Related papers: Proof systems: from nestings to sequents and back
We extend to natural deduction the approach of Linear Nested Sequents and of 2-sequents. Formulas are decorated with a spatial coordinate, which allows a formulation of formal systems in the original spirit of natural deduction -- only one…
Display calculi are generalized sequent calculi which enjoy a `canonical' cut elimination strategy. That is, their cut elimination is uniformly obtained by verifying the assumptions of a meta-theorem, and is preserved by adding or removing…
A formal sequent system dealing with Menelaus' configurations is introduced in this paper. The axiomatic sequents of the system stem from 2-cycles of Delta-complexes. The Euclidean and projective interpretations of the sequents are defined…
We present a proof system for a multimodal logic, based on our previous work on a multimodal Martin-Loef type theory. The specification of modes, modalities, and implications between them is given as a mode theory, i.e. a small 2-category.…
A system of nested dichotomies is a method of decomposing a multi-class problem into a collection of binary problems. Such a system recursively splits the set of classes into two subsets, and trains a binary classifier to distinguish…
This paper is a brief and informal presentation of cirquent calculus, a novel proof system for resource-conscious logics. As such, it is a refinement of sequent calculus with mechanisms that allow to explicitly account for the possibility…
We propose a method for reasoning about trust in multi-agent systems, specifying a language for describing communication protocols and making trust assumptions and derivations. This is given an interpretation in a modal logic for describing…
We introduce neural networks for end-to-end differentiable proving of queries to knowledge bases by operating on dense vector representations of symbols. These neural networks are constructed recursively by taking inspiration from the…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…
A modular proof-theoretic framework was recently developed to prove Craig interpolation for normal modal logics based on generalizations of sequent calculi (e.g., nested sequents, hypersequents, and labelled sequents). In this paper, we…
When doing inference in ProbLog, a probabilistic extension of Prolog, we extend SLD resolution with some additional bookkeeping. This additional information is used to compute the probabilistic results for a probabilistic query. In Prolog's…
These Course Notes provide an introduction to mathematical proofs for undergraduate students transitioning from computational calculus to abstract mathematics. Topics include propositional logic, proof techniques, mathematical induction,…
We introduce cut-free nested sequent systems for a broad class of quantified modal logics (QMLs). The QMLs we consider are semantically defined using relational models that assign both an inner and outer domain to each world. This rich…
As language models (LMs) deliver increasing performance on a range of NLP tasks, probing classifiers have become an indispensable technique in the effort to better understand their inner workings. A typical setup involves (1) defining an…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
In this paper, we introduce the concept of a nested family of torsion pairs and will prove that this concept is strongly related to the existence of stratifying systems. Specifically, every stratifying system induces a nested family of…
A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…
We investigate multi-label classification involving large sets of labels, where the output labels may be known to satisfy some logical constraints. We look at an architecture in which classifiers for individual labels are fed into an…
The task of assigning label sequences to a set of observed sequences is common in computational linguistics. Several models for sequence labeling have been proposed over the last few years. Here, we focus on discriminative models for…
Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in…