Related papers: Can many-valued logic help to comprehend quantum p…
The linear mathematics of quantum mechanics gives many versions of reality instead of the single version we perceive, with the perceived version chosen at random according to a probability law. Because of these peculiarities, the theory…
According to Heisenberg's uncertainty relation, there is an ultimate limit to how precisely we may predict the outcome of position and momentum measurements on a quantum system. We show that this limit may be violated by an arbitrarily…
This paper builds on a recent article co-authored by the present author, H. Hosni and F. Montagna. It is meant to contribute to the logical foundations of probability theory on many-valued events and, specifically, to a deeper understanding…
We propose a conjugate logic that can capture the behavior of quantum and quantum-like systems. The proposal is similar to the more generic concept of epistemic logic: it encodes knowledge or perhaps more correctly, predictions about…
We review recent work that employs the framework of logical inference to establish a bridge between data gathered through experiments and their objective description in terms of human-made concepts. It is shown that logical inference…
After a brief digression on the current landscape of theoretical physics and on some open questions pertaining to coherence with experimental results, still to be settled, it is shown that the properties of the Deformed Minkowski space lead…
In human consciousness perceptions are distinct or atomistic events despite being perceived by an apparently undivided inner observer. This paper applies both classical (Boolean) and quantum logic to analysis of the Liar paradox which is…
The best mathematical arguments against a realistic interpretation of quantum mechanics - that gives definite but partially unknown values to all observables - are analysed and shown to be based on reasoning that is not compelling. This…
We combine the concepts of modal logics and many-valued logics in a general and comprehensive way. Namely, given any finite linearly ordered set of truth values and any set of propositional connectives defined by truth tables, we define the…
Many seemingly paradoxical effects are known in the predictions for outcomes of measurements made on pre- and post-selected quantum systems. A class of such effects, which we call ``logical pre- and post-selection paradoxes'', bear a…
We develop a general, non-probabilistic model of prediction which is suitable for assessing the (un)predictability of individual physical events. We use this model to provide, for the first time, a rigorous proof of the unpredictability of…
To understand the foundations of quantum mechanics, we have to think carefully about how theoretical concepts are rooted in -- and limited by -- the nature of experience, as Bohr attempted to show. Geometrical pictures of physical phenomena…
Anhomomorphic logic is a new interpretation of Quantum Theory (due to R. Sorkin). It is a histories formulation (c.f. consistent histories, quantum measure theory). In this approach, reality is a co-event, which is essentially an assignment…
We present a propositional logic %which can be used 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…
We analyze a single-particle Mach-Zehnder interferometer experiment in which the path length of one arm may change (randomly or systematically) according to the value of an external two-valued variable $x$, for each passage of a particle…
Applications of quantum mechanics have led to many successful predictions and explanations of puzzling phenomena, and we now apply quantum mechanics to gain, process, and communicate information in novel ways. We can understand quantum…
The paper explores properties of {\L}ukasiewicz mu-calculus, a version of the quantitative/probabilistic modal mu-calculus containing both weak and strong conjunctions and disjunctions from {\L}ukasiewicz (fuzzy) logic. We show that this…
Human agents happen to judge that a conjunction of two terms is more probable than one of the terms, in contradiction with the rules of classical probabilities---this is the conjunction fallacy. One of the most discussed accounts of this…
One of quantum theory's salient features is its apparent indeterminism, i.e. measurement outcomes are typically probabilistic. We formally define and address whether this uncertainty is unavoidable or whether post-quantum theories can offer…
We design an expansion of Belnap--Dunn logic with belief and plausibility functions that allow non-trivial reasoning with inconsistent and incomplete probabilistic information. We also formalise reasoning with non-standard probabilities and…