Related papers: Generating collection transformations from proofs
In this paper, we introduce a method of converting implicit equations to the usual forms of functions locally without differentiability. For a system of implicit equations which are equipped with continuous functions, if there are unique…
The automated generation of exercises may substantially reduce the time educators devote to manual exercise design. A major obstacle to the integration of such automation into teaching practice, however, lies in the ability to control the…
Argumentation is the process of constructing arguments about propositions, and the assignment of statements of confidence to those propositions based on the nature and relative strength of their supporting arguments. The process is modelled…
In this paper I will present a novel way of combining proof net proof search with neural networks. It contrasts with the 'standard' approach which has been applied to proof search in type-logical grammars in various different forms. In the…
Form a pure mathematical point of view, common functional forms representing different physical phenomena can be defined. For example, rates of chemical reactions, diffusion and heat transfer are all governed by exponential-type…
In settings from fact-checking to question answering, we frequently want to know whether a collection of evidence (premises) entails a hypothesis. Existing methods primarily focus on the end-to-end discriminative version of this task, but…
We generalize the notion of proof term to the realm of transfinite reduction. Proof terms represent reductions in the first-order term format, thereby facilitating their formal analysis. We show that any transfinite reduction can be…
When trained on language data, do transformers learn some arbitrary computation that utilizes the full capacity of the architecture or do they learn a simpler, tree-like computation, hypothesized to underlie compositional meaning systems…
Pretraining on large, semantically rich datasets is key for developing language models. Surprisingly, recent studies have shown that even synthetic data, generated procedurally through simple semantic-free algorithms, can yield some of the…
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 provide a sound and complete proof system for an extension of Kleene's ternary logic to predicates. The concept of theory is extended with, for each function symbol, a formula that specifies when the function is defined. The notion of…
Formal transformations somehow resembling the usual derivative are surprisingly common in computer science, with two notable examples being derivatives of regular expressions and derivatives of types. A newcomer to this list is the…
Formal proofs are challenging to write even for experienced experts. Recent progress in Neural Theorem Proving (NTP) shows promise in expediting this process. However, the formal corpora available on the Internet are limited compared to the…
An essential element of any verification technique is that of identifying and communicating to the user, system behaviour which leads to a deviation from the expected behaviour. Such behaviours are typically made available as long traces of…
Despite the broad application of deep reinforcement learning (RL), transferring and adapting the policy to unseen but similar environments is still a significant challenge. Recently, the language-conditioned policy is proposed to facilitate…
With the recent success of embeddings in natural language processing, research has been conducted into applying similar methods to code analysis. Most works attempt to process the code directly or use a syntactic tree representation,…
We propose a large language model explainability technique for obtaining faithful natural language explanations by grounding the explanations in a reasoning process. When converted to a sequence of tokens, the outputs of the reasoning…
Intensional computation derives concrete outputs from abstract function definitions; extensional computation defines functions through explicit input-output pairs. In formal semantics: intensional computation interprets expressions as…
Representing a signal as a continuous function parameterized by neural network (a.k.a. Implicit Neural Representations, INRs) has attracted increasing attention in recent years. Neural Processes (NPs), which model the distributions over…
Given a set of Datalog rules, facts, and a query, answers to the query can be inferred bottom-up starting from the facts or top-down starting from the query. For efficiency, top-down evaluation is extended with memoization of inferred…