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Description Logics (DLs) are used in knowledge-based systems to represent and reason about terminological knowledge of the application domain in a semantically well-defined manner. In this thesis, we establish a number of novel complexity…
The work is devoted to Computability Logic (CoL) -- the philosophical/mathematical platform and long-term project for redeveloping classical logic after replacing truth} by computability in its underlying semantics (see…
Binary Neural Networks (BNNs) are receiving an upsurge of attention for bringing power-hungry deep learning towards edge devices. The traditional wisdom in this space is to employ sign() for binarizing featuremaps. We argue and illustrate…
This paper describes mathlib, a community-driven effort to build a unified library of mathematics formalized in the Lean proof assistant. Among proof assistant libraries, it is distinguished by its dependently typed foundations, focus on…
In this work, a novel quaternary algebra has been proposed that can be used to implement an arbitrary quaternary logic function in more than one systematic ways. The proposed logic has evolved from and is closely related to the Boolean…
Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can…
We propose LeanLTL, a unifying framework for linear temporal logics in Lean 4. LeanLTL supports reasoning about traces that represent either infinite or finite linear time. The library allows traditional LTL syntax to be combined with…
A rational number is dyadic if it has a finite binary representation $p/2^k$, where $p$ is an integer and $k$ is a nonnegative integer. Dyadic rationals are important for numerical computations because they have an exact representation in…
We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…
The Lean mathematical library mathlib is developed by a community of users with very different backgrounds and levels of experience. To lower the barrier of entry for contributors and to lessen the burden of reviewing contributions, we have…
When writing high-performance code for numerical computation in a scripting language like MATLAB, it is crucial to have the operations in a large for-loop vectorized. If not, the code becomes too slow to use, even for a moderately large…
We present three projects concerned with applications of proof assistants in the area of programming language theory and mathematics. The first project is about a certified compilation technique for a domain-specific programming language…
Important tasks such as reasoning and planning are fundamentally algorithmic, meaning that solving them robustly requires acquiring true reasoning or planning algorithms, rather than shortcuts. Large Language Models lack true algorithmic…
This paper presents differential-algebraic refinement logic (dARL) with which one can deductively verify both properties and relations of differential-algebraic programs (DAPs) that extend hybrid dynamical systems with…
Many tools used to process programs, like compilers, analyzers, or verifiers, perform transformations on their intermediate program representation, like abstract syntax trees. Implementing such program transformations is a non-trivial task,…
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…
We encode arrays as functions which, in turn, are encoded as sets of ordered pairs. The set cardinality of each of these functions coincides with the length of the array it is representing. Then we define a fragment of set theory that is…
We present a collection of modular open source C++ libraries for the development of logic synthesis applications. These libraries can be used to develop applications for the design of classical and emerging technologies, as well as for the…
Considering the challenges faced by large language models (LLMs) in logical reasoning and planning, prior efforts have sought to augment LLMs with access to external solvers. While progress has been made on simple reasoning problems,…
We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…