Related papers: Uniform Lyndon interpolation for intuitionistic mo…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
Spline interpolation has been used in several applications due to its favorable properties regarding smoothness and accuracy of the interpolant. However, when there exists a discontinuity or a steep gradient in the data, some artifacts can…
In this paper, we study a new Kripke-style semantics for classical modal logic, named as provability models. We study provability models for the propositional modal logics K, K4, S4 GL, GLP and the interpretability logic ILM. Provability…
Data-driven generation of molecules with desired properties, also known as inverse molecular design (IMD), has attracted significant attention in recent years. Despite the significant progress in the accuracy and diversity of solutions,…
This chapter surveys some of the main results on interpolation in several of the most prominent families of non-classical logics. Special attention is given to the distinction between the two most commonly studied variants of…
The versatility of data-driven approximation by interpolatory methods, originally settled for model approximation purpose, is illustrated in the context of linear controller design and stability analysis of irrational models. To this aim,…
The minimum-norm interpolator (MNI) framework has recently attracted considerable attention as a tool for understanding generalization in overparameterized models, such as neural networks. In this work, we study the MNI under a $2$-uniform…
This paper develops stable canonical rules for intuitionistic modal logics, which were first introduced for superintuitionistic logics and transitive nor mal modal logics in [1] and [2] respectively. We first prove that every in…
Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, significantly relaxing…
Invariant inference algorithms such as interpolation-based inference and IC3/PDR show that it is feasible, in practice, to find inductive invariants for many interesting systems, but non-trivial upper bounds on the computational complexity…
Strict anonymity of model responses is a key for the reliability of voting-based leaderboards, such as LM Arena. While prior studies have attempted to compromise this assumption using simple statistical features like TF-IDF or bag-ofwords,…
The interpretability logic of a mathematical theory describes the structural behavior of interpretations over that theory. Different theories have different logics. This paper from 2011 revolves around the question what logic describes the…
We study the system IFP of intuitionistic fixed point logic, an extension of intuitionistic first-order logic by strictly positive inductive and coinductive definitions. We define a realizability interpretation of IFP and use it to extract…
Open bisimilarity is defined for open process terms in which free variables may appear. The insight is, in order to characterise open bisimilarity, we move to the setting of intuitionistic modal logics. The intuitionistic modal logic…
Universal machine learned interatomic potentials (uMLIPs) embody a growing area of interest due to their transferability across the periodic table, displaying an error of about 0.6 kcal/mol against the Matbench Discovery test set. However,…
We devise three strategies for recognizing admissibility of non-standard inference rules via interpolation, uniform interpolation, and model completions. We apply our machinery to the case of symmetric implication calculus $\mathsf{S^2IC}$,…
The ability to accurately model interatomic interactions in large-scale systems is fundamental to understanding a wide range of physical and chemical phenomena, from drug-protein binding to the behavior of next-generation materials. While…
Ludics is peculiar in the panorama of game semantics: we first have the definition of interaction-composition and then we have semantical types, as a set of strategies which "behave well" and react in the same way to a set of tests. The…
This paper introduces a natural deduction calculus for intuitionistic logic of belief $\mathsf{IEL}^{-}$ which is easily turned into a modal $\lambda$-calculus giving a computational semantics for deductions in $\mathsf{IEL}^{-}$. By using…
Propositional term modal logic is interpreted over Kripke structures with unboundedly many accessibility relations and hence the syntax admits variables indexing modalities and quantification over them. This logic is undecidable, and we…