Related papers: A Quantum Logic of Down Below

The unification of low-level perception and high-level reasoning is a long-standing problem in artificial intelligence, which has the potential to not only bring the areas of logic and learning closer together but also demonstrate how…

The ontology proposed in this paper is aimed at demonstrating that it is possible to understand the counter-intuitive predictions of quantum mechanics while still retaining much of the framework underlying classical physics, the implication…

We show that in quantum logic of closed subspaces of Hilbert space one cannot substitute quantum operations for classical (standard Hilbert space) ones and treat them as primitive operations. We consider two possible ways of such a…

Quantum measurement theory is applied to quantum-like modeling of coherent generation of perceptions and emotions and generally for emotional coloring of conscious experiences. In quantum theory, a system should be separated from an…

We can recognize two modes in which 'quantum appears' in macro domains: (i) a 'micro-physical appearance', where quantum laws are assumed to be universal and they are transferred from the micro to the macro level if suitable 'quantum…

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…

Physical symbol systems are needed for open-ended cognition. A good way to understand physical symbol systems is by comparison of thought to chemistry. Both have systematicity, productivity and compositionality. The state of the art in…

Quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister, a system of qubits, representing a…

Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of…

A decade ago, Isham and Butterfield proposed a topos-theoretic approach to quantum mechanics, which meanwhile has been extended by Doering and Isham so as to provide a new mathematical foundation for all of physics. Last year, three of the…

A logical model of spatiotemporal structures is pictured as a succession of processes in time. One usual way to formalize time structure is to assume the global existence of time points and then collect some of them to form time intervals…

We show that the modern quantum mechanics, and particularly the theory of decoherence, allows formulating a sort of a physical metatheory of consciousness. Particularly, the analysis of the necessary conditions for the occurrence of…

In this paper we consider the phenomenon of superpositions in quantum mechanics and suggest a way to deal with the idea in a logical setting from a syntactical point of view, that is, as subsumed in the language of the formalism, and not…

The interpretation of quantum mechanics has been a problem since its founding days. A large contribution to the discussion of possible interpretations of quantum mechanics is given by the so-called impossibility proofs for hidden variable…

We use classes of Hilbert lattice equations for an alternative representation of Hilbert lattices and Hilbert spaces of arbitrary quantum systems that might enable a direct introduction of the states of the systems into quantum computers.…

A general approach describing quantum decision procedures is developed. The approach can be applied to quantum information processing, quantum computing, creation of artificial quantum intelligence, as well as to analyzing decision…

Orthomodular logic is a weakening of quantum logic in the sense of Birkhoff and von Neumann. Orthomodular logic is shown to be a nonlinear noncommutative logic. Sequents are given a physically motivated semantics that is consistent with…

We consider categorical logic on the category of Hilbert spaces. More generally, in fact, any pre-Hilbert category suffices. We characterise closed subobjects, and prove that they form orthomodular lattices. This shows that quantum logic is…

Our aim in this paper is to take quite seriously Heinz Post's claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry…

Nonreflexive quantum mechanics is a formulation of quantum theory based on a non-classical logic termed \ita{nonreflexive logic} (a.k.a. `non-reflexive'). In these logics, the standard notion of identity, as encapsulated in classical logic…