Related papers: Can many-valued logic help to comprehend quantum p…
Quantum theory's irreducible empirical core is a probability calculus. While it presupposes the events to which (and on the basis of which) it serves to assign probabilities, and therefore cannot account for their occurrence, it has to be…
The most peculiar, specifically quantum, features of quantum mechanics --- quantum nonlocality, indeterminism, interference of probabilities, quantization, wave function collapse during measurement --- are explained on a logical-geometrical…
Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and…
Quantum logic has been introduced by Birkhoff and von Neumann as an attempt to base the logical primitives, the propositions and the relations and operations among them, on quantum theoretical entities, and thus on the related empirical…
This essay is a two-step reflection on the question 'Which events (can be said to) occur in quantum phenomena?' The first step regiments the ontological category of "statistical phenomena" and studies the adequacy of "probabilistic event…
In recent years, quantum mechanics has been actively used in areas outside of physics, such as psychology, sociology, theory of decision-making, game theory, and others. In particular, quantum mechanics is used to explain the paradoxes…
Contextuality is a hallmark feature of the quantum theory that captures its incompatibility with any noncontextual hidden-variable model. The Greenberger--Horne--Zeilinger (GHZ)-type paradoxes are proofs of contextuality that reveal this…
In this work we first illustrate the subjective theory of de Finetti. We recall the notion of coherence for both the betting scheme and the penalty criterion, by considering the unconditional and conditional cases. We show the equivalence…
We introduce a logic for reasoning about evidence, that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete…
We introduce a logic for reasoning about evidence that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete…
There are many ways we can not know. Even in systems that we created ourselves, as, for example, systems in mathematical logic, Go\"edel and Tarski's theorems impose limits on what we can know. As we try to speak of the real world, things…
We study a real valued propositional logic with unbounded positive and negative truth values that we call R-valued logic. Such logic slightly extends continuous propositional logic which, in turn, builds on Lukasiewicz many-valued logic.…
Counterfactual reasoning plays a crucial role in exploring hypothetical scenarios, by comparing some consequent under conditions identical except as results from a differing antecedent. David Lewis' well-known analysis evaluates…
Why does such a successful theory like Quantum Mechanics have so many mysteries? The history of this theory is replete with dubious interpretations and controversies, and yet a knowledge of its predictions, however, contributed to the…
We investigate whether quantum theory can be understood as the continuum limit of a mechanical theory, in which there is a huge, but finite, number of classical 'worlds', and quantum effects arise solely from a universal interaction between…
I offer an account of how the quantum theory we have helps us explain so much. The account depends on a pragmatist interpretation of the theory: This takes a quantum state to serve solely as a source of sound advice to physically situated…
We present a propositional logic to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization…
We show how to construct Greenberger-Horn-Zeilinger type paradoxes for continuous variable systems. We give two examples corresponding to 3 party and 5 party paradoxes. The paradoxes are revealed by carrying out position and momentum…
We recently described a formalism for reasoning with if-then rules that re expressed with different levels of firmness [18]. The formalism interprets these rules as extreme conditional probability statements, specifying orders of magnitude…
If a quantum system is prepared and later post-selected in certain states, "paradoxical" predictions for intermediate measurements can be obtained. This is the case both when the intermediate measurement is strong, i.e. a projective…