Related papers: A Generalized Resolution Proof Schema and the Pige…

In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The…

Algorithmic recourse is a process that leverages counterfactual explanations, going beyond understanding why a system produced a given classification, to providing a user with actions they can take to change their predicted outcome.…

CPEG is an extended parsing expression grammar with regex-like capture annotation. Two annotations (capture and left-folding) allow a flexible construction of syntax trees from arbitrary parsing patterns. More importantly, CPEG is designed…

A rule for constructing interpolation nodes for $n$th degree polynomials on the simplex is presented. These nodes are simple to define recursively from families of 1D node sets, such as the Lobatto-Gauss-Legendre (LGL) nodes. The resulting…

As a generalization of Hermite interpolation problem, Birkhoff interpolation is an important subject in numerical approximation. This paper generalizes the existing Generalized Recursive Polynomial Interpolation Algorithm (GRPIA) that is…

We study normalising reduction strategies for infinitary Combinatory Reduction Systems (iCRSs). We prove that all fair, outermost-fair, and needed-fair strategies are normalising for orthogonal, fully-extended iCRSs. These facts properly…

In kernel-based approximation, the tuning of the so-called shape parameter is a fundamental step for achieving an accurate reconstruction. Recently, the popular Rippa's algorithm [14] has been extended to a more general cross validation…

Proof formats for SAT solvers have diversified over the last decade, enabling new features such as extended resolution-like capabilities, very general extension-free rules, inclusion of proof hints, and pseudo-boolean reasoning.…

The cut-elimination procedure for the provability logic is known to be problematic: a L\"ob-like rule keeps cut-formulae intact on reduction, even in the principal case, thereby complicating the proof of termination. In this paper, we…

Operating System (OS) fingerprinting is critical for network security, but conventional methods do not provide formal uncertainty quantification mechanisms. Conformal Prediction (CP) could be directly wrapped around existing methods to…

We propose a method for generating rule sets as global and local explanations for tree-ensemble learning methods using Answer Set Programming (ASP). To this end, we adopt a decompositional approach where the split structures of the base…

The Ideal Proof System (IPS) of Grochow & Pitassi (FOCS 2014, J. ACM, 2018) is an algebraic proof system that uses algebraic circuits to refute the solvability of unsatisfiable systems of polynomial equations. One potential drawback of IPS…

Sequential pattern mining under constraints is a challenging data mining task. Many efficient ad hoc methods have been developed for mining sequential patterns, but they are all suffering from a lack of genericity. Recent works have…

Large Language Models (LLMs) often struggle with maintaining coherent multi-step reasoning traces, particularly in tasks that require a structured logical flow. This work introduces a quantum-inspired approach to address the challenge by…

In recent years, the effort to formalize erotetic inferences---i.e., inferences to and from questions---has become a central concern for those working in erotetic logic. However, few have sought to formulate a proof theory for these…

Polynomial Pigeonhole Principle (PPP) is an important subclass of TFNP with profound connections to the complexity of the fundamental cryptographic primitives: collision-resistant hash functions and one-way permutations. In contrast to most…

This work, shows how propositional resolution can be generalized to obtain a resolution proof system for constrained pseudo-propositional logic (CPPL), which is an extension resulted from inserting the natural numbers with few constraints…

The infinite pigeonhole principle for 2-partitions ($\mathsf{RT}^1_2$) asserts the existence, for every set $A$, of an infinite subset of $A$ or of its complement. In this paper, we study the infinite pigeonhole principle from a…

Counterfactual Explanations (CEs) help address the question: How can the factors that influence the prediction of a predictive model be changed to achieve a more favorable outcome from a user's perspective? Thus, they bear the potential to…

This extended abstract introduces Self-Explaining Contrastive Evidence Re-Ranking (CER), a novel method that restructures retrieval around factual evidence by fine-tuning embeddings with contrastive learning and generating token-level…