Related papers: Teaching Functional Programmers Logic and Metatheo…
LF has been designed and successfully used as a meta-logical framework to represent and reason about object logics. Here we design a representation of the Isabelle logical framework in LF using the recently introduced module system for LF.…
Procedural computer languages have long been used in many aspects of mathematics pedagogy. In this work, we examine the use of Prolog, a declarative language for the same purpose. We find the facts+rules aspect of Prolog to be a novel…
A key feature of inductive logic programming (ILP) is its ability to learn first-order programs, which are intrinsically more expressive than propositional programs. In this paper, we introduce techniques to learn higher-order programs.…
Computational Logic is the use of computers to establish facts in a logical formalism. Originating in 19th-century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms,…
Large language models (LLMs) are increasingly evaluated on reasoning tasks, yet their logical abilities remain contested. To address this, we study LLMs' reasoning in a well-defined fragment of logic: syllogistic reasoning. We cast the…
Structural proof theory is praised for being a symbolic approach to reasoning and proofs, in which one can define schemas for reasoning steps and manipulate proofs as a mathematical structure. For this to be possible, proof systems must be…
Starting from a generalization of the standard axioms for a monoid we present a stepwise development of various, mutually equivalent foundational axiom systems for category theory. Our axiom sets have been formalized in the Isabelle/HOL…
We unify functional and logic programming by treating predicatesas functions equipped with their support: the set of inputs whose output is nonzero. Datalog, for instance, is a language of finitely supported boolean functions. Finite…
Linear programming describes the problem of optimising a linear objective function over a set of constraints on its variables. In this paper we present a solver for linear programs implemented in the proof assistant Isabelle/HOL. This…
This position statement looks back on two decades of work on shallow embeddings of non-classical logics in classical higher-order logic (HOL), a line of research that expanded into a range of logic embeddings in HOL and inspired the LogiKEy…
Teaching logic effectively requires an understanding of the factors which cause logic students to struggle. Formalization exercises, which require the student to produce a formula corresponding to the natural language sentence, are a good…
Recently, a growing number of researchers have applied machine learning to assist users of interactive theorem provers. However, the expressive nature of underlying logics and esoteric structures of proof documents impede machine learning…
Algorithmic reasoning refers to the ability to understand the complex patterns behind the problem and decompose them into a sequence of reasoning steps towards the solution. Such nature of algorithmic reasoning makes it a challenge for…
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…
Inductive theorem proving is an important long-standing challenge in computer science. In this extended abstract, we first summarize the recent developments of proof by induction for Isabelle/HOL. Then, we propose united reasoning, a novel…
In contrast to Computer Science, where the fundamental role of Logic is widely recognized, it plays a practically non-existent role in Information Systems curricula. In this paper we argue that instead of Logic's exclusion from the IS…
Functional logic languages are a high-level approach to programming by combining the most important declarative features. They abstract from small-step operational details so that programmers can concentrate on the logical aspects of an…
The logic embedding tool provides a procedural encoding for non-classical reasoning problems into classical higher-order logic. It is extensible and can support an increasing number of different non-classical logics as reasoning targets.…
This is a tutorial on logic programming and Prolog appropriate for a course on programming languages for students familiar with imperative programming.
While proof is a central component of postsecondary mathematical study, proof construction has historically posed significant difficulties for students who intend to earn mathematics degrees at the undergraduate level. This work is…