5,605 research outputs found
Categories for Dynamic Epistemic Logic
The primary goal of this paper is to recast the semantics of modal logic, and
dynamic epistemic logic (DEL) in particular, in category-theoretic terms. We
first review the category of relations and categories of Kripke frames, with
particular emphasis on the duality between relations and adjoint homomorphisms.
Using these categories, we then reformulate the semantics of DEL in a more
categorical and algebraic form. Several virtues of the new formulation will be
demonstrated: The DEL idea of updating a model into another is captured
naturally by the categorical perspective -- which emphasizes a family of
objects and structural relationships among them, as opposed to a single object
and structure on it. Also, the categorical semantics of DEL can be merged
straightforwardly with a standard categorical semantics for first-order logic,
providing a semantics for first-order DEL.Comment: In Proceedings TARK 2017, arXiv:1707.0825
Stochastic Relational Presheaves and Dynamic Logic for Contextuality
Presheaf models provide a formulation of labelled transition systems that is
useful for, among other things, modelling concurrent computation. This paper
aims to extend such models further to represent stochastic dynamics such as
shown in quantum systems. After reviewing what presheaf models represent and
what certain operations on them mean in terms of notions such as internal and
external choices, composition of systems, and so on, I will show how to extend
those models and ideas by combining them with ideas from other
category-theoretic approaches to relational models and to stochastic processes.
It turns out that my extension yields a transitional formulation of
sheaf-theoretic structures that Abramsky and Brandenburger proposed to
characterize non-locality and contextuality. An alternative characterization of
contextuality will then be given in terms of a dynamic modal logic of the
models I put forward.Comment: In Proceedings QPL 2014, arXiv:1412.810
Topos Semantics for Higher-Order Modal Logic
We define the notion of a model of higher-order modal logic in an arbitrary
elementary topos . In contrast to the well-known interpretation of
(non-modal) higher-order logic, the type of propositions is not interpreted by
the subobject classifier , but rather by a suitable
complete Heyting algebra . The canonical map relating and
both serves to interpret equality and provides a modal
operator on in the form of a comonad. Examples of such structures arise
from surjective geometric morphisms , where . The logic differs from non-modal higher-order
logic in that the principles of functional and propositional extensionality are
no longer valid but may be replaced by modalized versions. The usual Kripke,
neighborhood, and sheaf semantics for propositional and first-order modal logic
are subsumed by this notion
Multiresolution approximation of the vector fields on T^3
Multiresolution approximation (MRA) of the vector fields on T^3 is studied.
We introduced in the Fourier space a triad of vector fields called helical
vectors which derived from the spherical coordinate system basis. Utilizing the
helical vectors, we proved the orthogonal decomposition of L^2(T^3) which is a
synthesis of the Hodge decomposition of the differential 1- or 2-form on T^3
and the Beltrami decomposition that decompose the space of solenoidal vector
fields into the eigenspaces of curl operator. In the course of proof, a general
construction procedure of the divergence-free orthonormal complete basis from
the basis of scalar function space is presented. Applying this procedure to MRA
of L^2(T^3), we discussed the MRA of vector fields on T^3 and the analyticity
and regularity of vector wavelets. It is conjectured that the solenoidal
wavelet basis must break r-regular condition, i.e. some wavelet functions
cannot be rapidly decreasing function because of the inevitable singularities
of helical vectors. The localization property and spatial structure of
solenoidal wavelets derived from the Littlewood-Paley type MRA (Meyer's
wavelet) are also investigated numerically.Comment: LaTeX, 33 Pages, 3 figures. submitted to J. Math. Phy
Reflexive Binding and Attitudes de se
In this paper we develop an analysis of reflexive binding involving the reflexive zibun in Japanese. We argue that the reflexive zibun is bound by a POV (point of view) holder that minimally c-commands zibun. The POV holder is defined as an argument (typically subject and Experiencer) that can be a locus of de se belief. Some predicates are incapable of hosting POV holders thus defined in combination with zibun and we call such predicates \u27anti-reflexive\u27 predicates, which are marked as such in the lexicon. De se interpretation plays a key role in both local and long distance binding of zibun
ミクロ柔軟細孔を有する配位高分子の合成および混合ガスからのエチレン分離
京都大学0048新制・論文博士博士(工学)乙第12846号論工博第4103号新制||工||1601(附属図書館)31429(主査)教授 北川 進, 教授 杉野目 道紀, 教授 松田 建児学位規則第4条第2項該当Doctor of Philosophy (Engineering)Kyoto UniversityDGA
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