Related papers: Minimal Sequent Calculus for Teaching First-Order …

In this paper we present a cut-free sequent calculus, called SeqS, for some standard conditional logics, namely CK, CK+ID, CK+MP and CK+MP+ID. The calculus uses labels and transition formulas and can be used to prove decidability and space…

For a sequence of classification tasks that arrive over time, it is common that tasks are evolving in the sense that consecutive tasks often have a higher similarity. The incremental learning of a growing sequence of tasks holds promise to…

We introduce Wasm Logic, a sound program logic for first-order, encapsulated WebAssembly. We design a novel assertion syntax, tailored to WebAssembly's stack-based semantics and the strong guarantees given by WebAssembly's type system, and…

Extending and generalizing the approach of 2-sequents (Masini, 1992), we present sequent calculi for the classical modal logics in the K, D, T, S4 spectrum. The systems are presented in a uniform way-different logics are obtained by tuning…

In this work we explore the connections between (linear) nested sequent calculi and ordinary sequent calculi for normal and non-normal modal logics. By proposing local versions to ordinary sequent rules we obtain linear nested sequent…

Many studies on the cost-sensitive learning assumed that a unique cost matrix is known for a problem. However, this assumption may not hold for many real-world problems. For example, a classifier might need to be applied in several…

We consider the problem of sequential prediction and provide tools to study the minimax value of the associated game. Classical statistical learning theory provides several useful complexity measures to study learning with i.i.d. data. Our…

First year calculus is often taught in a way that is very burdensome to the student. Students have to memorize a diversity of processes for essentially performing the same task. However, many calculus processes can be simplified and…

Commonly used proof strategies by automated reasoners organise proof search either by ordering-based saturation or by reducing goals to subgoals. In this paper, we combine these two approaches and advocate a SAT-based method with symmetry…

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…

The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain…

With the increasing ability of large language models (LLMs), in-context learning (ICL) has evolved as a new paradigm for natural language processing (NLP), where instead of fine-tuning the parameters of an LLM specific to a downstream task…

First-order logic has been established as an important tool for modeling and verifying intricate systems such as distributed protocols and concurrent systems. These systems are parametric in the number of nodes in the network or the number…

Paraconsistent logics constitute an important class of formalisms dealing with non-trivial reasoning from inconsistent premisses. In this paper, we introduce uniform axiomatisations for a family of nonmonotonic paraconsistent logics based…

We propose to use MapReduce to quickly test new retrieval approaches on a cluster of machines by sequentially scanning all documents. We present a small case study in which we use a cluster of 15 low cost ma- chines to search a web crawl of…

Interactive theorem provers have developed dramatically over the past four decades, from primitive beginnings to today's powerful systems. Here, we focus on Isabelle/HOL and its distinctive strengths. They include automatic proof search,…

This paper is an example-based demonstration of our initial results on the formal specification of programs written in the computer algebra language MiniMaple (a substantial subset of Maple with slight extensions). The main goal of this…

Proust is a small Racket program offering rudimentary interactive assistance in the development of verified proofs for propositional and predicate logic. It is constructed in stages, some of which are done by students before using it to…

An interactive theorem prover, Isabelle, is under development. In LCF, each inference rule is represented by one function for forwards proof and another (a tactic) for backwards proof. In Isabelle, each inference rule is represented by a…

miniKanren is a lightweight embedded language for logic and relational programming. Many of its useful features come from a distinctive search strategy, called interleaving search. However, with interleaving search conventional ways of…