Arkady Bolotin - Academia.edu (original) (raw)

Papers by Arkady Bolotin

arXiv (Cornell University), Dec 6, 2022

The stipulation that no measurable quantity could have an infinite value is indispensable in phys... more The stipulation that no measurable quantity could have an infinite value is indispensable in physics. At the same time, in mathematics, the possibility of considering an infinite procedure as a whole is usually taken for granted. However, not only does such possibility run counter to computational feasibleness, but it also leads to the most serious problem in modern physics, to wit, the emergence of infinities in calculated physical quantities. Particularly, having agreed on the axiom of infinity for set theory-the backbone of the theoretical foundations of calculus integrated in every branch of physics-one could no longer rule out the existence of a classical field theory which is not quantizable, let alone renormalizable. By contrast, the present paper shows that negating the axiom of infinity results in physics acting in a finite geometry where it is ensured that all classical field theories are quantizable.

arXiv (Cornell University), May 16, 2019

A common way of stating the non-cloning theorem-one of distinguishing characteristics of quantum ... more A common way of stating the non-cloning theorem-one of distinguishing characteristics of quantum theory-is that one cannot make a copy of an arbitrary unknown quantum state. Even though this theorem is an important part of the ongoing discussion of the nature of a quantum state, the role of the theorem in the logical-algebraic approach to quantum theory has not yet been systematically studied. According to the standard point of view (which is in line with the logical tradition), quantum cloning amounts to two classical rules of inference, namely, monotonicity and idempotency of entailment. One can conclude then that the whole of quantum theory should be described through a logic wherein these rules do not hold, which is linear logic. However, in accordance with a supervaluational semantics (that allows one to retain all the theorems of classical logic while admitting "truth-value gaps"), quantum cloning necessitates the permanent loss of the truth values of experimental quantum propositions which violates the unalterability of the past. The present paper demonstrates this.

arXiv (Cornell University), May 8, 2018

In contrast to conjunctions of commutable projection operators unambiguously represented by their... more In contrast to conjunctions of commutable projection operators unambiguously represented by their meets, the mathematical representation of conjunctions of incommutable projection operators is a question that has yet to be solved. This question relates to another asking whether the set of the column spaces of the projection operators, commutable and incommutable alike, forms a lattice. As it is demonstrated in the paper, if the Hilbert space is finite, the column spaces of the incommutable projection operators cannot be elements of one partially ordered set in accordance with Burnside's theorem on matrix algebras.

Journal of Mathematical Physics, 2017

As it is known, neither classical logical conjunction “and” nor classical logical alternative “ei... more As it is known, neither classical logical conjunction “and” nor classical logical alternative “either…or” can replace “+” representing a linear superposition of two quantum states. Therefore, to provide a logical account of the quantum superposition, one must either reconsider the standard interpretation of quantum mechanics (making it fit for classical bivalent logic) or replace the standard logic with a deviant logic suitable for describing the superposition. In this paper, a supervaluation approach to the description of the quantum superposition is considered. In accordance with this approach, the indefinite propositions, which correspond to the superposition states, lack truth-values of any kind, even granting that their compounds (such as logical alternative “either…or”) can have truth-values. As an illustration, the supervaluationist account of the superposition of spin states is presented.

arXiv: Quantum Physics, 2016

The existence of higher than pairwise quantum interference in the set-up, in which there are more... more The existence of higher than pairwise quantum interference in the set-up, in which there are more than two slits, is currently under experimental investigation. However, it is still unclear what the confirmation of existence of such interference would mean for quantum theory -- whether that usual quantum mechanics is merely a limiting case of some more general theory or whether that some assumption of quantum theory taken as a fundamental one does not actually hold true. The present paper tries to understand why quantum theory is limited only to a certain kind of interference.

