相关论文: Definability of initial segments
Prototypical Learning is based on the idea that there is a point (which we call prototype) around which the embeddings of a class are clustered. It has shown promising results in scenarios with little labeled data or to design explainable…
Nearly all identifiability results in unsupervised representation learning inspired by, e.g., independent component analysis, factor analysis, and causal representation learning, rely on assumptions of additive independent noise or…
This expository paper treats the model theory of probability spaces using the framework of continuous $[0,1]$-valued first order logic. The metric structures discussed, which we call probability algebras, are obtained from probability…
Let $T$ be a (first order complete) dependent theory, ${\mathfrak{C}}$ a $\bar\kappa$-saturated model of $T$ and $G$ a definable subgroup which is abelian. Among subgroups of bounded index which are the union of $<\bar\kappa$ type definable…
We study the complexity of deciding the equality of infinite objects specified by systems of equations, and of infinite objects specified by lambda-terms. For equational specifications there are several natural notions of equality: equality…
We present a method to prove the decidability of provability in several well-known inference systems. This method generalizes both cut-elimination and the construction of an automaton recognizing the provable propositions.
We establish an assume-guarantee (AG) framework for compositional reasoning about multi-objective queries in parametric probabilistic automata (pPA) - an extension to probabilistic automata (PA), where transition probabilities are functions…
We consider the question of when sets definable in first-order expansions of groups contain the product of two infinite sets (we refer to this as the "productset property"). We first show that the productset property holds for any definable…
We review generalized additive models as a type of ``transparent'' model that has recently seen renewed interest in the deep learning community as neural additive models. We highlight multiple types of nonidentifiability in this model class…
Classification theory of elementary classes deals with first order (elementary) classes of structures (i.e. fixing a set T of first order sentences, we investigate the class of models of T with the elementary submodel notion). It tries to…
We start by presenting a theory of finite sets using the approach which is essentially that taken by Whitehead and Russell in Principia Mathematica}, and which does not involve the natural numbers (or any other infinite set). This theory is…
The condition of parameter identifiability is essential for the consistency of all estimators and is often challenging to prove. As a consequence, this condition is often assumed for simplicity although this may not be straightforward to…
Assumption-based Argumentation (ABA) is a well-established form of structured argumentation. ABA frameworks with an underlying atomic language are widely studied, but their applicability is limited by a representational restriction to…
We study the structure of the partial order induced by the definability relation on definitions of truth for the language of arithmetic. Formally, a definition of truth is any sentence $\alpha$ which extends a weak arithmetical theory…
Tennenbaum's theorem states that PA does not admit any nonstandard computable model. In 2022, Pakhomov proved that this theorem is fragile in regards to how PA is expressed, by constructing a theory that is definitionally equivalent to PA…
What does it mean to say that a quantity is identifiable from the data? Statisticians seem to agree on a definition in the context of parametric statistical models --- roughly, a parameter $\theta$ in a model $\mathcal{P} = \{P_\theta:…
The nonstandard approach to program semantics has successfully resolved the completeness problem of Floyd-Hoare logic. The known versions of nonstandard semantics, the Hungary semantics and axiomatic semantics, are so general that they are…
A general method for constructing essential uniform algebras with prescribed properties is presented. Using the method, the following examples are constructed: an essential, natural, regular uniform algebra on the closed unit disc; an…
This paper gives a generic form of the diamond lemma, which includes support for additive and topological structures of the base set, and which does not require any further structure (e.g. an associative multiplication operation) to be…
A pointwise definable model is one in which every object is definable without parameters. In a model of set theory, this property strengthens V=HOD, but is not first-order expressible. Nevertheless, if ZFC is consistent, then there are…