相关论文: Book review "The Haskell Road to Logic, Maths and …
We are interested in algorithms that manipulate mathematical expressions in mathematically meaningful ways. Expressions are syntactic, but most logics do not allow one to discuss syntax. ${\rm CTT}_{\rm qe}$ is a version of Church's type…
We present a small, formal language for specifying the behavior of simple console I/O programs. The design is driven by the concrete application case of testing interactive Haskell programs written by students. Specifications are…
A reliable technique for deductive program verification should be proven sound with respect to the semantics of the programming language. For each different language, the construction of a separate soundness proof is often a laborious…
Destination-passing style programming introduces destinations, which represent the address of a write-once memory cell. These destinations can be passed as function parameters, allowing the caller to control memory management: the callee…
Partial correctness of imperative or functional programming divides in logic programming into two notions. Correctness means that all answers of the program are compatible with the specification. Completeness means that the program produces…
A new computational method that uses polynomial equations and dynamical systems to evaluate logical propositions is introduced and applied to Goedel's incompleteness theorems. The truth value of a logical formula subject to a set of axioms…
Type classes are one of Haskell's most popular features and extend its type system with ad-hoc polymorphism. Since their conception, there were useful features that could not be offered because of the desire to offer two correctness…
We describe several views of the semantics of a simple programming language as formal documents in the calculus of inductive constructions that can be verified by the Coq proof system. Covered aspects are natural semantics, denotational…
Large Language Models (LLMs) have succeeded remarkably in various natural language processing (NLP) tasks, yet their reasoning capabilities remain a fundamental challenge. While LLMs exhibit impressive fluency and factual recall, their…
Uncertainty in Logic Programming has been investigated since about 25 years, publishing papers dealing with various approaches to semantics and different applications. This report is intended as a first step towards the investigation of…
Starting with Hoare Logic over 50 years ago, numerous program logics have been devised to reason about the diverse programs encountered in the real world. This includes reasoning about computational effects, particularly those effects that…
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…
Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving…
Mathematical reasoning has long represented one of the most fundamental and challenging frontiers in artificial intelligence research. In recent years, large language models (LLMs) have achieved significant advances in this area. This…
Large Language Models (LLMs) have been shown to achieve breakthrough performance on complex logical reasoning tasks. Nevertheless, most existing research focuses on employing formal language to guide LLMs to derive reliable reasoning paths,…
Ordered logics and type systems have been used in a variety of applications including computational linguistics, memory allocation, stream processing, logical frameworks, parametricity, and enforcing security protocols. In most…
Reasoning, as an essential ability for complex problem-solving, can provide back-end support for various real-world applications, such as medical diagnosis, negotiation, etc. This paper provides a comprehensive survey of cutting-edge…
Recent research in extensions of Answer Set Programming has included a renewed interest in the language of Epistemic Specifications, which adds modal operators K ("known") and M ("may be true") to provide for more powerful introspective…
Bialgebrae provide an abstract framework encompassing the semantics of different kinds of computational models. In this paper we propose a bialgebraic approach to the semantics of logic programming. Our methodology is to study logic…
We present an experimental system strongly inspired by miniKanren, implemented on top of the tactics mechanism of the HOL~Light theorem prover. Our tool is at the same time a mechanism for enabling the logic programming style for reasoning…