Moscow Center for Continuous Mathematical Education

Bolshoj Vlasjevsky per. 11

Conference Hall, August 23, 2010

See the map and directions.

9:15 – 9:30 | Coffee |

9:30 – 11:00 | Roman Kontchakov and Michael Zakharyaschev (London, UK)Reasoning challenges in description logic: semantic module extraction and ontology-based data access, Part I |

11:00 – 11:30 | Coffee |

11:30 – 13:00 | Sonja Smets (Groningen, NL)Quantum Dynamic Modal Logic, Part I |

13:00 – 15:00 | Lunch |

15:00 – 16:30 | Roman Kontchakov and Michael Zakharyaschev (London, UK)Reasoning challenges in description logic: semantic module extraction and ontology-based data access, Part II |

16:30 – 17:00 | Coffee |

17:00 – 18:30 | Sonja Smets (Groningen, NL)Quantum Dynamic Modal Logic, Part II |

Reasoning challenges in description logic: semantic module extraction and ontology-based data access

**Roman Kontchakov and Michael Zakharyaschev**

*Birkbeck College London*

In this mini-course, we discuss two recently emerged directions in ontology-based information systems. One of them is answering queries by taking into account both the data stored in a database and the information about the application domain presented as an ontology. The other is computing semantic modules of an ontology with respect to a given vocabulary. Our aim is to analyse the computational complexity of these problems and present implementation ideas for algorithms that can solve them. We also discuss the description logics for which these problems are computationally feasible, namely, the DL-Lite and EL families, which underly the OWL 2 QL and OWL 2 EL profiles of the most recent Web Ontology Language OWL 2.

** Sonja Smets**

*University of Groningen*

This course is based on joint work with A. Baltag on using concepts and techniques from Dynamic Logic (and Dynamic-Epistemic Logic) to model and reason about quantum behavior.

I start with a brief overview of traditional Quantum Logic and its algebraic and relational semantics. Next I present a dynamic-logic setting for single quantum systems modeled as "quantum transition systems", i.e. non-classical relational models for the classical language of Propositional Dynamic Logic, in which the "test" modalities correspond to successful yes-no measurements of a quantum system. I give an argument for the thesis that understanding Quantum Mechanics at a logical level does not require any modification of the classical laws of "static" propositional logic, but only a non-classical dynamics of information. I also give an abstract completeness result for quantum dynamic modal logic with respect to a Hilbert-space semantics.

In the second part of the course, I introduce epistemic modalities, to express "knowledge" as localised information in a compound quantum system: any localised subsystem is taken as an "agent", whose "knowledge" is given by the information potentially available at that location. I use the resulting Quantum Dynamic-Epistemic Logic to characterise physical-computational properties, such as separation, entanglement, correlations between local measurements, various quantum-logical gates, Bell states etc. I present a proof system for this logic, which can capture important quantum-computational features. Finally, I use this logic to analyze (and sketch the formal correctness proof of) some quantum programs, such as the famous Teleportation Protocol.