Related papers: Class-Forcing in Class Theory
For any first order theory T we construct a Boolean valued model M, in which precisely the T--provable formulas hold, and in which every (Boolean valued) subset which is invariant under all automorphisms of M is definable by a first order…
Manna and Waldinger's theory of substitutions and unification has been verified using the Cambridge LCF theorem prover. A proof of the monotonicity of substitution is presented in detail, as an example of interaction with LCF. Translating…
Using a variation of Woodin's $\mathbb{P}_{\mathrm{max}}$ forcing, we force over a model of the Axiom of Determinacy to produce a model of ZFC containing a very strongly increasing sequence of length $\omega_{2}$ consisting of functions…
Scientific theories of consciousness should be falsifiable and non-trivial. Recent research has given us formal tools to analyze these requirements of falsifiability and non-triviality for theories of consciousness. Surprisingly, many…
In contrast to conventional (single-label) classification, the setting of multilabel classification (MLC) allows an instance to belong to several classes simultaneously. Thus, instead of selecting a single class label, predictions take the…
Most model-free reinforcement learning methods leverage state representations (embeddings) for generalization, but either ignore structure in the space of actions or assume the structure is provided a priori. We show how a policy can be…
In this paper, without the axiom of choice, we show that if a certain downward L\"owenheim-Skolem property holds then all grounds are uniformly definable. We also prove that the axiom of choice is forceable if and only if the universe is a…
In Ben-David et al.'s "Learnability Can Be Undecidable," they prove an independence result in theoretical machine learning. In particular, they define a new type of learnability, called Estimating The Maximum (EMX) learnability. They argue…
A complementary label (CL) simply indicates an incorrect class of an example, but learning with CLs results in multi-class classifiers that can predict the correct class. Unfortunately, the problem setting only allows a single CL for each…
Complex classifiers may exhibit "embarassing" failures in cases where humans can easily provide a justified classification. Avoiding such failures is obviously of key importance. In this work, we focus on one such setting, where a label is…
In this paper we look at popular fairness methods that use causal counterfactuals. These methods capture the intuitive notion that a prediction is fair if it coincides with the prediction that would have been made if someone's race, gender…
In this paper, we confront the problem of applying reinforcement learning to agents that perceive the environment through many sensors and that can perform parallel actions using many actuators as is the case in complex autonomous robots.…
We introduce an iteration of forcing notions satisfying the countable chain condition with minimal damage to a strong coloring. Applying this method, we prove that Martin's axiom is strictly stronger than its restriction to forcing notions…
We prove two general results about the preservation of extendible and $C^{(n)}$-extendible cardinals under a wide class of forcing iterations (Theorems 5.4 and 7.5). As applications we give new proofs of the preservation of Vop\v{e}nka's…
It is well known that the completeness theorem for $\mathrm{L}_{\omega_1\omega}$ fails with respect to Tarski semantics. Mansfield showed that it holds for $\mathrm{L}_{\infty\infty}$ if one replaces Tarski semantics with boolean valued…
Fairness-aware classification is receiving increasing attention in the machine learning fields. Recently research proposes to formulate the fairness-aware classification as constrained optimization problems. However, several limitations…
I prove preservation theorems for countable support iteration of proper forcing concerning certain classes of capacities and submeasures. New examples of forcing notions and connections with measure theory are included.
Scientific reasoning rarely stops at what is directly observable; it often requires uncovering hidden structure from data. From estimating reaction constants in chemistry to inferring demand elasticities in economics, this latent structure…
The sequential form of a statement $\forall\xi(B(\xi) \rightarrow \exists\zeta A(\xi,\zeta))$ is the statement $\forall\xi(\forall n B(\xi_n) \rightarrow \exists\zeta \forall n A(\xi_n,\zeta_n))$. There are many classically true statements…
We prove that if Q is a nw-nep forcing then it cannot add a dominating real. We also prove that Amoeba forcing cannot be P(X)/I if I is an aleph_1-complete ideal.