Related papers: Proof nets for the Displacement calculus
Proofs are traditionally syntactic, inductively generated objects. This paper reformulates first-order logic (predicate calculus) with proofs which are graph-theoretic rather than syntactic. It defines a combinatorial proof of a formula…
This paper provides numerical results that demonstrate the validity of the nonclassical diffusion approximation to the nonclassical transport equation in certain 1-D diffusive systems. This result provides a more solid foundation in which…
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,…
Consider a particle whose position evolves along the edges of a network. One definition for the displacement of a particle is the length of the shortest path on the network between the current and initial positions of the particle. Such a…
Multiplicative linear logic is a very well studied formal system, and most such studies are concerned with the one-sided sequent calculus. In this paper we look in detail at existing translations between a deep inference system and the…
We study the correspondence between Bayesian Networks and graphical representation of proofs in linear logic. The goal of this paper is threefold: to develop a proof-theoretical account of Bayesian inference (in the spirit of the…
Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the top-level logical symbol of that formula. We…
We present a novel logic-based concept called Space Explanations for classifying neural networks that gives provable guarantees of the behavior of the network in continuous areas of the input feature space. To automatically generate space…
We discuss a practical method for assessing mathematical proof online. We examine the use of faded worked examples and reading comprehension questions to understand proof. By breaking down a given proof, we formulate a checklist that can be…
The textbook proofs of Commoner's theorem characterizing liveness in free-choice Petri nets are given in contexts of technical notions and claims that make the proofs look a bit long. The aim of this note is to give a concise self-contained…
A cyclic proof system allows us to perform inductive reasoning without explicit inductions. We propose a cyclic proof system for HFLN, which is a higher-order predicate logic with natural numbers and alternating fixed-points. Ours is the…
We extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima facie "non-computational" proofs from probability theory,…
The connection method has earned good reputation in the area of automated theorem proving, due to its simplicity, efficiency and rational use of memory. This method has been applied recently in automatic provers that reason over ontologies…
The origins of proof-theoretic semantics lie in the question of what constitutes the meaning of the logical connectives and its response: the rules of inference that govern the use of the connective. However, what if we go a step further…
The displacement and deviation vectors in spaces (manifolds), the tangent bundle of which is endowed with a transport along paths, are introduced. In case these spaces are equipped with a linear connection, the deviation equations (between…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
Based on a natural connection between ResNet and transport equation or its characteristic equation, we propose a continuous flow model for both ResNet and plain net. Through this continuous model, a ResNet can be explicitly constructed as a…
In this paper we prove a general theorem on the extensions of local nets which was inspired by recent examples of exotic extensions for Virasoro nets with central charge less than one and earlier work on cosets and conformal inclusions.…
Networks are essential models in many applications such as information technology, chemistry, power systems, transportation, neuroscience, and social sciences. In light of such broad applicability, a general theory of dynamical systems on…
Transit functions were introduced as models of betweenness on undirected structures. Here we introduce directed transit function as the directed analogue on directed structures such as posets and directed graphs. We first show that…