Benedikt Löwe

The modal logic of forcing

A set theoretical assertion psi is forceable or possible, written lozenge psi, if psi holds in some forcing extension, and necessary, written square psi, if psi holds in all forcing extensions. In this forcing interpretation of modal logic, we establish that if ZFC is consistent, then the ZFC-provable principles of forcing are exactly those in the modal theory S4.2.

Solovay-type characterizations for forcing algebras

We give characterizations for the (in ZFC unprovable) sentences “Every -set is measurable” and “Every -set is measurable” for various notions of measurability derived from well-known forcing partial orderings.

DEL planning and some tractable cases

We describe the planning problem within the framework of dynamic epistemic logic (DEL), considering the tree of sequences of events as the underlying structure. In general, the DEL planning problem is computationally difficult to solve. On the other hand, a great deal of fruitful technical advances have led to deep insights into the way DEL works, and these can be exploited in special cases. We present a few properties that will lead to considerable simplifications of the DEL planning problem and apply them in a toy example.

Programs, Proofs, Processes

F. FerreiraDepartamento de Matematica, Faculdade de Ciencias, Universidade de Lisboa, Campo Grande,1749-016 Lisboa, Portugale-mail: fjferreira@fc.ul.ptB. Lowe ( )Institute for Logic, Language and Computation, Universiteit van Amsterdam, Postbus 94242,1090 GE Amsterdam, The Netherlandse-mail: bloewe@science.uva.nlB. LoweDepartment Mathematik, Universitat Hamburg, Bundesstrasse 55, 20146 Hamburg, GermanyE. MayordomoDepartamento de Informatica e Ingenieria de Sistemas, Instituto de Investigacion en Ingenieria deAragon (I3A), Universidad de Zaragoza, 50015 Zaragoza, Spaine-mail: elvira@unizar.es

How the World Computes

Partial Cylindrical Algebraic Decomposition I: The Lifting Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560 Grant Olney Passmore and Paul B. Jackson Multi-valued Functions in Computability Theory . . . . . . . . . . . . . . . . . . . . . 571 Arno Pauly Relative Randomness for Martin-Löf Random Sets . . . . . . . . . . . . . . . . . . . 581 NingNing Peng, Kojiro Higuchi, Takeshi Yamazaki, and Kazuyuki Tanaka Table ofThe idea that the Universe is a program in a giant quantum computer is both fascinating and suffers from various problems. Nonetheless, it can provide a unified picture of physics and this can be very useful for the problem of Quantum Gravity where such a unification is necessary. In previous work we proposed Quantum Graphity, a simple way to model a dynamical spacetime as a quantum computation. In this paper, we give an easily readable introduction to the idea of the universe as a quantum computation, the problem of quantum gravity, and the graphity models.

Revision Sequences and Computers with an Infinite Amount of Time

The author establishes a connection between Revision Theory of Truth and Infinite Time Turing Machines as developed by Hamkins and Kidder. The ideas from this paper have incited Welch to solve the limit rule problem of revision theory.

Silver measurability and its relation to other regularity properties

For a ⊆ b ⊆ ω with b\a infinite, the set D = {x ∈ [ω] : a ⊆ x ⊆ b} is called a doughnut. Doughnuts are equivalent to conditions of Silver forcing, and so, a set S ⊆ [ω] is called Silver measurable, also known as completely doughnut, if for every doughnut D there is a doughnut D′ ⊆ D which is contained or disjoint from S. In this paper, we investigate the Silver measurability of ∆2 and Σ 1 2 sets of reals and compare it to other regularity properties like the Baire and the Ramsey property and Miller and Sacks measurability.

Models of Computation in Context

This book constitutes the refereed proceedings of the 7th Conference on Computability in Europe, CiE 2011, held in Sofia, Bulgaria, in June/July 2011. The 22 revised papers presented together with 11 invited lectures were carefully reviewed and selected with an acceptance rate of under 40%. The papers cover the topics computability in analysis, algebra, and geometry; classical computability theory; natural computing; relations between the physical world and formal models of computability; theory of transfinite computations; and computational linguistics.

Set-Theoretic Absoluteness and the Revision Theory of Truth

We describe the solution of the Limit Rule Problem of Revision Theory and discuss the philosophical consequences of the fact that the truth set of Revision Theory is a complete Π1/2 set.

The synchronicity of dynamic epistemic logic

In a recent paper, van Benthem, Gerbrandy, Hoshi and Pacuit gave a natural translation of dynamic epistemic logic (DEL) into epistemic temporal logic (ETL) and proved a representation theorem, characterizing those ETL models that are translations of some DEL protocol; among the characterizing properties we also find synchronicity. In this paper, we argue that synchronicity is not an inherent property of DEL, but rather of the translation that van Benthem et al. used. We provide a different translation that produces asynchronous ETL models and discuss a minimal temporal extension of DEL that removes the ambiguities between the possible translations. This allows us a first attempt at assessing which of the epistemic-temporal properties are intrinsic to DEL and which are properties of the translation.