Foundations of Physics, 2021

The traditional analysis of the basic version of the double-slit experiment leads to the conclusi... more The traditional analysis of the basic version of the double-slit experiment leads to the conclusion that wave-particle duality is a fundamental fact of nature. However, such a conclusion means to imply that we are not only required to have two contradictory pictures of reality but also compelled to abandon the objectiveness of the truth values, "true" and "false". Yet, even if we could accept wave-like behavior of quantum particles as the best explanation for the build-up of an interference pattern in the double-slit experiment, without the objectivity of the truth values we would never have certainty regarding any statement about the world. The present paper discusses ways to reconcile the correct description of the double-slit experiment with the objectiveness of "true" and "false".

Quantum Studies: Mathematics and Foundations, 2018

In the paper, it is argued that the phenomenon known as the quantum pigeonhole principle (namely,... more In the paper, it is argued that the phenomenon known as the quantum pigeonhole principle (namely, three quantum particles are put in two boxes, yet no two particles are in the same box) can be explained not as a violation of Dirichlet's box principle in the case of quantum particles but as a nonvalidness of a bivalent logic for describing not-yet verified propositions relating to quantum mechanical experiments.

Applied Physics Research, 2015

Unlike mathematics, in which the notion of truth might be abstract, in physics, the emphasis must... more Unlike mathematics, in which the notion of truth might be abstract, in physics, the emphasis must be placed on algorithmic procedures for obtaining numerical results subject to the experimental verifiability. For, a physical science is exactly that: algorithmic procedures (built on a certain mathematical formalism) for obtaining verifiable conclusions from a set of basic hypotheses. By admitting non-constructivist statements a physical theory loses its concrete applicability and thus verifiability of its predictions. Accordingly, the requirement of constructivism must be indispensable to any physical theory. Nevertheless, in at least some physical theories, and especially in quantum mechanics, one can find examples of non-constructive statements. The present paper demonstrates a couple of such examples dealing with macroscopic quantum states (i.e., with the applicability of the standard quantum formalism to macroscopic systems). As it is shown, in these examples the proofs of the existence of macroscopic quantum states are based on logical principles allowing one to decide the truth of predicates over an infinite number of things.

arXiv: Quantum Physics, 2019

The failure of distributivity in quantum logic is motivated by the principle of quantum superposi... more The failure of distributivity in quantum logic is motivated by the principle of quantum superposition. However, this principle can be encoded differently, i.e., in different logical-algebraic objects. As a result, the logic of experimental quantum propositions might have various semantics: e.g., a semantics, in which the distributive law of propositional logic fails (quantum logic), or a semantics, in which this law holds but the valuation relation -- i.e., the function from atomic propositions into the set of two objects, true and false -- is not total (called supervaluationism). Consequently, closed linear subspaces of a Hilbert space (representing experimental quantum propositions) could be organized in different structures -- i.e., a Hilbert lattice (or its generalizations) identified with quantum logic, or a collection of invariant-subspace lattices (Boolean blocks of contexts) identified with the supervaluational semantics. Then again, because one can verify simultaneously onl...

arXiv: Quantum Physics, 2020

Within context of quantum logic, it is possible to assign dispersion-free probabilities to experi... more Within context of quantum logic, it is possible to assign dispersion-free probabilities to experimental propositions pertaining to qubits. This makes qubits distinct from the rest of quantum systems since the latter do not admit probabilities having only values 0 and 1. The present paper shows that erasing qubit discrimination leads to a model of computation which permits execution of many primitive operations in a massive parallel way. In the paper, it is demonstrated that such a model (that can be called a quantum parallel random-access machine, QPRAM) is quantum mechanically plausible.

New England Journal of Medicine, 2008

In many ways, biomedical analysis is analogous to possibilistic reasoning. In spite of that, ther... more In many ways, biomedical analysis is analogous to possibilistic reasoning. In spite of that, there are hardly any applications of possibility theory in biology or medicine. The aim of this work is to demonstrate the use of possibility theory in an epidemiological study. In the paper, we build the possibility distribution for the controlled bloodstream concentrations of any physiologically active substance through few approximate considerations. This possibility distribution is tested later against the empirical histograms obtained from the panel study of the eight different physiologically active substances in 417 individuals.

