Related papers: On the problem of computing the well-founded seman…
Many learning algorithms are formulated in terms of finding model parameters which minimize a data-fitting loss function plus a regularizer. When the regularizer involves the l0 pseudo-norm, the resulting regularization path consists of a…
In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…
We provide a comprehensive elaboration of the theoretical foundations of variable instantiation, or grounding, in Answer Set Programming (ASP). Building on the semantics of ASP's modeling language, we introduce a formal characterization of…
Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…
It is a consequence of existing literature that least and greatest fixed-points of monotone polynomials on Heyting algebras-that is, the alge- braic models of the Intuitionistic Propositional Calculus-always exist, even when these algebras…
Refinement calculus provides a structured framework for the progressive and modular development of programs, ensuring their correctness throughout the refinement process. This paper introduces a refinement calculus tailored for quantum…
The paper presents two equivalent definitions of answer sets for logic programs with aggregates. These definitions build on the notion of unfolding of aggregates, and they are aimed at creating methodologies to translate logic programs with…
Recent advances in large language models (LLMs) have shown promise in formal theorem proving, yet evaluating semantic correctness remains challenging. Existing evaluations rely on indirect proxies such as lexical overlap with…
We study the parameterized complexity of algorithmic problems whose input is an integer set $A$ in terms of the doubling constant $C := |A + A|/|A|$, a fundamental measure of additive structure. We present evidence that this new…
To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…
Fine-tuning large pre-trained language models on various downstream tasks with whole parameters is prohibitively expensive. Hence, Parameter-efficient fine-tuning has attracted attention that only optimizes a few task-specific parameters…
Revision programming is a formalism to describe and enforce updates of belief sets and databases. That formalism was extended by Fitting who assigned annotations to revision atoms. Annotations provide a way to quantify the confidence…
Automated theorem proving, or more broadly automated reasoning, aims at using computer programs to automatically prove or disprove mathematical theorems and logical statements. It takes on an essential role across a vast array of…
Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…
We study the foundations of variational inference, which frames posterior inference as an optimisation problem, for probabilistic programming. The dominant approach for optimisation in practice is stochastic gradient descent. In particular,…
We describe an algorithm computing an optimal prefix free code for $n$ unsorted positive weights in time within $O(n(1+\lg \alpha))\subseteq O(n\lg n)$, where the alternation $\alpha\in[1..n-1]$ measures the amount of sorting required by…
Equilibrium logic is an approach to nonmonotonic reasoning that extends the stable-model and answer-set semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations…
We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
In this work, a functional variant of the polynomial analogue of the classical Gandy's fixed point theorem is obtained. Sufficient conditions have been found to ensure that the complexity of the recursive function does not go beyond the…