Results 1 to 10 of about 7,196 (114)

Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism [PDF]

, 2019
This essay examines the philosophical significance of $\Omega$-logic in Zermelo-Fraenkel set theory with choice (ZFC). The duality between coalgebra and algebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras.
A Baltag, A Kanamori, A Kanamori, A Kanamori, A Kanamori, A Kurz, A Wilson, C Chihara, C Rittberg, C Wright, C Wright, C Wright, C Wright, C Wright, D Deutsch, D Deutsch, D Lewis, D Wallace, F Arntzenius, G Frege, G Marcus, G Uzquiano, H Putnam, H Rasiowa, J Hawthorne, J McKinsey, K Fine, L Henkin, M Dummett, M Takeuchi, Michael Rescorla, P Koellner, P Lewis, P Maddy, P Maddy, S Saunders, S Shapiro, S Shapiro, T Jech, T Lando, V Halbach, W Reinhardt, WH Woodin, WV Quine, Y Venema, Y Venema   +45 more
core   +9 more sources

Strongly Complete Logics for Coalgebras [PDF]

, 2012
Coalgebras for a functor model different types of transition systems in a uniform way. This paper focuses on a uniform account of finitary logics for set-based coalgebras.
Alexander Kurz, Jiri Rosicky, Yde Venema
core   +3 more sources

Stone-Type Dualities for Separation Logics [PDF]

, 2019
Stone-type duality theorems, which relate algebraic and relational/topological models, are important tools in logic because -- in addition to elegant abstraction -- they strengthen soundness and completeness to a categorical equivalence, yielding a ...
Docherty, Simon, Pym, David
core   +2 more sources

Orthomodular-Valued Models for Quantum Set Theory [PDF]

, 2017
In 1981, Takeuti introduced quantum set theory by constructing a model of set theory based on quantum logic represented by the lattice of closed linear subspaces of a Hilbert space in a manner analogous to Boolean-valued models of set theory, and showed ...
Araki, Bruns, Cohen, Dirac, Husimi, Johnstone, Kalmbach, MASANAO OZAWA, Pulmannová, Sasaki, Scott, von Neumann   +11 more
core   +2 more sources

The complexity of the list homomorphism problem for graphs [PDF]

, 2010
We completely classify the computational complexity of the list H-colouring problem for graphs (with possible loops) in combinatorial and algebraic terms: for every graph H the problem is either NP-complete, NL-complete, L-complete or is first-order ...
Egri, Laszlo, Krokhin, Andrei, Larose, Benoit, Tesson, Pascal   +3 more
core   +4 more sources

New Directions in Categorical Logic, for Classical, Probabilistic and Quantum Logic [PDF]

, 2014
Intuitionistic logic, in which the double negation law not-not-P = P fails, is dominant in categorical logic, notably in topos theory. This paper follows a different direction in which double negation does hold.
Bart Jacobs, Prakash Panangaden
core   +4 more sources

Topos theory and `neo-realist' quantum theory

, 2007
Topos theory, a branch of category theory, has been proposed as mathematical basis for the formulation of physical theories. In this article, we give a brief introduction to this approach, emphasising the logical aspects.
A. Döring, B. Banaschewski, C. J. Isham, C. J. Isham, C. J. Isham, C. J. Isham, C. J. Isham, C. J. Isham, F. W. Lawvere, G. Birkhoff, J. L. Bell, J. Lambek, M. H. Stone, M. P. Olson, P. T. Johnstone, P. T. Johnstone, R. Goldblatt, R. V. Kadison, S. Kochen, S. M. Lane, S. M. Lane   +20 more
core   +2 more sources

Information completeness in Nelson algebras of rough sets induced by quasiorders

, 2012
In this paper, we give an algebraic completeness theorem for constructive logic with strong negation in terms of finite rough set-based Nelson algebras determined by quasiorders. We show how for a quasiorder $R$, its rough set-based Nelson algebra can be
A. Sendlewski, A.H. Stone, D. Nelson, D. Vakarelov, D.M. Gabbay, G. Kreisel, H. Rasiowa, J. Barwise, J. Järvinen, J. Järvinen, J.-Y. Girard, Jouni Järvinen, P. Miglioli, P. Miglioli, P. Pagliani, P. Pagliani, P. Pagliani, Piero Pagliani, R. Cignoli, S. Vickers, Sándor Radeleczki, T.S. Blyth, Z. Pawlak   +22 more
core   +1 more source

The extension problem for partial Boolean structures in Quantum Mechanics

, 2010
Alternative partial Boolean structures, implicit in the discussion of classical representability of sets of quantum mechanical predictions, are characterized, with definite general conclusions on the equivalence of the approaches going back to Bell and ...
Bell J. S., Costantino Budroni, Giovanni Morchio, Givant S., Gleason A. M., Kochen S., Motzkin T., Pitowsky I., Sikorski R.   +8 more
core   +1 more source

Semilattices global valuations in the topos approach to quantum mechanics [PDF]

, 2017
In the framework of the topos approach to quantum mechanics a kind of global valuation is introduced and studied. It allows us to represent certain features related to the logical consequences of properties about quantum systems when its phase space is ...
de Ronde, Christian, Domenech, Graciela, Freytes Solari, Hector Carlos   +2 more
core   +1 more source