Related papers: Open class determinacy is preserved by forcing
Continual learning is an emerging paradigm in machine learning, wherein a model is exposed in an online fashion to data from multiple different distributions (i.e. environments), and is expected to adapt to the distribution change.…
The superamalgamation property is a strong form of the amalgamation property which applies to ordered structures; it has found many applications in algebraic logic. We show that superamalgamation has some interest also from the pure…
Constructor rewriting systems are said to be cons-free if, roughly, constructor terms in the right-hand sides of rules are subterms of the left-hand sides; the computational intuition is that rules cannot build new data structures. In…
Identity teacher forcing (ITF) enables stable training of deterministic recurrent surrogates for chaotic dynamical systems and has been highly effective for dynamical systems reconstruction (DSR) with recurrent neural networks (RNNs),…
The world is structured in countless ways. It may be prudent to enforce corresponding structural properties to a learning algorithm's solution, such as incorporating prior beliefs, natural constraints, or causal structures. Doing so may…
The foundations of forcing theory are reworked to streamline the presentation and to show how the most basic results are applicable in very general contexts.
Let $\mathcal M=(M,<,...)$ be a linearly ordered first-order structure and $T$ its complete theory. We investigate conditions for $T$ that could guarantee that $\mathcal M$ is not much more complex than some colored orders (linear orders…
Early Exiting is one of the most popular methods to achieve efficient inference. Current early exiting methods adopt the (weighted) sum of the cross entropy loss of all internal classifiers during training, imposing all these classifiers to…
Forking is a central notion of model theory, generalizing linear independence in vector spaces and algebraic independence in fields. We develop the theory of forking in abstract, category-theoretic terms, for reasons both practical (we…
The \emph{Entscheidungsproblem}, or the classical decision problem, asks whether a given formula of first-order logic is satisfiable. In this work, we consider an extension of this problem to regular first-order \emph{theories}, i.e.,…
We show how to force, with finite conditions, the forcing axiom PFA(T), a relativization of PFA to proper forcing notions preserving a given Souslin tree T. The proof uses a Neeman style iteration with generalized side conditions consisting…
Assuming that there is no inner model with a strong cardinal, the following is shown: any subset of \omega_1 can be made \Delta^1_3 (in the codes) by a reasonable set-forcing; there is a reasonable set-generic extension with a \Delta^1_3…
We show that the common theory of all modules over a tubular algebra (over a recursive algebraically closed field) is decidable. This result supports a long standing conjecture of Mike Prest which says that a finite-dimensional algebra…
We present gradual type theory, a logic and type theory for call-by-name gradual typing. We define the central constructions of gradual typing (the dynamic type, type casts and type error) in a novel way, by universal properties relative to…
The stability-plasticity dilemma is a major challenge in continual learning, as it involves balancing the conflicting objectives of maintaining performance on previous tasks while learning new tasks. In this paper, we propose the…
What are the most general principles in set theory relating forceability and truth? As with Solovay's celebrated analysis of provability, both this question and its answer are naturally formulated with modal logic. We aim to do for…
Existential rules are an expressive knowledge representation language mainly developed to query data. In the literature, they are often supposed to be in some normal form that simplifies technical developments. For instance, a common…
We present decidability results for termination of classes of term rewriting systems modulo permutative theories. Termination and innermost termination modulo permutative theories are shown to be decidable for term rewrite systems (TRS)…
First-order applicative term rewriting systems provide a natural framework for modeling higher-order aspects. In earlier work we introduced an uncurrying transformation which is termination preserving and reflecting. In this paper we…
Supervised classification methods often assume that evaluation data is drawn from the same distribution as training data and that all classes are present for training. However, real-world classifiers must handle inputs that are far from the…