Related papers: Non-Deterministic Approximation Fixpoint Theory an…
Fine-tuning large language models (LLMs) often causes overfitting to specific prompt wording, where minor phrasing variations drastically reduce performance. To address this, we propose Prompt-Agnostic Fine-Tuning (PAFT), a method that…
Developing suitable formal semantics can be of great help in the understanding, design and implementation of a programming language, and act as a guide for software development tools like analyzers or partial evaluators. In this sense, full…
Answer-set programming (ASP) has emerged recently as a viable programming paradigm well attuned to search problems in AI, constraint satisfaction and combinatorics. Propositional logic is, arguably, the simplest ASP system with an intuitive…
Effective field theories (EFTs) are widely considered by physicists to be explanatory and to be the appropriate frameworks for modelling various phenomena at different scales. At the same time, they are known to be approximate, restricted,…
Density functional theory (DFT) serves as the basis for computational discovery in materials science and chemistry, yet each calculation demands extensive human effort: adjusting algorithms when convergence stalls, revising plans when…
A new analytical approximation function is proposed to accurately fit the solution of a fractional differential equation of order one-half, whose nonhomogeneous term is defined by a modified Bessel function of the first kind. The exact…
Attribution maps are popular tools for explaining neural networks predictions. By assigning an importance value to each input dimension that represents its impact towards the outcome, they give an intuitive explanation of the decision…
Answer Set Programming (ASP) is a well-established formalism for nonmonotonic reasoning. An ASP program can have no answer set due to cyclic default negation. In this case, it is not possible to draw any conclusion, even if this is not…
Powerful formalisms for abstract argumentation have been proposed, among them abstract dialectical frameworks (ADFs) that allow for a succinct and flexible specification of the relationship between arguments, and the GRAPPA framework which…
Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…
Answer Set Programming (ASP) is a purely declarative formalism developed in the field of logic programming and nonmonotonic reasoning: computational problems are encoded by logic programs whose answer sets, corresponding to solutions, are…
We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents…
We present a differentiation framework for plane-wave density-functional theory (DFT) that combines the strengths of forward-mode algorithmic differentiation (AD) and density-functional perturbation theory (DFPT). In the resulting AD-DFPT…
The thesis describes a logical formalization of natural-language database interfacing. We assume the existence of a ``natural language engine'' capable of mediating between surface linguistic string and their representations as ``literal''…
Axiomatic set theory is almost universally accepted as the basic theory which provides the foundations of mathematics, and in which the whole of present day mathematics can be developed. As such, it is the most natural framework for…
Default logic can be regarded as a mechanism to represent families of belief sets of a reasoning agent. As such, it is inherently second-order. In this paper, we study the problem of representability of a family of theories as the set of…
We look at characterizing which formulas are expressible in rich decidable logics such as guarded fixpoint logic, unary negation fixpoint logic, and guarded negation fixpoint logic. We consider semantic characterizations of definability, as…
Abstraction is a well-known approach to simplify a complex problem by over-approximating it with a deliberate loss of information. It was not considered so far in Answer Set Programming (ASP), a convenient tool for problem solving. We…
We describe a technique that can be used for the fusion of multiple sources of information as well as for the evaluation and selection of alternatives under multi-criteria. Three important properties contribute to the uniqueness of the…
This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness…