Related papers: Minimal Sequent Calculus for Teaching First-Order …
Applied process calculi include advanced programming constructs such as type systems, communication with pattern matching, encryption primitives, concurrent constraints, nondeterminism, process creation, and dynamic connection topologies.…
Attribution and fact verification are critical challenges in natural language processing for assessing information reliability. While automated systems and Large Language Models (LLMs) aim to retrieve and select concise evidence to support…
First-order optimization methods have attracted a lot of attention due to their practical success in many applications, including in machine learning. Obtaining convergence guarantees and worst-case performance certificates for first-order…
The Bayesian Mallows model is a flexible tool for analyzing data in the form of complete or partial rankings, and transitive or intransitive pairwise preferences. In many potential applications of preference learning, data arrive…
Classical supervised learning via empirical risk (or negative log-likelihood) minimization hinges upon the assumption that the testing distribution coincides with the training distribution. This assumption can be challenged in modern…
In the field of large language model (LLM)-based proof generation, despite extensive training on large datasets such as ArXiv, LLMs still exhibit only modest performance on proving tasks of moderate difficulty. We believe that this is…
Large Language Models (LLMs) have a natural role in answering complex queries about data streams, but the high computational cost of LLM inference makes them infeasible in many such tasks. We propose online cascade learning, the first…
Interpolation is an important property of classical and many non-classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the non-monotonic system of…
Proof Blocks is a software tool that provides students with a scaffolded proof-writing experience, allowing them to drag and drop prewritten proof lines into the correct order instead of starting from scratch. In this paper we describe a…
Motivated by recent commentary that has questioned today's pursuit of ever-more complex models and mathematical formalisms in applied machine learning and whether meaningful empirical progress is actually being made, this paper tries to…
We describe a graph-theoretic syntax for self-referential formulas as well as a four-valued logic to include contradictory and independent formulas. We then explore the degree to which generalized truth tables can be realized in our theory,…
Using SCM higher mathematics course allows you to: more clearly understandable apply theoretical material; deprive students of routine calculations; provide multilevel learning process, and therefore enhances cognitive interest and most…
In this paper we show that cut-free derivations in the epsilon format of sequent calculus provide for a non-elementary speed-up w.r.t. cut-free proofs in usual sequent calculi in first-order language.
A program is a finite piece of data that produces a (possibly infinite) sequence of primitive instructions. From scratch we develop a linear notation for sequential, imperative programs, using a familiar class of primitive instructions and…
Interactive systems are commonly prototyped as web applications. This approach enables studies with functional prototypes on a large scale. However, setting up these studies can be complex due to implementing experiment procedures,…
Recent advances in large language models (LLMs) enable effective in-context learning (ICL) with many-shot examples, but at the cost of high computational demand due to longer input tokens. To address this, we propose cheat-sheet ICL, which…
In this work, we conduct an experiment using state-of-the-art LLMs to translate MiniF2F into Rocq. The translation task focuses on generating a Rocq theorem based on three sources: a natural language description, the Lean formalization, and…
The framework of psi-calculi extends the pi-calculus with nominal datatypes for data structures and for logical assertions and conditions. These can be transmitted between processes and their names can be statically scoped as in the…
We commonly think of mathematics as bringing precision to application domains, but its relationship with computer science is more complex. This experience report on the use of Racket and Haskell to teach a required first university CS…
In this paper I discuss what, according to my long experience, every computer scientist should know from logic. We concentrate on issues of modeling, interpretability and levels of abstraction. We discuss what the minimal toolbox of logic…