Related papers: Mechanized HOL Reasoning in Set Theory
The aim of this article is to employ the Lazy Set algorithm as an example for a mathematical framework for proving the linearizability of distributed systems. The proof in this approach is divided into two stages of lower and higher…
Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a…
This thesis develops a framework for formalizing reasoning about specifications of systems written in LF. This formalization centers around the development of a reasoning logic that can express the sorts of properties which arise in…
Complex logical reasoning tasks require a long sequence of reasoning, which a large language model (LLM) with chain-of-thought prompting still falls short. To alleviate this issue, neurosymbolic approaches incorporate a symbolic solver.…
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…
First Order Logic (FOL) is a powerful reasoning tool for program verification. Recent work on Ivy shows that FOL is well suited for verification of parameterized distributed systems. However, specifying many natural objects, such as a ring…
We present a systematic approach to logical predicates based on universal coalgebra and higher-order abstract GSOS, thus making a first step towards a unifying theory of logical relations. We first observe that logical predicates are…
Large language models (LLMs) have shown an impressive ability to perform tasks believed to require thought processes. When the model does not document an explicit thought process, it becomes difficult to understand the processes occurring…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…
To support reasoning about properties of programs operating with boolean values one needs theorem provers to be able to natively deal with the boolean sort. This way, program properties can be translated to first-order logic and theorem…
These notes present the essentials of first- and second-order monadic logics on strings with introductory purposes. We discuss Monadic First-Order logic and show that it is strictly less expressive than Finite-State Automata, in that it…
Type checking algorithms and theorem provers rely on unification algorithms. In presence of type families or higher-order logic, higher-order (pre)unification (HOU) is required. Many HOU algorithms are expressed in terms of…
Ontology embeddings map classes, relations, and individuals in ontologies into $\mathbb{R}^n$, and within $\mathbb{R}^n$ similarity between entities can be computed or new axioms inferred. For ontologies in the Description Logic…
An FOL-program consists of a background theory in a decidable fragment of first-order logic and a collection of rules possibly containing first-order formulas. The formalism stems from recent approaches to tight integrations of ASP with…
Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…
Recent advances in the integration of deep learning with automated theorem proving have centered around the representation of logical formulae as inputs to deep learning systems. In particular, there has been a growing interest in adapting…
Liquid Haskell is an extension to the Haskell programming language that adds support for refinement types: data types augmented with SMT-decidable logical predicates that refine the set of values that can inhabit a type. Furthermore, Liquid…
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…
Most of the engineering and physical systems are generally characterized by differential and difference equations based on their continuous-time and discrete-time dynamics, respectively. Moreover, these dynamical models are analyzed using…