One-way functions are functions that are easy to compute but hard to invert. Their existence is a... more One-way functions are functions that are easy to compute but hard to invert. Their existence is an open conjecture; it would imply the existence of intractable problems (i.e. NP-problems which are not in the P complexity class). If true, the existence of one-way functions would have an impact on the theoretical framework of physics, in particularly, quantum mechanics. Such aspect of one-way functions has never been shown before. In the present work, we put forward the following. We can calculate the microscopic state (say, the particle spin in the z direction) of a macroscopic system (a measuring apparatus registering the particle z-spin) by the system macroscopic state (the apparatus output); let us call this association the function F. The question is: can we compute the function F in the inverse direction? In other words, can we compute the macroscopic state of the system through its microscopic state (the preimage F -1)? In the paper, we assume that the function F is a one-way f...

arXiv: Quantum Physics, 2019

In the statement "The vector is an element of the closed linear subspace of the Hilbert spac... more In the statement "The vector is an element of the closed linear subspace of the Hilbert space H", the predicate "... is an element of ..." might be not only determined, that is, either true or false (depending on whether set membership is applicable or inapplicable to the specified vector and subspace) but also undetermined, that is, neither true nor false. To evaluate the vagueness of set membership among arbitrary vectors and closed linear subspaces of H, the notion of the entropy of the predicate "... is an element of ..." is introduced in the present paper. Since each closed linear subspace in H uniquely represents the atomic proposition P about a quantum system, the entropy of this predicate can also be considered as the valuational entropy that measures the uncertainty about the assignment of truth values to the proposition P. As it is demonstrated in the paper, in the Hilbert space H of the dimension greater than or equal to 2, there always exist...

arXiv: Quantum Physics, 2016

In the present paper, the decision problem of the Schrodinger equation (asking whether or not a g... more In the present paper, the decision problem of the Schrodinger equation (asking whether or not a given Hamiltonian operator has the nonempty solution set) is represented as a logical statement. As it is shown in the paper, the law of excluded middle would be applicable to the introduced statement if and only if quantum fundamentalism (asserting that everything in the universe is ultimately describable in quantum-mechanical terms) held. But, since the decision problem of the Schrodinger equation is in general undecidable, such a statement is allowed to be other than true or false, explicitly, it may fail to have truth values at all. This makes possible to abandon the law of excluded middle together with quantum fundamentalism in the proposed intuitionistic interpretation of quantum mechanics.

arXiv: Quantum Physics, 2018

In quantum logic, i.e., within the structure of the Hilbert lattice imposed on all closed linear ... more In quantum logic, i.e., within the structure of the Hilbert lattice imposed on all closed linear subspaces of a Hilbert space, the assignment of truth values to quantum propositions (i.e., experimentally verifiable propositions relating to a quantum system) is unambiguously determined by the state of the system. So, if only pure states of the system are considered, can a probability measure mapping the probability space for truth values to the unit interval be assigned to quantum propositions? In other words, is a probability concept contingent or emergent in the logic of quantum propositions? Until this question is answered, the cause of probabilities in quantum theory cannot be completely understood. In the present paper it is shown that the interaction of the quantum system with its environment causes the irreducible randomness in the relation between quantum propositions and truth values.

arXiv: Quantum Physics, 2018

In the paper it is shown that the Kochen-Specker theorem follows from Burnside's theorem on n... more In the paper it is shown that the Kochen-Specker theorem follows from Burnside's theorem on noncommutative algebras. Accordingly, contextuality (as an impossibility of assigning binary values to projection operators independently of their contexts) is merely an inference from Burnside's fundamental theorem of the algebra of linear transformations on a Hilbert space of finite dimension.

