Related papers: Computing with Equations
This is a story about making quantum computers speak, and doing so in a quantum-native, compositional and meaning-aware manner. Recently we did question-answering with an actual quantum computer. We explain what we did, stress that this was…
Can AI solve all math? What do we actually mean by doing mathematics? How do we communicate mathematics? What is mathematics beyond problem solving? This essay is my attempt to answer these questions.
The combined approach of the Qualitative Reasoning and Probabilistic Functions for the knowledge representation is proposed. The method aims at represent uncertain, qualitative knowledge that is essential for the moving blocks task's…
We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…
While modern software development heavily uses versioned packages, programming languages rarely support the concept of versions in their semantics, which makes software updates more bulky and unsafe. This paper proposes a programming…
Interactive proof assistants make it possible for ordinary mathematicians to write definitions and theorems in a formal proof language, like a programming language, so that a computer can parse them and check them against the rules of a…
The purpose of this note is to present a formulation of a given nonlinear ordinary differential equation into an equivalent system of linear ordinary differential equations. It is evident that the easiness of a such procedure would be able…
Programming languages serve a dual purpose: to communicate programs to computers, and to communicate programs to humans. Indeed, it is this dual purpose that makes programming language design a constrained and challenging problem.…
This short note discusses the role of syntax vs. semantics and the interplay between logic, philosophy, and language in computer science and game theory.
The semantics of assignment and mutual exclusion in concurrent and multi-core/multi-processor systems is presented with attention to low level architectural features in an attempt to make the presentation realistic. Recursive functions on…
"Natural languages are programming languages for minds." Can we or should we take this slogan seriously? If so, how? Can answers be found by looking at the various "dynamic" treatments of natural language developed over the last decade or…
Teaching proofs is a crucial component of any undergraduate-level program that covers formal reasoning. We have developed a calculational reasoning format and refined it over several years of teaching a freshman-level course, "Logic and…
Qualification has been recently introduced as a generalization of uncertainty in the field of Logic Programming. In this report we investigate a more expressive language for First-Order Functional Logic Programming with Constraints and…
This paper reports on the "Learning Computational Grammars" (LCG) project, a postdoc network devoted to studying the application of machine learning techniques to grammars suitable for computational use. We were interested in a more…
"Natural Language," whether spoken and attended to by humans, or processed and generated by computers, requires networked structures that reflect creative processes in semantic, syntactic, phonetic, linguistic, social, emotional, and…
We introduce the language QML, a functional language for quantum computations on finite types. Its design is guided by its categorical semantics: QML programs are interpreted by morphisms in the category FQC of finite quantum computations,…
Electromagnetic theory is central to physics. An undergraduate major in physics typically takes a semester or a year of electromagnetic theory as a junior or senior, and a graduate student in physics typically takes an additional semester…
Programming is about automation in a wide variety of domains. Developing itself is one of those. As a side-effect, progress in automated coding may make people less willing to learn computer programming. This could become an issue, if the…
These notes provide a quick introduction to the Coq system and show how it can be used to define logical concepts and functions and reason about them. It is designed as a tutorial, so that readers can quickly start their own experiments,…
Many interesting and useful symbolic computation algorithms manipulate mathematical expressions in mathematically meaningful ways. Although these algorithms are commonplace in computer algebra systems, they can be surprisingly difficult to…