Related papers: Cheap Non-standard Analysis and Computability
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
Approximate Bayesian computation (ABC) is a popular likelihood-free inference method for models with intractable likelihood functions. As ABC methods usually rely on comparing summary statistics of observed and simulated data, the choice of…
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…
The paper gives a soundness and completeness proof for the implicative fragment of intuitionistic calculus with respect to the semantics of computability logic, which understands intuitionistic implication as interactive algorithmic…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
Can a deep neural network be approximated by a small decision tree based on simple features? This question and its variants are behind the growing demand for machine learning models that are *interpretable* by humans. In this work we study…
In this work we describe preferential Description Logics of typicality, a nonmonotonic extension of standard Description Logics by means of a typicality operator T allowing to extend a knowledge base with inclusions of the form T(C) v D,…
The Infinitesimal Calculus explores mainly two measurements: the instantaneous rates of change and the accumulation of quantities. This work shows that scientists, engineers, mathematicians, and teachers increasingly apply another change…
We introduce the notions of triviality and order-triviality for global invariant types in an arbitrary first-order theory and show that they are well behaved in the NIP context. We show that these two notions agree for invariant global…
We show that the field of complex numbers $\mathbb C$ contains non-zero infinitesimals by observing that $\mathbb C$ contains non-Archimedean subfields. Our observation is based on an old theorem in algebra due to E. Steinitz, discussed in…
Artificial Intelligence (AI) has become an integral part of domains such as security, finance, healthcare, medicine, and criminal justice. Explaining the decisions of AI systems in human terms is a key challenge--due to the high complexity…
Turing's famous 'machine' framework provides an intuitively clear conception of 'computing with real numbers'. A recursive counterexample to a theorem shows that the theorem does not hold when restricted to computable objects. These…
We mathematically analyze a simple market model where trading at each point in time involves only two agents with the sum of their money being conserved and with neither parties resulting with negative money after the interaction process.…
In computable analysis typically topological spaces with countable bases are considered. The Theorem of Kreitz-Weihrauch implies that the subbase representation of a second-countable $T_0$ space is admissible with respect to the topology…
We study the range of prices at which a rational agent should contemplate transacting a financial contract outside a given securities market. Trading is subject to nonproportional transaction costs and portfolio constraints and full…
A new unbiased Monte Carlo technique called Tensor Network Monte Carlo (TNMC) is introduced based on sampling all possible renormalizations (or course-grainings) of tensor networks, in this case matrix-product states. Tensor networks are a…
Interpretability is the study of explaining models in understandable terms to humans. At present, interpretability is divided into two paradigms: the intrinsic paradigm, which believes that only models designed to be explained can be…
By the sometimes so-called MAIN THEOREM of Recursive Analysis, every computable real function is necessarily continuous. Weihrauch and Zheng (TCS'2000), Brattka (MLQ'2005), and Ziegler (ToCS'2006) have considered different relaxed notions…
We introduce proper display calculi for basic monotonic modal logic,the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…
We propose a method for unsupervised opinion summarization that encodes sentences from customer reviews into a hierarchical discrete latent space, then identifies common opinions based on the frequency of their encodings. We are able to…