Related papers: Proof nets for the Displacement calculus

In this paper, we explore a process called neural teleportation, a mathematical consequence of applying quiver representation theory to neural networks. Neural teleportation "teleports" a network to a new position in the weight space and…

Proof search in non-confluent tableau calculi, such as the connection tableau calculus, suffers from excess backtracking, but simple restrictions on backtracking are incomplete. We adopt constraint learning to reduce backtracking in the…

We study a well-known technique of using absoluteness for giving choice-free proofs to some statements which are known to be provable with the axiom of choice. The idea is to reduce the problem to an inner model where the axiom of choice…

We show that it is coNP-complete to decide whether a given proof structure of pomset logic is a correct proof net, using the graph-theoretic used in a previous paper of ours (arXiv:1901.10247).

Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…

We offer a simple graphical representation for proofs of intuitionistic logic, which is inspired by proof nets and interaction nets (two formalisms originating in linear logic). This graphical calculus of proofs inherits good features from…

We present a novel neural-networks-based algorithm to compute optimal transport maps and plans for strong and weak transport costs. To justify the usage of neural networks, we prove that they are universal approximators of transport plans…

The article proposes a new technique for proving the undefinability of logical connectives through each other and illustrates the technique with several examples. Some of the obtained results are new proofs of the existing theorems, others…

This paper describes a stand-alone, no-frills tool supporting the analysis of (labelled) place/transition Petri nets and the synthesis of labelled transition systems into Petri nets. It is implemented as a collection of independent,…

In this paper we propose a calculus for expressing algorithms for programming languages transformations. We present the type system and operational semantics of the calculus, and we prove that it is type sound. We have implemented our…

We present a proof-theoretical study of the interpretability logic IL, providing a wellfounded and a non-wellfounded sequent calculus for IL. The non-wellfounded calculus is used to establish a cut elimination argument for both calculi. In…

In this note we give a wellfoundedness proof of a computable notation system for first-order reflection.

In this paper some proof theory for propositional Lax Logic is developed. A cut free terminating sequent calculus is introduced for the logic, and based on that calculus it is shown that the logic has uniform interpolation. Furthermore, a…

To study implementations and optimisations of interaction net systems we propose a calculus to allow us to reason about nets, a concrete data-structure that is in close correspondence with the calculus, and a low-level language to create…

A diagrammatic logical calculus for the syllogistic reasoning is introduced and discussed. We prove that a syllogism is valid if and only if it is provable in the calculus.

We prove a lower and an upper bound on the number of block moves necessary to sort a permutation. We put our results in contrast with existing results on sorting by block transpositions, and raise some open questions.

Proofs of Tychonoff's theorem often seem to require a bit of magic. Machinery such as ultrafilters, nets or maximal families with the finite intersection property are employed to give proofs that can be very neat, but not the kind of thing…

In this paper, we introduce directed networks called `divergence network' in order to perform graphical calculation of divergence functions. By using the divergence networks, we can easily understand the geometric meaning of calculation…

Several algebraic criteria, reflecting displacement properties of transformation groups, have been used in the past years to prove vanishing of bounded cohomology and stable commutator length. Recently, the authors introduced the property…

Many concurrent and distributed systems are safety-critical and therefore have to provide a high degree of assurance. Important properties of such systems are frequently proved on the specification level, but implementations typically…