Related papers: A General Framework for the Derivation of Regular …
We study the generalization abilities of language models when translating natural language into formal specifications with complex semantics. In particular, we fine-tune language models on three datasets consisting of English sentences and…
Given a causal graph representing the data-generating process shared across different domains/distributions, enforcing sufficient graph-implied conditional independencies can identify domain-general (non-spurious) feature representations.…
Derivative of a function can be expressed in terms of integration over a small neighborhood of the point of differentiation, so-called differentiation by integration method. In this text a maximal generalization of existing results which…
The unification algorithm has long been a target for program synthesis research, but a fully automatic derivation remains a research goal. In deductive program synthesis, computer programming is phrased as a task in theorem proving; a…
Domain generalization (DG) is about learning models that generalize well to new domains that are related to, but different from, the training domain(s). It is a fundamental problem in machine learning and has attracted much attention in…
Significant work has been done on learning regular expressions from a set of data values. Depending on the domain, this approach can be very successful. However, significant time is required to learn these expressions and the resulting…
The goal of this paper is to construct a multivariate generalisation of the Grunwald-Letnikov derivative, a classical fractional derivative operator. To do so, we first produce a formalism of fractional derivatives in terms of infinitesimal…
Narrowing is a procedure that was first studied in the context of equational E-unification and that has been used in a wide range of applications. The classic completeness result due to Hullot states that any term rewriting derivation…
This paper is devoted to the study of generalized differentiation properties of the infimal convolution. This class of functions covers a large spectrum of nonsmooth functions well known in the literature. The subdifferential formulas…
In this paper, we show that if the product $(D_1D_2, d_1d_2)$ of generalized derivations $(D_1, d_1)$ and $(D_2, d_2)$ on an algebra $A$ is a generalized derivation, then $d_1D_2$ and $d_2D_1$ map $A$ into $\hbox{rad}(A)$. Also, for…
We present a general framework for studying regularized estimators; such estimators are pervasive in estimation problems wherein "plug-in" type estimators are either ill-defined or ill-behaved. Within this framework, we derive, under…
Monadic decomposibility --- the ability to determine whether a formula in a given logical theory can be decomposed into a boolean combination of monadic formulas --- is a powerful tool for devising a decision procedure for a given logical…
An abstract argumentation framework is a commonly used formalism to provide a static representation of a dialogue. However, the order of enunciation of the arguments in an argumentative dialogue is very important and can affect the outcome…
This article revisits standard theorems from elementary number theory from a constructive, algorithmic, and proof-theoretic perspective, framed within the theory of computable functionals TCF. Key examples include B\'ezout's identity, the…
Each finite-dimensional algebra can be identified to the cubic matrix given by structural constants defining the multiplication between the basis elements of the algebra. In this paper we introduce the notion of flow (depending on time) of…
This paper extends the classical Ostrogradsky-Hermite reduction for rational functions to more general functions in primitive extensions of certain types. For an element $f$ in such an extension $K$, the extended reduction decomposes $f$ as…
Analogous to regular string and tree languages, regular languages of directed acyclic graphs (DAGs) are defined in the literature. Although called regular, those DAG-languages are more powerful and, consequently, standard problems have a…
As a supplement to my talk at the workshop, this extended abstract motivates and summarizes my work with co-authors on problems in two separate areas: first, in the lambda-calculus with letrec, a universal model of computation, and second,…
We generalize the concept of a number derivative, and examine one particular instance of a deformed number derivative for finite field elements. We find that the derivative is linear when the deformation is a Frobenius map and go on to…
Detection and elimination of redundant clauses from propositional formulas in Conjunctive Normal Form (CNF) is a fundamental problem with numerous application domains, including AI, and has been the subject of extensive research. Moreover,…