相关论文: Logical Consistency as a Dynamical Invariant: A Qu…
We propose a semantic representation of the standard quantum logic QL within a classical, normal modal logic, and this via a lattice-embedding of orthomodular lattices into Boolean algebras with one modal operator. Thus our classical logic…
In the histories formulation of quantum theory, sets of coarse-grained histories that are consistent obey the classical probability rules. It has been argued that these sets can describe the quasi-classical behaviour of closed quantum…
This paper presents an elementary introduction to Consistent Quantum Theory (CQT), as developed by Griffiths and others over the past 25 years. The theory is a version of orthodox(Copenhagen) quantum mechanics, based on the notion that the…
Statistical classical mechanics and quantum mechanics are developed and well-known theories that represent a basis for modern physics. The two described theories are well known and have been well studied. As these theories contain numerous…
This paper is concerned with the paraconsistent first-order logic LPQ$^{\supset,\mathsf{F}}$, Priest's LPQ enriched with an implication connective and a falsity constant. A sequent-style natural deduction proof system for this logic is…
Typical studies of quantum error correction assume probabilistic Pauli noise, largely because it is relatively easy to analyze and simulate. Consequently, the effective logical noise due to physically realistic coherent errors is relatively…
The concept of informal mathematical proof considered in intuitionism is apparently vulnerable to a version of the liar paradox. However, a careful reevaluation of this concept reveals a subtle error whose correction blocks the…
The emphasis is made on the juxtaposition of (quantum~theorem) proving versus quantum (theorem~proving). The logical contents of verification of the statements concerning quantum systems is outlined. The Zittereingang (trembling input)…
Because contemporary large software systems are pervasively inconsistent, it is not safe to reason about them using classical logic. The goal of Direct Logic is to be a minimal fix to classical mathematical logic that meets the requirements…
We recently performed cognitive experiments on conjunctions and negations of two concepts with the aim of investigating the combination problem of concepts. Our experiments confirmed the deviations (conceptual vagueness, underextension,…
The Quantum Decision Theory, developed recently by the authors, is applied to clarify the role of risk and uncertainty in decision making and in particular in relation to the phenomenon of dynamic inconsistency. By formulating this notion…
In classical physics, a single measurement can in principle reveal the state of a system. However, quantum theory permits numerous non-equivalent measurements on a physical system, each providing only limited information about the state.…
In consistent history quantum theory, a description of the time development of a quantum system requires choosing a framework or consistent family, and then calculating probabilities for the different histories which it contains. It is…
We describe a method to axiomatize computations in deterministic Turing machines. When applied to computations in non-deterministic Turing machines, this method may produce contradictory (and therefore trivial) theories, considering…
At the onset of quantum mechanics, it was argued that the new theory would entail a rejection of classical logic. The main arguments to support this claim come from the non-commutativity of quantum observables, which allegedly would…
Large language models (LLMs) are a promising venue for natural language understanding and generation. However, current LLMs are far from reliable: they are prone to generating non-factual information and, more crucially, to contradicting…
While quantum computers are expected to yield considerable advantages over classical devices, the precise features of quantum theory enabling these advantages remain unclear. Contextuality--the denial of a notion of classical physical…
The formalism of abstracted quantum mechanics is applied in a model of the generalized Liar Paradox. Here, the Liar Paradox, a consistently testable configuration of logical truth properties, is considered a dynamic conceptual entity in the…
In many situations humans have to reason with inconsistent knowledge. These inconsistencies may occur due to not fully reliable sources of information. In order to reason with inconsistent knowledge, it is not possible to view a set of…
We consider a proper propositional quantum logic and show that it has multiple disjoint lattice models, only one of which is an orthomodular lattice (algebra) underlying Hilbert (quantum) space. We give an equivalent proof for the classical…