arXiv: Quantum Physics, 2017

In the paper it is argued that the Kochen-Specker theorem necessitates a conclusion that for a qu... more In the paper it is argued that the Kochen-Specker theorem necessitates a conclusion that for a quantum system it is possible to find a set of projection operators which is not truth-value bivalent; that is, a bivalent truth-value assignment function imposed on such a set cannot be total. This means that at least one proposition associated with the said set must be neither true nor false.

arXiv: Quantum Physics, 2019

Of what are experimental quantum propositions primary bearers? As it is widely accepted in the mo... more Of what are experimental quantum propositions primary bearers? As it is widely accepted in the modern literature, rather than being bearers of truth and falsity, these entities are bearers of probability values. Consequently, their truth values can be regarded as no more than degenerate probabilities (i.e., ones that have only the values 0 and 1). The mathematical motivation for precedence of probabilistic semantics over propositional semantic for the logic of experimental quantum propositions is Gleason's theorem. It proves that the theory of probability measures on closed linear subspaces of a Hilbert space (which represent experimental quantum propositions) does not admit any probability measure having only the values 0 and 1. -- By contrast, in the present paper, it is proclaimed that experimental propositions about quantum systems are primary bearers of truth values. As this paper demonstrates, algebraic properties of separable Hilbert spaces of finite dimension equal or gr...

In the paper, the EPR paradox is explored by the approach of quantum supervaluationism that leads... more In the paper, the EPR paradox is explored by the approach of quantum supervaluationism that leads to a "gappy" semantics with the propositions giving rise to truth-value gaps. Within this approach, the statement, which asserts that in the singlet state the system of two (i.e., A and B) spin-1/2 particles possesses the a priori property "spin A is up and spin B is down along the same axis" or "spin A is down and spin B is up along the same axis", does not have the truth-value at all. Consequently, after the verification of, say, the proposition "spin A is up along the z-axis", the statistical population describing the valuation of the logical connective "spin B is down along the z-axis and spin B is up (down) along the x-axis" would have no elements.

arXiv (Cornell University), Dec 6, 2022

The stipulation that no measurable quantity could have an infinite value is indispensable in phys... more The stipulation that no measurable quantity could have an infinite value is indispensable in physics. At the same time, in mathematics, the possibility of considering an infinite procedure as a whole is usually taken for granted. However, not only does such possibility run counter to computational feasibleness, but it also leads to the most serious problem in modern physics, to wit, the emergence of infinities in calculated physical quantities. Particularly, having agreed on the axiom of infinity for set theory-the backbone of the theoretical foundations of calculus integrated in every branch of physics-one could no longer rule out the existence of a classical field theory which is not quantizable, let alone renormalizable. By contrast, the present paper shows that negating the axiom of infinity results in physics acting in a finite geometry where it is ensured that all classical field theories are quantizable.

arXiv (Cornell University), May 16, 2019

A common way of stating the non-cloning theorem-one of distinguishing characteristics of quantum ... more A common way of stating the non-cloning theorem-one of distinguishing characteristics of quantum theory-is that one cannot make a copy of an arbitrary unknown quantum state. Even though this theorem is an important part of the ongoing discussion of the nature of a quantum state, the role of the theorem in the logical-algebraic approach to quantum theory has not yet been systematically studied. According to the standard point of view (which is in line with the logical tradition), quantum cloning amounts to two classical rules of inference, namely, monotonicity and idempotency of entailment. One can conclude then that the whole of quantum theory should be described through a logic wherein these rules do not hold, which is linear logic. However, in accordance with a supervaluational semantics (that allows one to retain all the theorems of classical logic while admitting "truth-value gaps"), quantum cloning necessitates the permanent loss of the truth values of experimental quantum propositions which violates the unalterability of the past. The present paper demonstrates this.

arXiv (Cornell University), May 8, 2018

In contrast to conjunctions of commutable projection operators unambiguously represented by their... more In contrast to conjunctions of commutable projection operators unambiguously represented by their meets, the mathematical representation of conjunctions of incommutable projection operators is a question that has yet to be solved. This question relates to another asking whether the set of the column spaces of the projection operators, commutable and incommutable alike, forms a lattice. As it is demonstrated in the paper, if the Hilbert space is finite, the column spaces of the incommutable projection operators cannot be elements of one partially ordered set in accordance with Burnside's theorem on matrix algebras.

