labeled natural deduction systems for a family of tense logics extending the basic linear tense logic Kl. We prove that our systems are sound and complete with respect to the usual Kripke semantics, and that they possess a number of…
We develop a domain-theoretic framework for imprecise probability reasoning and inference on general topological spaces with a countably based continuous lattice of open sets. We address two distinct forms of uncertainty: partial or…
We establish, in the setting of equivariant motivic homotopy theory for a finite group, a version of tom Dieck's splitting theorem for the fixed points of a suspension spectrum. Along the way we establish structural results and…
This paper presents a novel possible worlds semantics, designed to elucidate the underpinnings of ultrafinitism. By constructing a careful modification of the well-known Kripke models for inuitionistic logic, we seek to extend our…
We present two logical systems based on dependent types that are comparable to ZFC, both in terms of simplicity and having natural set theoretic interpretations. Our perspective is that of a mathematician trained in classical logic, but…
The concepts of independence and totalness of subspaces are introduced in the context of quasi-probability distributions in phase space, for quantum systems with finite-dimensional Hilbert space. It is shown that due to the…
The Perfectly Transparent Equilibrium is algorithmically defined, for any game in normal form with perfect information and no ties, as the iterated deletion of non-individually-rational strategy profiles until at most one remains. In this…
We introduce the concepts of dependence and independence in a very general framework. We use a concept of rank to study dependence and independence. By means of the rank we identify (total) dependence with inability to create more…
For any ordinal \Lambda, we can define a polymodal logic GLP(\Lambda), with a modality [\xi] for each \xi<\Lambda. These represent provability predicates of increasing strength. Although GLP(\Lambda) has no Kripke models, Ignatiev showed…
A theorem is proved to verify incremental stability of a feedback system via a homotopy from a known incrementally stable system. A first corollary of that result is that incremental stability may be verified by separation of Scaled…
In this work we extend the Mackey's theory of induced unitary representations on a wide class of Krein-isometric induced representations in Krein spaces. The subgroup theorem and the Kronecker product theorem are shown to be valid for the…