Related papers: Forking in NTP_2 theories
We give a criterion when a planar tree-like curve, i.e. a generic immersed plane curve each double point of which cuts it into two disjoint parts, can be send by a diffeomorphism of the plane onto a curve with no inflection points. We also…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
Consider the class of k-independent bond, respectively site, percolations with parameter p on an infinite tree T. We derive tight bounds on p for both a.s. percolation and a.s. nonpercolation. The bounds are continuous functions of k and…
We address an open question of Francis and Steel about phylogenetic networks and trees. They give a polynomial time algorithm to decide if a phylogenetic network, N, is tree-based and pose the problem: given a fixed tree T and network N, is…
We prove a general Ramsey theorem for trees with a successor operation. This theorem is a common generalization of the Carlson-Simpson Theorem and the Milliken Tree Theorem for regularly branching trees. Our theorem has a number of…
Field theory and gauge theory on noncommutative spaces have been established as their own areas of research in recent years. The hope prevails that a noncommutative gauge theory will deliver testable experimental predictions and will thus…
Typed feature structures are used extensively for the specification of linguistic information in many formalisms. The subsumption relation orders TFSs by their information content. We prove that subsumption of acyclic TFSs is well-founded,…
We introduce judgemental theories and their calculi as a general framework to present and study deductive systems. As an exemplification of their expressivity, we approach dependent type theory and natural deduction as special kinds of…
Many fruitful analogies have emerged between the theories of quantum entanglement and thermodynamics, motivating the pursuit of an axiomatic description of entanglement akin to the laws of thermodynamics. A long-standing open problem has…
A well-known result by Frick and Grohe shows that deciding FO logic on trees involves a parameter dependence that is a tower of exponentials. Though this lower bound is tight for Courcelle's theorem, it has been evaded by a series of recent…
In this paper, we show that \phi is a dependent formula if and only if all \phi-types have an extension to a \phi-isolated \phi-type that is an "elementary \phi-extension" (see Definition 2.3 in the paper). Moreover, we show that the domain…
This paper develops a version of dependent type theory in which isomorphism is handled through a direct generalization of the 1939 definitions of Bourbaki. More specifically we generalize the Bourbaki definition of structure from simple…
We give a definition of finitary type theories that subsumes many examples of dependent type theories, such as variants of Martin-L\"of type theory, simple type theories, first-order and higher-order logics, and homotopy type theory. We…
We demonstrate that a tree-based theory for various dynamical processes yields extremely accurate results for several networks with high levels of clustering. We find that such a theory works well as long as the mean intervertex distance…
In this paper, we propose an abstract definition of dependent type theories as essentially algebraic theories. One of the main advantages of this definition is its composability: simple theories can be combined into more complex ones, and…
A dichotomy result of Sevenster (2014) completely classified the quantifier prefixes of regular Independence-Friendly (IF) logic according to the patterns of quantifier dependence they contain. On one hand, prefixes that contain "Henkin" or…
We give definitions of the properties OP, IP, $k$-TP, TP$_1$, $k$-TP$_2$, SOP$_1$, SOP$_2$ and SOP$_3$ in positive logic, and prove various implications and equivalences between them. We also provide a characterisation of stability in…
Exchangeability is a central notion in statistics and probability theory. The assumption that an infinite sequence of data points is exchangeable is at the core of Bayesian statistics. However, finite exchangeability as a statistical…
Two results are presented concerning the entailment problem in Separation Logic with inductively defined predicate symbols and theory reasoning. First, we show that the entailment problem is undecidable for rules with bounded tree-width, if…
We show that, for any graph or matroid, there is a tree that simultaneously distinguishes its maximal tangles, and, for each maximal tangle $\mathcal{T}$ that satisfies an additional robustness condition, displays all of the non-trivial…