Related papers: Calculational HoTT
Chain-of-Thought (CoT) prompting substantially improves the sample efficiency of transformers, reducing the complexity of tasks like parity learning from exponential to polynomial in the input length. However, generating explicit reasoning…
Dedukti is a Logical Framework based on the $\lambda$$\Pi$-Calculus Modulo Theory. We show that many theories can be expressed in Dedukti: constructive and classical predicate logic, Simple type theory, programming languages, Pure type…
We give a new formulation of Turing reducibility in terms of higher modalities, inspired by an embedding of the Turing degrees in the lattice of subtoposes of the effective topos discovered by Hyland. In this definition, higher modalities…
In previous work [Lewitzka, Log. J. IGPL 2017], we presented a hierarchy of classical modal systems, along with algebraic semantics, for the reasoning about intuitionistic truth, belief and knowledge. Deviating from G\"odel's interpretation…
In-Context Learning (ICL) enables pretrained LLMs to adapt to downstream tasks by conditioning on a small set of input-output demonstrations, without any parameter updates. Although there have been many theoretical efforts to explain how…
Verification problems of programs written in various paradigms (such as imperative, logic, concurrent, functional, and object-oriented ones) can be reduced to problems of solving Horn clause constraints on predicate variables that represent…
In this paper, we study finitary 1-truncated higher inductive types (HITs) in homotopy type theory. We start by showing that all these types can be constructed from the groupoid quotient. We define an internal notion of signatures for HITs,…
Large Language Models have demonstrated remarkable abilities across various tasks, with Chain-of-Thought (CoT) prompting emerging as a key technique to enhance reasoning capabilities. However, existing research primarily focuses on…
This work is a mathematician's attempt to understand intuitionistic logic. It can be read in two ways: as a research paper interspersed with lengthy digressions into rethinking of standard material; or as an elementary (but highly…
Isomorphism between formulae is defined with respect to categories formalizing equality of deductions in classical propositional logic and in the multiplicative fragment of classical linear propositional logic caught by proof nets. This…
An inductive inference system for proving validity of formulas in the initial algebra $T_{\mathcal{E}}$ of an order-sorted equational theory $\mathcal{E}$ is presented. It has 20 inference rules, but only 9 of them require user interaction;…
This article presents iALC, an intuitionistic version of the classical description logic ALC, based on the framework for constructive modal logics presented by Simpson \cite{simpson95} and related to description languages, via hybrid…
When faced with the question of how to represent properties in a formal proof system any user has to make design decisions. We have proved three of the theorems from Maskin's 2004 survey article on Auction Theory using the Isabelle/HOL…
Program-of-Thought (PoT) replaces natural language-based Chain-of-Thought (CoT) as the most popular method in Large Language Models (LLMs) mathematical reasoning tasks by utilizing external tool calls to circumvent computational errors.…
We use Dedukti as a logical framework for interoperability. We use automated tools to translate different developments made in HOL and in Coq to Dedukti, and we combine them to prove new results. We illustrate our approach with a concrete…
Inference-Time-Compute (ITC) methods like Best-of-N and Tree-of-Thoughts are meant to produce output candidates that are both high-quality and diverse, but their use of high-temperature sampling often fails to achieve meaningful output…
Dependent type theory gives an expressive type system facilitating succinct formalizations of mathematical concepts. In practice, it is mainly used for interactive theorem proving with intensional type theories, with PVS being a notable…
Large Language Models (LLMs) have become ubiquitous in NLP and deep learning. In-Context Learning (ICL) has been suggested as a bridging paradigm between the training-free and fine-tuning LLMs settings. In ICL, an LLM is conditioned to…
[...] The most famous model checking (MC) techniques were developed from the late 80s, bearing in mind the well-known "point-based" temporal logics LTL and CTL. However, while the expressiveness of such logics is beyond doubt, there are…
A common approach to hallucination detection casts it as a natural language inference (NLI) task, often using LLMs to classify whether the generated text is entailed by corresponding reference texts. Since entailment classification is a…