Related papers: Decidability of All Minimal Models (Revised Versio…
The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory $T$ in which all partially recursive functions are representable, yet $T$…
Many counterexamples are known in the class of small theories due to Goncharov and Millar. The prime model of a decidable small theory is not necessarily decidable. The saturated model of a hereditarily decidable small theory is not…
Two types of explanations have been receiving increased attention in the literature when analyzing the decisions made by classifiers. The first type explains why a decision was made and is known as a sufficient reason for the decision, also…
Let $M$ be a finitely generated module over a ring $\Lambda$. With certain mild assumptions on $\Lambda$, it is proven that $M$ is a reflexive $\Lambda$-module, once $M \cong M^{**}$ as a $\Lambda$-module.
The ubiquity of machine learning based predictive models in modern society naturally leads people to ask how trustworthy those models are? In predictive modeling, it is quite common to induce a trade-off between accuracy and…
The Minimum Description Length (MDL) principle selects the model that has the shortest code for data plus model. We show that for a countable class of models, MDL predictions are close to the true distribution in a strong sense. The result…
Providing explanations along with predictions is crucial in some text processing tasks. Therefore, we propose a new self-interpretable model that performs output prediction and simultaneously provides an explanation in terms of the presence…
This paper presents a type theory with a form of equality reflection: provable equalities can be used to coerce the type of a term. Coercions and other annotations, including implicit arguments, are dropped during reduction of terms. We…
In this paper we consider propositional calculi, which are finitely axiomatizable extensions of intuitionistic implicational propositional calculus together with the rules of modus ponens and substitution. We give a proof of undecidability…
There have been controversies among statisticians on (i) what to model and (ii) how to make inferences from models with unobservables. One such controversy concerns the difference between estimation methods for the marginal means not…
This paper establishes fundamental results for statistical inference of diagnostic classification models (DCM). The results are developed at a high level of generality, applicable to essentially all diagnostic classification models. In…
Diekert, Matiyasevich and Muscholl proved that the existential first-order theory of a trace monoid over a finite alphabet is decidable. We extend this result to a natural class of trace monoids with infinitely many generators. As an…
We show that all--instances termination of chase is undecidable. More precisely, there is no algorithm deciding, for a given set $\cal T$ consisting of Tuple Generating Dependencies (a.k.a. Datalog$^\exists$ program), whether the $\cal…
Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…
The central result of this paper is the small-is-very-small principle for restricted sequential theories. The principle says roughly that whenever the given theory shows that a property has a small witness, i.e. a witness in every definable…
A typical kind of question in mathematical logic is that for the necessity of a certain axiom: Given a proof of some statement $\phi$ in some axiomatic system $T$, one looks for minimal subsystems of $T$ that allow deriving $\phi$. In…
Morrill and Valentin in the paper "Computational coverage of TLG: Nonlinearity" considered an extension of the Lambek calculus enriched by a so-called "exponential" modality. This modality behaves in the "relevant" style, that is, it allows…
Interpretable classification models are built with the purpose of providing a comprehensible description of the decision logic to an external oversight agent. When considered in isolation, a decision tree, a set of classification rules, or…
We investigate the use of an extension of rule-based modelling for cellular signalling to create a structured space of model variants. This enables the incremental development of rule sets that start from simple mechanisms and which, by a…
The dynamical behavior of non-uniform cellular automata is compared with the one of classical cellular automata. Several differences and similarities are pointed out by a series of examples. Decidability of basic properties like…