Related papers: On Permuting Cut with Contraction
We investigate how sorting algorithms efficiently overcome the exponential size of the permutation space. Our main contribution is a new continuous-time formulation of sorting as a gradient flow on the permutohedron, yielding an independent…
This paper introduces the exponential substitution calculus (ESC), a new presentation of cut elimination for IMELL, based on proof terms and building on the idea that exponentials can be seen as explicit substitutions. The idea in itself is…
In large-scale industrial LLM systems, prompt templates often expand to thousands of tokens as teams iteratively incorporate sections such as task instructions, few-shot examples, and heuristic rules to enhance robustness and coverage. This…
It is well-known that the size of propositional classical proofs can be huge. Proof theoretical studies discovered exponential gaps between normal or cut free proofs and their respective non-normal proofs. The aim of this work is to study…
We generalise the termination method of higher-order polynomial interpretations to a setting with impredicative polymorphism. Instead of using weakly monotonic functionals, we interpret terms in a suitable extension of System F-omega. This…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
The $\epsilon$-substitution method is a technique for giving consistency proofs for theories of arithmetic. We use this technique to give a proof of the consistency of the impredicative theory $ID_1$ using a variant of the cut-elimination…
Elimination theory has many applications, in particular, it describes explicitly an image of a complex line under rational transformation and determines the number of common zeroes of two polynomials in one variable. We generalize classical…
Infinitary and cyclic proof systems are proof systems for logical formulas with fixed-point operators or inductive definitions. A cyclic proof system is a restriction of the corresponding infinitary proof system. Hence, these proof systems…
Convolutional neural networks are prevailing in deep learning tasks. However, they suffer from massive cost issues when working on mobile devices. Network pruning is an effective method of model compression to handle such problems. This…
We study the classic cake cutting problem from a mechanism design perspective, in particular focusing on deterministic mechanisms that are strategyproof and fair. We begin by looking at mechanisms that are non-wasteful and primarily show…
This paper presents a generalized technology of extraction of explicit knowledge from data. The main ideas are 1) maximal reduction of network complexity (not only removal of neurons or synapses, but removal all the unnecessary elements and…
Argumentation accommodates various rhetorical devices, such as questions, reported speech, and imperatives. These rhetorical tools usually assert argumentatively relevant propositions rather implicitly, so understanding their true meaning…
Linear logic is a substructural logic proposed as a refinement of classical and intuitionistic logics, with applications in programming languages, game semantics, and quantum physics. We present a template for Gentzen-style linear logic…
We present a sequent calculus for the Grzegorczyk modal logic Grz allowing cyclic and other non-well-founded proofs and obtain the cut-elimination theorem for it by constructing a continuous cut-elimination mapping acting on these proofs.…
Indexed Linear Logic has been introduced by Ehrhard and Bucciarelli, it can be seen as a logical presentation of non-idempotent intersection types extended through the relational semantics to the full linear logic. We introduce an…
In this paper we provide an algorithm for solving constrained composite primal-dual monotone inclusions, i.e., monotone inclusions in which a priori information on primal-dual solutions is represented via closed convex sets. The proposed…
Logic-based abduction finds important applications in artificial intelligence and related areas. One application example is in finding explanations for observed phenomena. Propositional abduction is a restriction of abduction to the…
Existing high-performance deep learning models require very intensive computing. For this reason, it is difficult to embed a deep learning model into a system with limited resources. In this paper, we propose the novel idea of the network…
We introduce a new method for studying the Baum-Connes conjecture, which we call the direct splitting method. The method can simplify and clarify proofs of some of the known cases of the conjecture. In a separate paper, with J. Brodzki, E.…