Related papers: When Are Prime Formulae Characteristic?
A graph class $\mathscr{C}$ is called monadically stable if one cannot interpret, in first-order logic, arbitrary large linear orders in colored graphs from $\mathscr{C}$. We prove that the model checking problem for first-order logic is…
We derive a large deviation principle for families of random variables in the basin of attraction of spectrally positive stable distributions by proving a uniform version of the Tauberian theorem for Laplace-Stieltjes transforms. The main…
We prove that in a theory $T$ stable over a predicate $P$, for any $\lambda > |T|$, there is a $\lambda$-prime model over any complete set A with a $\lambda$-saturated $P$-part.
Given a machine learning (ML) model and a prediction, explanations can be defined as sets of features which are sufficient for the prediction. In some applications, and besides asking for an explanation, it is also critical to understand…
Algorithms for learning database queries from examples and unique characterisations of queries by examples are prominent starting points for developing automated support for query construction and explanation. We investigate how far recent…
Rule-based explanations provide simple reasons explaining the behavior of machine learning classifiers at given points in the feature space. Several recent methods (Anchors, LORE, etc.) purport to generate rule-based explanations for…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
This paper is about equality of proofs in which a binary predicate formalizing properties of equality occurs, besides conjunction and the constant true proposition. The properties of equality in question are those of a preordering relation,…
We present a logical framework for the verification of relational properties in imperative programs. Our work is motivated by relational properties which come from security applications and often require reasoning about formulas with…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
The boundary conditions of a non-trivial string background are classified. To this end we need traces on various spaces of conformal blocks, for which generalizations of the Verlinde formula are presented.
We propose a verified approach to the formal verification of timed properties using model-checking techniques. We focus on properties expressed using real-time specification patterns, which can be viewed as a subset of timed temporal logics…
Aspects of the theory of characteristic modes, based on their variational formulation, are presented and an explicit form of a related functional, involving only currents in a spatial domain, is derived. The new formulation leads to deeper…
Conditional logics play an important role in recent attempts to formulate theories of default reasoning. This paper investigates first-order conditional logic. We show that, as for first-order probabilistic logic, it is important not to…
First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies…
This paper explores the fine-grained structure of classes of regular languages maintainable in fragments of first-order logic within the dynamic descriptive complexity framework of Patnaik and Immerman. A result by Hesse states that the…
Conditional probabilities are a core concept in machine learning. For example, optimal prediction of a label $Y$ given an input $X$ corresponds to maximizing the conditional probability of $Y$ given $X$. A common approach to inference tasks…
We present results and examples which show that the consideration of a certain tubular mutation is advantageous in the study of noncommutative curves which parametrize the simple regular representations of a tame bimodule. We classify all…
A foundational question in the theory of linear compartmental models is how to assess whether a model is structurally identifiable -- that is, whether parameter values can be inferred from noiseless data -- directly from the combinatorics…
Lin and Zhaos theorem on loop formulas states that in the propositional case the stable model semantics of a logic program can be completely characterized by propositional loop formulas, but this result does not fully carry over to the…