arXiv subjects

Giulia Battilotti

Publications and source records attributed to Giulia Battilotti.

6 recordsLinked to original sources

arXiv2025

Establishing a pre-logical setting in a quantum model of psycho-analytic theory

A crucial issue both in cognitive and psychoanalytical theories deals with the origin of mental representations. In order to explore this issue, the paper analyzes a pre-logical setting, by considering a formalized approach to the foundations of psychoanalysis in logic, interpreting and integrating the views by Freud, Matte Blanco, Klein and Bion. The formalized approach derives from a quantum model of spin states. A representation of the spin state of a particle in first order logic is abstracted to get a modality interpretable as an abstract projector. The last can be decomposed into a positive, negative and irreal component. The irreal component cannot emerge and, in logic, is absorbed by the two others, giving rise to logical duality. Due to its treatment of undefiniteness and coherence, the paper is meant to contribute to quantum cognition, in its particular sense of affective quantum cognition.

physics.soc-ph↗

arXiv2013

Quantum states as virtual singletons: converting duality into symmetry

In a predicative framework from basic logic, defined for a model of quantum parallelism by sequents, we characterize a class of first order domains, termed {\em virtual singletons}, which allows a generalization of the notion of duality, termed {\em symmetry}. Although consistent with the classical notion of duality, symmetry creates an environment where negation has fixed points, for which the direction of logical consequence is irrelevant. Symmetry can model Bell's states. So, despite its nonsense in a traditional logical setting, symmetry can hide the peculiar advantage for the treatment of information, that is proper of quantum mechanics.

math.LO↗

arXiv2011

Characterization of quantum states in predicative logic

We develop a characterization of quantum states by means of first order variables and random variables, within a predicative logic with equality, in the framework of basic logic and its definitory equations. We introduce the notion of random first order domain and find a characterization of pure states in predicative logic and mixed states in propositional logic, due to a focusing condition. We discuss the role of first order variables and the related contextuality, in terms of sequents.

quant-ph↗

arXiv2005

Logical Interpretation of a Reversible Measurement in Quantum Computing

We give the logical description of a new kind of quantum measurement that is a reversible operation performed by an hypothetical insider observer, or, which is the same, a quantum measurement made in a quantum space background, like the fuzzy sphere. The result is that the non-contradiction and the excluded middle principles are both invalidated, leading to a paraconsistent, symmetric logic. Our conjecture is that, in this setting, one can develop the adequate logic of quantum computing. The role of standard quantum logic is then confined to describe the projective measurement scheme.

quant-ph↗

arXiv2004

The internal logic of Bell's states

We investigate the internal logic of a quantum computer with two qubits, in the two particular cases of non-entanglement (separable states) and maximal entanglement (Bell's states). To this aim, we consider an internal (reversible) measurement which preserves the probabilities by mirroring the states. We then obtain logical judgements for both cases of separable and Bell's states.

quant-ph↗

arXiv2004

Basic Logic and Quantum Computing: Logical Judgements by an Insider Observer

We consider the logical assertions of a hypothetical observer who is inside a quantum computer and performs a reversible quantum measurement, obtaining a symmetric couple of new axioms, valid only inside the quantum computer. The result is that, in this logical framework, symmetry and paraconsistency hold.

quant-ph↗