Journal of Mathematical Physics, 2017

As it is known, neither classical logical conjunction “and” nor classical logical alternative “ei... more As it is known, neither classical logical conjunction “and” nor classical logical alternative “either…or” can replace “+” representing a linear superposition of two quantum states. Therefore, to provide a logical account of the quantum superposition, one must either reconsider the standard interpretation of quantum mechanics (making it fit for classical bivalent logic) or replace the standard logic with a deviant logic suitable for describing the superposition. In this paper, a supervaluation approach to the description of the quantum superposition is considered. In accordance with this approach, the indefinite propositions, which correspond to the superposition states, lack truth-values of any kind, even granting that their compounds (such as logical alternative “either…or”) can have truth-values. As an illustration, the supervaluationist account of the superposition of spin states is presented.

arXiv: Quantum Physics, 2016

The existence of higher than pairwise quantum interference in the set-up, in which there are more... more The existence of higher than pairwise quantum interference in the set-up, in which there are more than two slits, is currently under experimental investigation. However, it is still unclear what the confirmation of existence of such interference would mean for quantum theory -- whether that usual quantum mechanics is merely a limiting case of some more general theory or whether that some assumption of quantum theory taken as a fundamental one does not actually hold true. The present paper tries to understand why quantum theory is limited only to a certain kind of interference.

Foundations of Physics, 2021

The traditional analysis of the basic version of the double-slit experiment leads to the conclusi... more The traditional analysis of the basic version of the double-slit experiment leads to the conclusion that wave-particle duality is a fundamental fact of nature. However, such a conclusion means to imply that we are not only required to have two contradictory pictures of reality but also compelled to abandon the objectiveness of the truth values, "true" and "false". Yet, even if we could accept wave-like behavior of quantum particles as the best explanation for the build-up of an interference pattern in the double-slit experiment, without the objectivity of the truth values we would never have certainty regarding any statement about the world. The present paper discusses ways to reconcile the correct description of the double-slit experiment with the objectiveness of "true" and "false".

Quantum Studies: Mathematics and Foundations, 2018

In the paper, it is argued that the phenomenon known as the quantum pigeonhole principle (namely,... more In the paper, it is argued that the phenomenon known as the quantum pigeonhole principle (namely, three quantum particles are put in two boxes, yet no two particles are in the same box) can be explained not as a violation of Dirichlet's box principle in the case of quantum particles but as a nonvalidness of a bivalent logic for describing not-yet verified propositions relating to quantum mechanical experiments.

Applied Physics Research, 2015

Unlike mathematics, in which the notion of truth might be abstract, in physics, the emphasis must... more Unlike mathematics, in which the notion of truth might be abstract, in physics, the emphasis must be placed on algorithmic procedures for obtaining numerical results subject to the experimental verifiability. For, a physical science is exactly that: algorithmic procedures (built on a certain mathematical formalism) for obtaining verifiable conclusions from a set of basic hypotheses. By admitting non-constructivist statements a physical theory loses its concrete applicability and thus verifiability of its predictions. Accordingly, the requirement of constructivism must be indispensable to any physical theory. Nevertheless, in at least some physical theories, and especially in quantum mechanics, one can find examples of non-constructive statements. The present paper demonstrates a couple of such examples dealing with macroscopic quantum states (i.e., with the applicability of the standard quantum formalism to macroscopic systems). As it is shown, in these examples the proofs of the existence of macroscopic quantum states are based on logical principles allowing one to decide the truth of predicates over an infinite number of things.

