Related papers: Distribution can be Dropped: Reply to Rumfitt
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…
Some notes about quantum physics, an interpretation if one wishes, are put forward, insisting on `closely following the mathematics/formalism, the `nuts and bolts of what quantum physics says'. These, basically well-known, issues seem to…
Doubts are raised concerning the usual interpretation of the alleged failure, by quantum mechanics, of the distributive law of classical logic. The difficulty raised by incompatible sets of observables is overcome within an epistemic…
It is shown that quantum logic is a logic in the very same way in which classical logic is a logic. Soundness and completeness of both quantum and classical logics have been proved for novel lattice models that are not orthomodular and…
General relativity required the abandonment of Euclidean geometry. Here we show that quantum theory requires the abandonment of classical logic. We show that the Hilbert space representation of quantum theory is logically inevitable. There…
A projective quantum logic in terms of relative states is developed, emphasizing the importance of information transfer between a system under study and its environment. The need for accounting for the historical evolution of system is…
This paper gives a thorough critique of the foundations of quantum physics in its mainstream interpretation (i.e., treating pure states as primitives, without reference to hidden variables, and without modifications of the quantum laws).…
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…
The aim of this paper is to promote quantum logic as one of the basic tools for analyzing human reasoning. We compare it with classical (Boolean) logic and highlight the role of violation of the distributive law for conjunction and…
Elimination of quantifiers is shown to fail dramatically for a group of well-known mathematical theories (classically enjoying the property) against a wide range of relevant logical backgrounds. Furthermore, it is suggested that only by…
We have proposed in several recent papers a critical view of some parts of quantum mechanics (QM) that is methodologically unusual because it rests on analysing the language of QM by using some elementary but fundamental tools of…
The epistemological interpretation of quantum mechanics is still in an unacceptable status. This becomes obvious if looking on the variety of interpretations currently under discussion. However, the physical community together with…
Claims that the standard methodology of scientific testing is inapplicable to Everettian quantum theory, and hence that the theory is untestable, are due to misconceptions about probability and about the logic of experimental testing.…
Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum…
A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of…
We critically discuss the apparent lack of logical rigor pervading the debate on quantum nonlocality. Strong convictions often prevail over rational assessment, leading to the acceptance of loose ideas that become entrenched dogmas. The…
We discuss how to simulate simple quantum logic operations with a large number of qubits. These simulations are needed for experimental testing of scalable solid-state quantum computers. Quantum logic for remote qubits is simulated in a…
The perturbation theory is developed based on small parameters which naturally appear in solid state quantum computation. We report the simulations of the dynamics of quantum logic operations with a large number of qubits (up to 1000). A…
Contrary to classical semantics, the disjunction of two experimental propositions relating to pure states of a quantum system ("quantum propositions" for short) can be true even in the case where neither disjunct is true. This suggests that…
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…