Related papers: Foundations of logic programming in hybrid-dynamic…
We address a fundamental mismatch between the combinations of dynamics that occur in cyber-physical systems and the limited kinds of dynamics supported in analysis. Modern applications combine communication, computation, and control. They…
We present a scheme for translating logic programs, which may use aggregation and arithmetic, into algebraic expressions that denote bag relations over ground terms of the Herbrand universe. To evaluate queries against these relations, we…
In recent work, Benjamin Schumacher and Michael~D. Westmoreland investigate a version of quantum mechanics which they call "modal quantum theory" but which we prefer to call "discrete quantum theory". This theory is obtained by…
We introduce proper display calculi for basic monotonic modal logic,the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…
Although logic of quantum mechanics has been studied for a long time, logic of QFT has not been studied before. We formulate logic of QFT by introducing the perspective of dynamic logic, because the nature of two fundamental operators in…
The fundamental algebraic concepts of quantum mechanics, as expressed by many authors, are reviewed and translated into the framework of the relatively new non-distributive system of Boolean fractions (also called conditional events or…
Quantum logic gates provide fundamental examples of conditional quantum dynamics. They could form the building blocks of general quantum information processing systems which have recently been shown to have many interesting non--classical…
We contribute to the refined understanding of the language-logic-algebra interplay in the context of first-order properties of countable words. We establish decidable algebraic characterizations of one variable fragment of FO as well as…
Standard epistemic logics introduce a modal operator K to represent knowledge, but in doing so they presuppose the logical apparatus they aim to explain. By contrast, this paper explores how logic may be derived from the structure of…
Many theories of semantic interpretation use lambda-term manipulation to compositionally compute the meaning of a sentence. These theories are usually implemented in a language such as Prolog that can simulate lambda-term operations with…
This paper examines language modeling based on the theory of quantum mechanics. It focuses on the introduction of quantum mechanics into the symbol-meaning pairs of language in order to build a representation model of natural language. At…
Relational verification of quantum programs has many potential applications in quantum and post-quantum security and other domains. We propose a relational program logic for quantum programs. The interpretation of our logic is based on a…
Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected…
The paper describes an extension of well-founded semantics for logic programs with two types of negation. In this extension information about preferences between rules can be expressed in the logical language and derived dynamically. This…
Adiabatic quantum programming defines the time-dependent mapping of a quantum algorithm into an underlying hardware or logical fabric. An essential step is embedding problem-specific information into the quantum logical fabric. We present…
The proposed framework provides a general model of concurrent imperative programming. Programs are modeled as formal languages and concurrency as an interleaving (or shuffle) operator. This yields a simple and elegant algebra of programs.…
We present a quantum computing approach to analyzing Large Language Model (LLM) embeddings, leveraging complex-valued representations and modeling semantic relationships using quantum mechanical principles. By establishing a direct mapping…
We introduce and investigate a weighted propositional configuration logic over commutative semirings. Our logic is intended to serve as a specification language for software architectures with quantitative features. We prove an efficient…
We introduce a novel quantum programming language featuring higher-order programs and quantum controlflow which ensures that all qubit transformations are unitary. Our language boasts a type system guaranteeingboth unitarity and…
We introduce a quantum extension of dynamic programming, a fundamental computational method that efficiently solves recursive problems using memory. Our innovation lies in showing how to coherently generate recursion step unitaries by using…