Related papers: New Directions in Categorical Logic, for Classical…
It is shown how a C*-algebra representation of the transformations of a physical system can be derived from two operational postulates: 1) the existence of dynamically independent systems}; 2) the existence of symmetric faithful states.…
From the existence of an efficient quantum algorithm for factoring, it is likely that quantum computation is intrinsically more powerful than classical computation. At present, the best upper bound known for the power of quantum computation…
A hallmark of human cognition is the ability to continually acquire and distill observations of the world into meaningful, predictive theories. In this paper we present a new mechanism for logical theory acquisition which takes a set of…
The principle of tomographic locality states that the operational state of a multipartite system can be fully characterized by the statistics obtained from measurements that are local to the individual subsystems. This property holds in…
This paper uncovers the fundamental relationship between total and partial computation in the form of an equivalence of certain categories. This equivalence involves on the one hand effectuses, which are categories for total computation,…
Categorical quantum mechanics studies quantum theory in the framework of dagger-compact closed categories. Using this framework, we establish a tight relationship between two key quantum theoretical notions: non-locality and…
Various effects in human cognition, often considered `non-classical', have been argued to be most naturally modelled by quantum-like models of decision making. We extend this approach to describe models of cognition and decision-making in…
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…
We stress the notion of statistical experiment, which is mandatory for quantum mechanics, and recall Ludwig's foundation of quantum mechanics, which provides the most general framework to deal with statistical experiments giving evidence…
We present natural deduction systems and associated modal lambda calculi for the necessity fragments of the normal modal logics K, T, K4, GL and S4. These systems are in the dual-context style: they feature two distinct zones of…
The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events. The paper is divided into two parts. In…
The subjective and the objective aspects of probabilities are incorporated in a simple duality axiom inspired by observer participation in quantum theory. Transcending the classical notion of probabilities, it is proposed and demonstrated…
We prove a theorem which shows that a collection of experimental data of probabilistic weights related to decisions with respect to situations and their disjunction cannot be modeled within a classical probabilistic weight structure in case…
We give a rigorous formulation of the intuitive idea that a differentiable map should be thesame thing as a locally, or infinitesimally, linear map: just as a linear map respects the operations of addition and multiplication by scalars ina…
A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…
The concept of complementarity in combination with a non-Boolean calculus of propositions refers to a pivotal feature of quantum systems which has long been regarded as a key to their distinction from classical systems. But a non-Boolean…
In order to reason about effects, we can define quantitative formulas to describe behavioural aspects of effectful programs. These formulas can for example express probabilities that (or sets of correct starting states for which) a program…
In a recent work, arXiv:2503.05884, we proposed a unified notion of nonclassicality that applies to arbitrary processes in quantum theory, including individual quantum states, measurements, channels, set of these, etc. This notion is…
Unitary quantum theory, having no Born Rule, is non-probabilistic. Hence the notorious problem of reconciling it with the unpredictability and appearance of stochasticity in quantum measurements. Generalising and improving upon the…