Related papers: HOL Light QE
Machine Translation Quality Estimation (MTQE) is the task of estimating the quality of machine-translated text in real time without the need for reference translations, which is of great importance for the development of MT. After two…
Symbolic execution helps check programs by exploring different paths based on symbolic inputs. Tools like KLEE are commonly used because they can automatically detect bugs and create test cases. But one of KLEE's biggest issues is how slow…
Matching logic is a formalism for specifying, and reasoning about, mathematical structures, using patterns and pattern matching. Growing in popularity, it has been used to define many logical systems such as separation logic with recursive…
Uncertainty in Logic Programming has been investigated during the last decades, dealing with various extensions of the classical LP paradigm and different applications. Existing proposals rely on different approaches, such as clause…
The term proposition usually denotes in quantum mechanics (QM) an element of (standard) quantum logic (QL). Within the orthodox interpretation of QM the propositions of QL cannot be associated with sentences of a language stating properties…
We propose a simple, yet expressive proof representation from which proofs for different proof assistants can easily be generated. The representation uses only a few inference rules and is based on a frag- ment of first-order logic called…
A quantum circuit is a computational unit that transforms an input quantum state to an output one. A natural way to reason about its behavior is to compute explicitly the unitary matrix implemented by it. However, when the number of qubits…
We present simple new Hoare logics and refinement calculi for hybrid systems in the style of differential dynamic logic. (Refinement) Kleene algebra with tests is used for reasoning about the program structure and generating verification…
Large language models (LLMs) excel in many tasks but struggle to accurately quantify uncertainty in their generated responses. This limitation makes it challenging to detect misinformation and ensure reliable decision-making. Existing…
We present a version of the HOL Light system that supports undoing definitions in such a way that this does not compromise the soundness of the logic. In our system the code that keeps track of the constants that have been defined thus far…
Chain-of-Thought (CoT) and Program-Aided Language Models (PAL) represent two distinct reasoning methods, each with its own strengths. CoT employs natural language, offering flexibility and interpretability, while PAL utilizes programming…
We propose a new type-theoretic approach to SLD-resolution and Horn-clause logic programming. It views Horn formulas as types, and derivations for a given query as a construction of the inhabitant (a proof-term) for the type given by the…
Solving systems of linear equations is a key subroutine in many quantum algorithms. In the last 15 years, many quantum linear solvers (QLS) have been developed, competing to achieve the best asymptotic worst-case complexity. Most QLS assume…
Chain-of-Though (CoT) represents a common strategy for reasoning in Large Language Models (LLMs) by decomposing complex tasks into intermediate inference steps. However, explanations generated via CoT are susceptible to content biases that…
The modal logic S4 can be used via a Curry-Howard style correspondence to obtain a lambda-calculus. Modal (boxed) types are intuitively interpreted as `closed syntax of the calculus'. This lambda-calculus is called modal type theory ---…
Large language models (LLMs) demand substantial computational and memory resources, posing challenges for efficient deployment. Two complementary approaches have emerged to address these issues: token-adaptive layer execution, which reduces…
We present a logic for reasoning about pairs of interactive quantum programs - quantum relational Hoare logic (qRHL). This logic follows the spirit of probabilistic relational Hoare logic (Barthe et al. 2009) and allows us to formulate how…
In order to combine operational and logical styles of specifications in one unified framework, the notion of logic labelled transition systems (Logic LTS, for short) has been presented and explored by L\"{u}ttgen and Vogler in [TCS…
Quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister, a system of qubits, representing a…
Uncertainty in Logic Programming has been investigated during the last decades, dealing with various extensions of the classical LP paradigm and different applications. Existing proposals rely on different approaches, such as clause…