Related papers: Explicit Auditing
We formally verify an abstract machine for a call-by-value lambda-calculus with de Bruijn terms, simple substitution, and small-step semantics. We follow a stepwise refinement approach starting with a naive stack machine with substitution.…
Canonical Correlation Analysis (CCA) has been exploited immensely for learning latent representations in various fields. This study takes a step further by demonstrating the potential of CCA in identifying Elementary Discourse Units(EDUs)…
Autodiff refers to the core of the automatic differentiation systems developed in projects like JAX and Dex. Autodiff has recently been formalised in a linear typed calculus by Radul et al in arXiv:2204.10923. Although this formalisation…
The present paper constructs three new systems of clarithmetic (arithmetic based on computability logic --- see http://www.cis.upenn.edu/~giorgi/cl.html): CLA8, CLA9 and CLA10. System CLA8 is shown to be sound and extensionally complete…
We propose a paradigm for concurrent natural language generation. In order to represent grammar rules distributively, we adopt categorial unification grammar (CUG) where each category owns its functional type. We augment typed lambda…
We present a sequent calculus for first-order logic with lambda terms and definite descriptions. The theory formalised by this calculus is essentially Russellian, but avoids some of its well known drawbacks and treats definite description…
Type-preserving (or typed) compilation uses typing derivations to certify correctness properties of compilation. We have designed and implemented a type-preserving compiler for a simply-typed dialect of Prolog we call T-Prolog. The crux of…
Separation logics are a family of extensions of Hoare logic for reasoning about programs that mutate memory. These logics are "abstract" because they are independent of any particular concrete memory model. Their assertion languages, called…
The higher-dimensional modal mu-calculus is an extension of the mu-calculus in which formulas are interpreted in tuples of states of a labeled transition system. Every property that can be expressed in this logic can be checked in…
A central prediction of the accompanying theoretical framework is that metacognitive calibration can vary even when content-level performance is held approximately fixed, depending on whether support structure is preserved in a globally…
Herewith, a fairly old concept is published for the first time and named "Lucas Interpretation". This has been implemented in a prototype, which has been proved useful in educational practice and has gained academic relevance with an…
The rapid growth of text data has motivated the development of machine-learning based automatic text summarization strategies that concisely capture the essential ideas in a larger text. This study aimed to devise an extractive…
Artificial intelligence (AI) is increasingly intervening in our lives, raising widespread concern about its unintended and undeclared side effects. These developments have brought attention to the problem of AI auditing: the systematic…
AI governance frameworks increasingly rely on audits, yet the results of their underlying evaluations require interpretation and context to be meaningfully informative. Even technically rigorous evaluations can offer little useful insight…
In this paper we describe how to leverage higher-order unification to type check a dependently typed language with meta-variables. The literature usually presents the unification algorithm as a standalone component, however the need to…
Dummett's logic LC is intuitionistic logic extended with Dummett's axiom: for every two statements the first implies the second or the second implies the first. We present a natural deduction and a Curry-Howard correspondence for…
Cylindrical Algebraic Decomposition (CAD) has long been one of the most important algorithms within Symbolic Computation, as a tool to perform quantifier elimination in first order logic over the reals. More recently it is finding…
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…
It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an…
Sampling multiple responses improves language model reasoning, but uniform compute allocation is inefficient: easy questions are over-sampled while hard questions remain under-explored. We propose Uncertainty-Aware Budget Allocation (UAB),…