34,273 research outputs found
"Modes of the universe" study of two-photon deterministic, passive quantum logical gates
We use the "modes of the universe" approach to study a cavity-mediated
two-photon logical gate recently proposed by Koshino, Ishizaka and Nakamura. We
clarify the relationship between the more commonly used input-output formalism,
and that of Koshino et al., and show that some elements of this gate had been
anticipated by other authors. We conclude that their proposed gate can work
both in the good and bad cavity limits, provided only that the pulses are long
enough. Our formalism allows us to estimate analytically the size of the
various error terms, and to follow the spectral evolution of the field + cavity
system in the course of the interaction.Comment: 9 pages, 8 figure
Takeuti's proof theory in the context of the Kyoto School
Gaisi Takeuti (1926–2017) is one of the most distinguished logicians in proof theory after Hilbert and Gentzen. He extensively extended Hilbert's program in the sense that he formulated Gentzen's sequent calculus, conjectured that cut-elimination holds for it (Takeuti's conjecture), and obtained several stunning results in the 1950–60s towards the solution of his conjecture. Though he has been known chiefly as a great mathematician, he wrote many papers in English and Japanese where he expressed his philosophical thoughts. In particular, he used several keywords such as "active intuition" and "self-reflection" from Nishida's philosophy. In this paper, we aim to describe a general outline of our project to investigate Takeuti's philosophy of mathematics. In particular, after reviewing Takeuti's proof-theoretic results briefly, we describe some key elements in Takeuti's texts. By explaining these texts, we point out the connection between Takeuti's proof theory and Nishida's philosophy and explain the future goals of our project
The ERA of FOLE: Superstructure
This paper discusses the representation of ontologies in the first-order
logical environment FOLE (Kent 2013). An ontology defines the primitives with
which to model the knowledge resources for a community of discourse (Gruber
2009). These primitives, consisting of classes, relationships and properties,
are represented by the ERA (entity-relationship-attribute) data model (Chen
1976). An ontology uses formal axioms to constrain the interpretation of these
primitives. In short, an ontology specifies a logical theory. This paper is the
second in a series of three papers that provide a rigorous mathematical
representation for the ERA data model in particular, and ontologies in general,
within the first-order logical environment FOLE. The first two papers show how
FOLE represents the formalism and semantics of (many-sorted) first-order logic
in a classification form corresponding to ideas discussed in the Information
Flow Framework (IFF). In particular, the first paper (Kent 2015) provided a
"foundation" that connected elements of the ERA data model with components of
the first-order logical environment FOLE, and this second paper provides a
"superstructure" that extends FOLE to the formalisms of first-order logic. The
third paper will define an "interpretation" of FOLE in terms of the
transformational passage, first described in (Kent 2013), from the
classification form of first-order logic to an equivalent interpretation form,
thereby defining the formalism and semantics of first-order logical/relational
database systems (Kent 2011). The FOLE representation follows a conceptual
structures approach, that is completely compatible with Formal Concept Analysis
(Ganter and Wille 1999) and Information Flow (Barwise and Seligman 1997)
Proposition structure in framed decision problems: A formal representation.
Framing effects, which may induce decision-makers to demonstrate preference description invariance violation for logically equivalent options varying in semantic emphasis, are an economically significant decision bias and an active area of research. Framing is an issue inter alia for the way in which options are presented in stated-choice studies where (often inadvertent) semantic emphasis may impact on preference responses. While research into both espoused preference effects and its cognitive substrate is highly active, interpretation and explanation of preference anomalies is beset by variation in the underlying structure of problems and latitude for decision-maker elaboration. A formal, general scheme for making transparent the parameter and proposition structure of framed decision stimuli is described. Interpretive and cognitive explanations for framing effects are reviewed. The formalism’s potential for describing extant, generating new stimulus tasks, detailing decision-maker task elaboration. The approach also provides a means of formalising stated-choice response stimuli and provides a metric of decision stimuli complexity. An immediate application is in the structuring of stated-choice test instruments
Arnošt Kolman’s Critique of Mathematical Fetishism
Arnošt Kolman (1892–1979) was a Czech mathematician, philosopher and Communist official. In this paper, we would like to look at Kolman’s arguments against logical positivism which revolve around the notion of the fetishization of mathematics. Kolman derives his notion of fetishism from Marx’s conception of commodity fetishism. Kolman is aiming to show the fact that an entity (system, structure, logical construction) acquires besides its real existence another formal existence. Fetishism means the fantastic detachment of the physical characteristics of real things or phenomena from these things. We identify Kolman’s two main arguments against logical positivism. In the first argument, Kolman applied Lenin’s arguments against Mach’s empiricism-criticism onto Russell’s neutral monism, i.e. mathematical fetishism is internally related to political conservativism. Kolman’s second main argument is that logical and mathematical fetishes are epistemologically deprived of any historical and dynamic dimension. In the final parts of our paper we place Kolman’s thinking into the context of his time, and furthermore we identify some tenets of mathematical fetishism appearing in Alain Badiou’s mathematical ontology today
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