Related papers: Towards a Coq formalization of a quantified modal …
We study the model-checking problem for a quantitative extension of the modal mu-calculus on a class of hybrid systems. Qualitative model checking has been proved decidable and implemented for several classes of systems, but this is not the…
We explore a simple approach to quantum logic based on hybrid and dynamic modal logic, where the set of states is given by some Hilbert space. In this setting, a notion of quantum clause is proposed in a similar way the notion of Horn…
A recent proof, couched in the symbolic language of modal logic, shows that a well-defined formulation of the question posed in the title is answered affirmatively. In a paper with the same title Unruh has tried in various ways to translate…
As an experiment to the application of proof assistant for logic research, we formalize the model and proof system for multi-agent modal logic S5 with PAL-style dynamic modality in Lean theorem prover. We provide a formal proof for the…
It is well known in the Constraint Programming community that any non-binary constraint satisfaction problem (with finite domains) can be transformed into an equivalent binary one. One of the most well-known translations is the Hidden…
Verifying the functional correctness of programs with both classical and quantum constructs is a challenging task. The presence of probabilistic behaviour entailed by quantum measurements and unbounded while loops complicate the…
Reasoning about quantum programs remains a fundamental challenge, regardless of the programming model or computational paradigm. Despite extensive research, existing verification techniques are insufficient -- even for quantum circuits, a…
Equational Unification is a critical problem in many areas such as automated theorem proving and security protocol analysis. In this paper, we focus on XOR-Unification, that is, unification modulo the theory of exclusive-or. This theory…
Robust modules guarantee to do only what they are supposed to do - even in the presence of untrusted, malicious clients, and considering not just the direct behaviour of individual methods, but also the emergent behaviour from calls to more…
In the last two decades, modal and description logics have been applied to numerous areas of computer science, including knowledge representation, formal verification, database theory, distributed computing and, more recently, semantic web…
We develop synthetic notions of oracle computability and Turing reducibility in the Calculus of Inductive Constructions (CIC), the constructive type theory underlying the Coq proof assistant. As usual in synthetic approaches, we employ a…
In this note, we study Schwarz's conjecture on application of Q-algebras to strict quantization. We prove that in the case of a torus with a constant Poisson structure, Schwarz's formalism gives the same star product as Rieffel…
This paper presents a Coq formalization of linear algebra over elementary divisor rings, that is, rings where every matrix is equivalent to a matrix in Smith normal form. The main results are the formalization that these rings support…
Scholars have wondered for a long time whether the language of quantum mechanics introduces a quantum notion of truth which is formalized by quantum logic (QL) and is incompatible with the classical (Tarskian) notion. We show that QL can be…
We introduce and investigate here a formalisation for conditionals that allows the definition of a broad class of reasoning systems. This framework covers the most popular kinds of conditional reasoning in logic-based KR: the semantics we…
In this paper we consider the problem of certified static checking of module-like constructs of programming languages. We argue that there are algorithms and properties related to modules that can be defined and proven in an abstract way.…
We present a sequent calculus for abstract focussing, equipped with proof-terms: in the tradition of Zeilberger's work, logical connectives and their introduction rules are left as a parameter of the system, which collapses the synchronous…
We present a set of tools for rewriting modulo associativity and commutativity (AC) in Coq, solving a long-standing practical problem. We use two building blocks: first, an extensible reflexive decision procedure for equality modulo AC;…
Large language models (LLMs) have demonstrated impressive performance in various natural language processing tasks, yet their ability to perform multi-step logical reasoning remains an open challenge. Although Chain-of-Thought prompting has…
We consider an extension of the modal logic of transitive closure K+ with some inifinitary derivations and present a sequent calculus for this extension, which allows non-well-founded proofs. For the given calculus, we obtain the…