Related papers: A note on Jerabek's paper "A simplified lower boun…

We design a proof system for propositional classical logic that integrates two languages for Boolean functions: standard conjunction-disjunction-negation and binary decision trees. We give two reasons to do so. The first is…

Orthomodular logic is a weakening of quantum logic in the sense of Birkhoff and von Neumann. Orthomodular logic is shown to be a nonlinear noncommutative logic. Sequents are given a physically motivated semantics that is consistent with…

For a graph $G$, the parameter treedepth measures the minimum depth among all forests $F$, called elimination forests, such that $G$ is a subgraph of the ancestor-descendant closure of $F$. We introduce a logic, called neighborhood operator…

This paper studies axioms for nonmonotonic consequences from a semantics-based point of view, focusing on a class of mathematical structures for reasoning about partial information without a predefined syntax/logic. This structure is called…

Implicit arguments are not syntactically connected to their predicates, and are therefore hard to extract. Previous work has used models with large numbers of features, evaluated on very small datasets. We propose to train models for…

This paper is motivated by questions such as P vs. NP and other questions in Boolean complexity theory. We describe an approach to attacking such questions with cohomology, and we show that using Grothendieck topologies and other ideas from…

Let $(a_n)_{n \geq 1}$ be a sequence of distinct positive integers. In a recent paper Rudnick established asymptotic upper bounds for the minimal gaps of $\{a_n \alpha \bmod 1, 1 \leq n \leq N\}$ as $N \to \infty$, valid for Lebesgue-almost…

We examine the structure of the insertion-elimination Lie algebra on rooted trees introduced in \cite{CK}. It possesses a triangular structure $\g = \n_+ \oplus \mathbb{C}.d \oplus \n_-$, like the Heisenberg, Virasoro, and affine algebras.…

We provide a lower complexity bound for the satisfiability problem of a multi-agent justification logic, establishing that the general NEXP upper bound from our previous work is tight. We then use a simple modification of the corresponding…

We propose a nonlinear reduced basis method for the efficient approximation of parametrized partial differential equations (PDEs), exploiting kernel proper orthogonal decomposition (KPOD) for the generation of a reduced-order space and…

In this article we show how any formula A with a proof in minimal implicational logic that is super-polynomially sized has a polynomially-sized proof in classical implicational propositional logic . This fact provides an argument in favor…

We explore the problem of explaining observations in contexts involving statements with truth degrees such as `the lift is loaded', `the symptoms are severe', etc. To formalise these contexts, we consider infinitely-valued {\L}ukasiewicz…

We put forward a new method for obtaining quantitative lower bounds on the top Lyapunov exponent of stochastic differential equations (SDEs). Our method combines (i) an (apparently new) identity connecting the top Lyapunov exponent to a…

We analyse how the standard reductions between constraint satisfaction problems affect their proof complexity. We show that, for the most studied propositional, algebraic, and semi-algebraic proof systems, the classical constructions of…

Intuitionistic grammar logics fuse constructive and multi-modal reasoning while permitting the use of converse modalities, serving as a generalization of standard intuitionistic modal logics. In this paper, we provide definitions of these…

Dependency distance minimization (DDm) is a well-established principle of word order. It has been predicted theoretically that DDm implies compression, namely the minimization of word lengths. This is a second order prediction because it…

We prove near-optimal trade-offs for quantifier depth versus number of variables in first-order logic by exhibiting pairs of $n$-element structures that can be distinguished by a $k$-variable first-order sentence but where every such…

This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is…

Logic-based methods for explaining neural network decisions offer formal guarantees of correctness and non-redundancy, but they often suffer from high computational costs, especially for large networks. In this work, we improve the…

Different techniques have been used to prove several transference theorems of the form "nontrivial algorithms for a circuit class C yield circuit lower bounds against C". In this survey we revisit many of these results. We discuss how…