Related papers: HOL Light QE
Formally reasoning about functional programs is supposed to be straightforward and elegant, however, it is not typically done as a matter of course. Reasoning in a proof assistant requires "reimplementing" the code in those tools, which is…
The time evolution operator plays a crucial role in the precise computation of chemical experiments on quantum computers and holds immense promise for advancing the fields of physical and computer sciences, with applications spanning…
Based on ideas of quantum theory of open systems we propose the consistent approach to the formulation of logic of plausible propositions. To this end we associate with every plausible proposition diagonal matrix of its likelihood and…
Competency Questions (CQs) are pivotal in knowledge engineering, guiding the design, validation, and testing of ontologies. A number of diverse formulation approaches have been proposed in the literature, ranging from completely manual to…
In this paper, we define an intuitionistic version of Computation Tree Logic. After explaining the semantic features of intuitionistic logic, we examine how these characteristics can be interesting for formal verification purposes.…
We introduce a novel framework, LM-Guided CoT, that leverages a lightweight (i.e., <1B) language model (LM) for guiding a black-box large (i.e., >10B) LM in reasoning tasks. Specifically, the lightweight LM first generates a rationale for…
In this paper we propose an extension of Answer Set Programming (ASP), and in particular, of its most general logical counterpart, Quantified Equilibrium Logic (QEL), to deal with partial functions. Although the treatment of equality in QEL…
Nondeterministic choice is a useful program construct that provides a way to describe the behaviour of a program without specifying the details of possible implementations. It supports the stepwise refinement of programs, a method that has…
Quantum Hamiltonian Computing is a recent approach that uses quantum systems, in particular a single molecule, to perform computational tasks. Within this approach, we present explicit methods to construct logic gates using two different…
We discuss the syntax and semantics of relational Horn logic (RHL) and partial Horn logic (PHL). RHL is an extension of the Datalog programming language that allows introducing and equating variables in conclusions. PHL is a syntactic…
We propose a validity preserving translation from a subset of epistemic Alternating-time Temporal Logic (ATL) to epistemic Computation Tree Logic (CTL). The considered subset of epistemic ATL is known to have the finite model property and…
Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…
A holistic extension of classical propositional logic is introduced in the framework of quantum computation with mixed states. The concepts of tautology and contradiction are investigated in this extensions. A special family of quantum…
Multi-hop question answering (QA) involves finding multiple relevant passages and performing step-by-step reasoning to answer complex questions. Previous works on multi-hop QA employ specific methods from different modeling perspectives…
This short note proposes a symbolic approach for representing and reasoning about quantum circuits using complex, vector or matrix-valued Boolean expressions. A major benefit of this approach is that it allows us to directly borrow the…
Quantum computing promises enabling solving large problem instances, e.g. large linear equation systems with HHL algorithm, once the hardware stack matures. For the foreseeable future quantum computing will remain in the so-called NISQ era,…
With the recent advance in neural machine translation demonstrating its importance, research on quality estimation (QE) has been steadily progressing. QE aims to automatically predict the quality of machine translation (MT) output without…
We introduce our implementation in HOL Light of the metatheory for G\"odel-L\"ob provability logic (GL), covering soundness and completeness w.r.t. possible world semantics and featuring a prototype of a theorem prover for GL itself. The…
Active learning aims to deliver maximum benefit when resources are scarce. We use COMET-QE, a reference-free evaluation metric, to select sentences for low-resource neural machine translation. Using Swahili, Kinyarwanda and Spanish for our…
In this work, we describe the design and architecture of the open-source Quantum Engine Compiler (qe-compiler) currently used in production for IBM Quantum systems. The qe-compiler is built using LLVM's Multi-Level Intermediate…