arXiv: Quantum Physics, 2019

The failure of distributivity in quantum logic is motivated by the principle of quantum superposi... more The failure of distributivity in quantum logic is motivated by the principle of quantum superposition. However, this principle can be encoded differently, i.e., in different logical-algebraic objects. As a result, the logic of experimental quantum propositions might have various semantics: e.g., a semantics, in which the distributive law of propositional logic fails (quantum logic), or a semantics, in which this law holds but the valuation relation -- i.e., the function from atomic propositions into the set of two objects, true and false -- is not total (called supervaluationism). Consequently, closed linear subspaces of a Hilbert space (representing experimental quantum propositions) could be organized in different structures -- i.e., a Hilbert lattice (or its generalizations) identified with quantum logic, or a collection of invariant-subspace lattices (Boolean blocks of contexts) identified with the supervaluational semantics. Then again, because one can verify simultaneously onl...

arXiv: Quantum Physics, 2020

Within context of quantum logic, it is possible to assign dispersion-free probabilities to experi... more Within context of quantum logic, it is possible to assign dispersion-free probabilities to experimental propositions pertaining to qubits. This makes qubits distinct from the rest of quantum systems since the latter do not admit probabilities having only values 0 and 1. The present paper shows that erasing qubit discrimination leads to a model of computation which permits execution of many primitive operations in a massive parallel way. In the paper, it is demonstrated that such a model (that can be called a quantum parallel random-access machine, QPRAM) is quantum mechanically plausible.

New England Journal of Medicine, 2008

In many ways, biomedical analysis is analogous to possibilistic reasoning. In spite of that, ther... more In many ways, biomedical analysis is analogous to possibilistic reasoning. In spite of that, there are hardly any applications of possibility theory in biology or medicine. The aim of this work is to demonstrate the use of possibility theory in an epidemiological study. In the paper, we build the possibility distribution for the controlled bloodstream concentrations of any physiologically active substance through few approximate considerations. This possibility distribution is tested later against the empirical histograms obtained from the panel study of the eight different physiologically active substances in 417 individuals.

One-way functions are functions that are easy to compute but hard to invert. Their existence is a... more One-way functions are functions that are easy to compute but hard to invert. Their existence is an open conjecture; it would imply the existence of intractable problems (i.e. NP-problems which are not in the P complexity class). If true, the existence of one-way functions would have an impact on the theoretical framework of physics, in particularly, quantum mechanics. Such aspect of one-way functions has never been shown before. In the present work, we put forward the following. We can calculate the microscopic state (say, the particle spin in the z direction) of a macroscopic system (a measuring apparatus registering the particle z-spin) by the system macroscopic state (the apparatus output); let us call this association the function F. The question is: can we compute the function F in the inverse direction? In other words, can we compute the macroscopic state of the system through its microscopic state (the preimage F -1)? In the paper, we assume that the function F is a one-way f...

arXiv: Quantum Physics, 2019

In the statement "The vector is an element of the closed linear subspace of the Hilbert spac... more In the statement "The vector is an element of the closed linear subspace of the Hilbert space H", the predicate "... is an element of ..." might be not only determined, that is, either true or false (depending on whether set membership is applicable or inapplicable to the specified vector and subspace) but also undetermined, that is, neither true nor false. To evaluate the vagueness of set membership among arbitrary vectors and closed linear subspaces of H, the notion of the entropy of the predicate "... is an element of ..." is introduced in the present paper. Since each closed linear subspace in H uniquely represents the atomic proposition P about a quantum system, the entropy of this predicate can also be considered as the valuational entropy that measures the uncertainty about the assignment of truth values to the proposition P. As it is demonstrated in the paper, in the Hilbert space H of the dimension greater than or equal to 2, there always exist...

