Related papers: What do ultraproducts remember about the original …
We provide a mathematical theory and methodology for synthesising equational logics from algebraic metatheories. We illustrate our methodology by means of two applications: a rational reconstruction of Birkhoff's Equational Logic and a new…
We introduce a construction of highly arc transitive digraphs using a layerwise direct product. This product generalizes some known classes of highly arc transitive digraphs but also allows to construct new such. We use the product to…
We develop semantics and syntax for bicategorical type theory. Bicategorical type theory features contexts, types, terms, and directed reductions between terms. This type theory is naturally interpreted in a class of structured…
We give a new proof of the well-known fact that all functions $(\mathbb{N} \to \mathbb{N}) \to \mathbb{N}$ which are definable in G\"odel's System T are continuous via a syntactic approach. Differing from the usual syntactic method, we…
In this note we observe that the notion of an induced representation has an analog for quasi-actions. We then use induced quasi-actions to refine some earlier rigidity results for product spaces.
Targeting to use contract-based design for the specification and refinement of extra-functional properties, this research abstract suggests to use type constraints and dependent types to ensure correct and consistent top-down decomposition…
Large language models are a form of artificial intelligence systems whose primary knowledge consists of the statistical patterns, semantic relationships, and syntactical structures of language1. Despite their limited forms of "knowledge",…
The concept of paradeduction is presented in order to justify that we can overlook contradictory information taking into account only what is consistent. Besides that, paradeduction is used to show that there is a way to transform any…
The aim of Logic2Text is to generate controllable and faithful texts conditioned on tables and logical forms, which not only requires a deep understanding of the tables and logical forms, but also warrants symbolic reasoning over the…
We propose a call-by-value lambda calculus extended with a new construct inspired by abductive inference and motivated by the programming idioms of machine learning. Although syntactically simple the abductive construct has a complex and…
The method of little groups describes the irreducible characters of semidirect products with abelian normal subgroups in terms of the irreducible characters of the factor groups. We modify this method to construct supercharacter theories of…
The ability to automatically generalise (interactive) proofs and use such generalisations to discharge related conjectures is a very hard problem which remains unsolved. Here, we develop a notion of goal types to capture key properties of…
We study induction on the program structure as a proof method for bisimulation-based compiler correctness. We consider a first-order language with mutually recursive function definitions, system calls, and an environment semantics. The…
To build intelligent machine learning systems, there are two broad approaches. One approach is to build inherently interpretable models, as endeavored by the growing field of causal representation learning. The other approach is to build…
A method based on mapping a symbolic sequence into a set of patterns (strings resulting from the sequence parsing) is proposed as a tool for the reconstruction of ancestral sequences. The set union of patterns comprises all the patterns…
A growing body of work studies how to answer a question or verify a claim by generating a natural language "proof": a chain of deductive inferences yielding the answer based on a set of premises. However, these methods can only make sound…
We study a new type of sequences whose elements are defined in terms of the position, sign and magnitude of another element of the sequence. The name ultra-recursive comes from the fact that these sequences possess terms that are generated…
In functional programming, monads are supposed to encapsulate computations, effectfully producing the final result, but keeping to themselves the means of acquiring it. For various reasons, we sometimes want to reveal the internals of a…
Our goal is to produce validation data that can be used as an efficient (pre) test set for structural stuck-at faults. In this paper, we detail an original test-oriented mutation sampling technique used for generating such data and we…
We show how to extrapolate an analytic function (or a smooth signal) by multiplying and dividing its values on geometric sequences that collapse to a point.