Related papers: Formal Metatheory of Second-Order Abstract Syntax
Synchronous languages rely on formal methods to ease the development of applications in an efficient and reusable way. Formal methods have been advocated as a means of increasing the reliability of systems, especially those which are safety…
We articulate here a series of specific metagoals designed to address the challenge of creating AGI systems that possess the ability to flexibly self-modify yet also have the propensity to maintain key invariant properties of their goal…
In this paper we provide a first analysis of the research questions that arise when dealing with the problem of communicating pieces of formal argumentation through natural language interfaces. It is a generally held opinion that formal…
Sign Language (SL) linguistic is dependent on the expensive task of annotating. Some automation is already available for low-level information (eg. body part tracking) and the lexical level has shown significant progresses. The syntactic…
Mechanical proofs by logical relations often involve tedious reasoning about substitution. In this paper, we show that this is not necessarily the case, by developing, in Agda, a proof that all simply typed lambda calculus expressions…
In this position paper, we propose a reasoning framework that can model the reasoning process underlying natural language inferences. The framework is based on the semantic tableau method, a well-studied proof system in formal logic. Like…
Most real-world document collections involve various types of metadata, such as author, source, and date, and yet the most commonly-used approaches to modeling text corpora ignore this information. While specialized models have been…
Early stages of system development involve outlining desired features such as functionality, availability, or usability. Specifications are derived from these features that concretize vague ideas presented in natural languages. The…
We present two metalanguages for developing $\textit{synthetic cost-aware denotational semantics}$ of programming languages. Extending the recent work of Niu et al. [2022] on $\textbf{calf}$, a dependent type theory for both cost and…
Legal reasoning requires both precise interpretation of statutory language and consistent application of complex rules, presenting significant challenges for AI systems. This paper introduces a modular multi-agent framework that decomposes…
We present Agentic AI Translate, an agentic translator prototype that operationalises the thesis of Yamada (forthcoming) -- that the metalanguage of Translation Studies has become an instruction code for generative AI. The system replaces…
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…
Mechanistic interpretability aims to reverse engineer the computation performed by a neural network in terms of its internal components. Although there is a growing body of research on mechanistic interpretation of neural networks, the…
Higher-order unification (HOU) concerns unification of (extensions of) $\lambda$-calculus and can be seen as an instance of equational unification ($E$-unification) modulo $\beta\eta$-equivalence of $\lambda$-terms. We study equational…
There are various interesting semantics' (extensions) designed for argumentation frameworks. They enable to assign a meaning, e.g., to odd-length cycles. Our main motivation is to transfer semantics' proposed by Baroni, Giacomin and Guida…
CSP-Agda is a library, which formalises the process algebra CSP in the interactive theorem prover Agda using coinductive data types. In CSP-Agda, CSP processes are in monadic form, which sup- ports a modular development of processes. In…
Logic rules are powerful for expressing complex reasoning and analysis problems. At the same time, they are inconvenient or impossible to use for many other aspects of applications. Integrating rules in a language with sets and functions,…
The lambda calculus, subject to typing restrictions, provides a syntax for the internal language of cartesian closed categories. This paper establishes a parallel result: staging annotations, subject to named level restrictions, provide a…
We give a formal treatment of simple type theories, such as the simply-typed $\lambda$-calculus, using the framework of abstract clones. Abstract clones traditionally describe first-order structures, but by equipping them with additional…
Cycles of attacking arguments pose non-trivial issues in Dung style argumentation theory, apparent behavioural difference between odd and even length cycles being a notable one. While a few methods were proposed for treating them, to - in…