arXiv: Quantum Physics, 2016

In the present paper, the decision problem of the Schrodinger equation (asking whether or not a g... more In the present paper, the decision problem of the Schrodinger equation (asking whether or not a given Hamiltonian operator has the nonempty solution set) is represented as a logical statement. As it is shown in the paper, the law of excluded middle would be applicable to the introduced statement if and only if quantum fundamentalism (asserting that everything in the universe is ultimately describable in quantum-mechanical terms) held. But, since the decision problem of the Schrodinger equation is in general undecidable, such a statement is allowed to be other than true or false, explicitly, it may fail to have truth values at all. This makes possible to abandon the law of excluded middle together with quantum fundamentalism in the proposed intuitionistic interpretation of quantum mechanics.

arXiv: Quantum Physics, 2018

In quantum logic, i.e., within the structure of the Hilbert lattice imposed on all closed linear ... more In quantum logic, i.e., within the structure of the Hilbert lattice imposed on all closed linear subspaces of a Hilbert space, the assignment of truth values to quantum propositions (i.e., experimentally verifiable propositions relating to a quantum system) is unambiguously determined by the state of the system. So, if only pure states of the system are considered, can a probability measure mapping the probability space for truth values to the unit interval be assigned to quantum propositions? In other words, is a probability concept contingent or emergent in the logic of quantum propositions? Until this question is answered, the cause of probabilities in quantum theory cannot be completely understood. In the present paper it is shown that the interaction of the quantum system with its environment causes the irreducible randomness in the relation between quantum propositions and truth values.

arXiv: Quantum Physics, 2018

In the paper it is shown that the Kochen-Specker theorem follows from Burnside's theorem on n... more In the paper it is shown that the Kochen-Specker theorem follows from Burnside's theorem on noncommutative algebras. Accordingly, contextuality (as an impossibility of assigning binary values to projection operators independently of their contexts) is merely an inference from Burnside's fundamental theorem of the algebra of linear transformations on a Hilbert space of finite dimension.

arXiv: Quantum Physics, 2017

In the paper it is argued that the Kochen-Specker theorem necessitates a conclusion that for a qu... more In the paper it is argued that the Kochen-Specker theorem necessitates a conclusion that for a quantum system it is possible to find a set of projection operators which is not truth-value bivalent; that is, a bivalent truth-value assignment function imposed on such a set cannot be total. This means that at least one proposition associated with the said set must be neither true nor false.

arXiv: Quantum Physics, 2019

Of what are experimental quantum propositions primary bearers? As it is widely accepted in the mo... more Of what are experimental quantum propositions primary bearers? As it is widely accepted in the modern literature, rather than being bearers of truth and falsity, these entities are bearers of probability values. Consequently, their truth values can be regarded as no more than degenerate probabilities (i.e., ones that have only the values 0 and 1). The mathematical motivation for precedence of probabilistic semantics over propositional semantic for the logic of experimental quantum propositions is Gleason's theorem. It proves that the theory of probability measures on closed linear subspaces of a Hilbert space (which represent experimental quantum propositions) does not admit any probability measure having only the values 0 and 1. -- By contrast, in the present paper, it is proclaimed that experimental propositions about quantum systems are primary bearers of truth values. As this paper demonstrates, algebraic properties of separable Hilbert spaces of finite dimension equal or gr...

In the paper, the EPR paradox is explored by the approach of quantum supervaluationism that leads... more In the paper, the EPR paradox is explored by the approach of quantum supervaluationism that leads to a "gappy" semantics with the propositions giving rise to truth-value gaps. Within this approach, the statement, which asserts that in the singlet state the system of two (i.e., A and B) spin-1/2 particles possesses the a priori property "spin A is up and spin B is down along the same axis" or "spin A is down and spin B is up along the same axis", does not have the truth-value at all. Consequently, after the verification of, say, the proposition "spin A is up along the z-axis", the statistical population describing the valuation of the logical connective "spin B is down along the z-axis and spin B is up (down) along the x-axis" would have no elements.