Related papers: What Does This Notation Mean Anyway?
Neural Machine Translation (NMT) is a new approach to machine translation that has made great progress in recent years. However, recent studies show that NMT generally produces fluent but inadequate translations (Tu et al. 2016b; Tu et al.…
The modal logic S4 can be used via a Curry-Howard style correspondence to obtain a lambda-calculus. Modal (boxed) types are intuitively interpreted as `closed syntax of the calculus'. This lambda-calculus is called modal type theory ---…
BPMN is a specification language widely used by industry and researchers for business process modeling and execution. It defines clearly how to articulate its concepts, but do not provide mechanism to represent the semantics of the produced…
This work is the first to propose the concept of a semantic numeration system (SNS) as a certain class of context-based numeration methods. The development of the SNS concept required the introduction of fundamentally new concepts such as a…
Many universities have courses and projects revolving around compiler or interpreter implementation as part of their degree programmes in computer science. In such teaching activities, tool support can be highly beneficial. While there are…
We present the design of a new functional programming language, MLTS, that uses the lambda-tree syntax approach to encoding bindings appearing within data structures. In this approach, bindings never become free nor escape their scope:…
New Foundations ($\mathrm{NF}$) is a set theory obtained from naive set theory by putting a stratification constraint on the comprehension schema; for example, it proves that there is a universal set $V$. $\mathrm{NFU}$ ($\mathrm{NF}$ with…
The automated synthesis of correct-by-construction Boolean functions from logical specifications is known as the Boolean Functional Synthesis (BFS) problem. BFS has many application areas that range from software engineering to circuit…
With the rapid advancement of Large Language Models (LLMs), AI-driven music generation has become a vibrant and fruitful area of research. However, the representation of musical data remains a significant challenge. To address this, a…
Ontologies and rules are usually loosely coupled in knowledge representation formalisms. In fact, ontologies use open-world reasoning while the leading semantics for rules use non-monotonic, closed-world reasoning. One exception is the…
This article introduces Newton, a specification language for notating the analytic form, units of measure, and sensor signal properties for physical-object-specific invariants and general physical laws. We designed Newton to provide a means…
Here we show, in the second paper in a series of articles, methods to calculate propositional statements with algebraic polyno mials as symbols for the connectives, which here are named operators. In the first article, we explained this…
We present a device for specifying and reasoning about syntax for datatypes, programming languages, and logic calculi. More precisely, we study a notion of "signature" for specifying syntactic constructions. In the spirit of Initial…
Given a Boolean formula F(X,Y), where X is a vector of outputs and Y is a vector of inputs, the Boolean functional synthesis problem requires us to compute a Skolem function vector G(Y)for X such that F(G(Y),Y) holds whenever \exists X…
We propose Pushdown Normal Form (PDNF) Bisimulation to verify contextual equivalence in higher-order functional programming languages with local state. Similar to previous work on Normal Form (NF) bisimulation, PDNF Bisimulation is sound…
Contextuality (or lack thereof) is a property of systems of random variables. Among the measures of the degree of contextuality, two have played important roles. One of them, Contextual Fraction ($\text{CNTF}$) was proposed within the…
Mathematical knowledge is a central component in science, engineering, and technology (documentation). Most of it is represented informally, and -- in contrast to published research mathematics -- subject to continual change. Unfortunately,…
Even though a linguistics-free sequence to sequence model in neural machine translation (NMT) has certain capability of implicitly learning syntactic information of source sentences, this paper shows that source syntax can be explicitly…
With the emerging applications that involve complex distributed systems branching-time specifications are specifically important as they reflect dynamic and non-deterministic nature of such applications. We describe the expressive power of…
We introduce MLFMF, a collection of data sets for benchmarking recommendation systems used to support formalization of mathematics with proof assistants. These systems help humans identify which previous entries (theorems, constructions,…