Related papers: Quantitative testing semantics for non-interleavin…
In logic there is a clear concept of what constitutes a proof and what not. A proof is essentially defined as a finite sequence of formulae which are either axioms or derived by proof rules from formulae earlier in the sequence.…
Cirquent calculus is a novel proof theory permitting component-sharing between logical expressions. Using it, the predecessor article "Elementary-base cirquent calculus I: Parallel and choice connectives" built the sound and complete…
We introduce an operational and statistically meaningful measure, the quantum tomographic transfer function, that possesses important physical invariance properties for judging whether a given informationally complete quantum measurement…
In recent years, quantum-based methods have promisingly integrated the traditional procedures in information retrieval (IR) and natural language processing (NLP). Inspired by our research on the identification and application of quantum…
Recent works have extended notions of feature importance to semantic concepts that are inherently interpretable to the users interacting with a black-box predictive model. Yet, precise statistical guarantees, such as false positive rate and…
This paper presents a substructural logic of sequents with very restricted exchange and weakening rules. It is sound with respect to sequences of measurements of a quantic system. A sound and complete semantics is provided. The semantic…
Null hypothesis significance testing remains popular despite decades of concern about misuse and misinterpretation. We believe that much of the problem is due to language: significance testing has little to do with other meanings of the…
We study the algebraic theory of computable functions, which can be viewed as arising from possibly non-halting computer programs or algorithms, acting on some state space, equipped with operations of composition, {\em if-then-else} and…
Classically, risk is characterized by a point value probability indicating the likelihood of occurrence of an adverse effect. However, there are domains where the attainability of objective numerical risk characterizations is increasingly…
In search for a foundational framework for reasoning about observable behavior of programs that may not terminate, we have previously devised a trace-based big-step semantics for While. In this semantics, both traces and evaluation…
To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…
Estimating nonlinear functions of quantum states, such as the moment $\tr(\rho^m)$, is of fundamental and practical interest in quantum science and technology. Here we show a quantum-classical hybrid framework to measure them, where the…
We introduce notions of simulation between semiring-weighted automata as models of quantitative systems. Our simulations are instances of the categorical/coalgebraic notions previously studied by Hasuo---hence soundness against language…
This Survey provides an overview of techniques in termination analysis for programs with numerical variables and transitions defined by linear constraints. This subarea of program analysis is challenging due to the existence of undecidable…
Completeness is a desirable property of test suites. Roughly, completeness guarantees that a non-equivalent implementation under test will always be identified. Several approaches proposed sufficient, and sometimes also necessary,…
Semantic role theory considers roles as a small universal set of unanalyzed entities. It means that formally there are no restrictions on role combinations. We argue that the semantic roles co-occur in verb representations. It means that…
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…
Significance tests are probably the most extended form of inference in empirical research, and significance is often interpreted as providing greater informational content than non-significance. In this article we show, however, that…
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components, as well as communications between these components. Moreover, to model concurrent and…
The representation of numbers by product states in quantum mechanics can be extended to the representation of words and word sequences in languages by product states. This can be used to study quantum systems that generate text that has…