主讲人简介：Roberto Giuntini教授是卡利亚里大学（University of Cagliari）的逻辑学与科学哲学全职教授（Full Professor of Logic and Philosophy of Science）。他是量子逻辑领域的世界知名专家，他与他人合作在Handbook of Philosophical Logic、Encyclopedia of Applied Physics和Handbook of Quantum Structure and Quantum Logic等参考书中写作介绍量子逻辑的章节。他还曾担任国际量子结构协会（International Quantum Structures Association） 的主席。
讲座1: Reasoning in Quantum Theory: An Introduction to Quantum Logic
时间: 4月11日 星期二 19:00 - 21:00
We introduce some different forms of quantum logic arising from the sharp and the unsharp approach to quantum mechanics, respectively: Orthomodular Quantum Logic (OML) and Brouwer-Zadeh Logic (BZL). The former originates from the algebraic structure of all projectors (of a Hilbert space), i.e., the mathematical representatives of the notion of “sharp quantum property”, while the latter arises from the mathematical representatives of the notion of “unsharp quantum property” (effects). We finally compare these logics with their corresponding classical analogues: Classical Logic for OQL and Multi-valued logic for BZL.
讲座2: A Gentle Introduction to the Logic of Quantum Computation
时间: 4月13日 星期四 19:00 - 21:00
In the first part of the lecture, we will motivate why quantum computation strongly impacts on contemporary logical research. In the second part, we will introduce the basic notions of quantum computation with particular reference to quantum gates, i.e., unitary operators of a Hilbert space. In particular, we will present the “logical” features of such gates, showing that quantum gates give rise to a completely new form of quantum logic that, unlike the standard (Birkhoff-von Neumann) quantum logic (OML), violates the non-contradiction principle. Finally, we will compare the main features of traditional semantic theories with the new semantic framework underpinning the quantum computational logic. As is well known, the traditional semantic theories, based on classical logic, are “desperately" analytical and antiholistic. A basic principle in these theories is a compositionality-assumption, according to which the meaning of any compound expression is determined by the meanings of its parts. Furthermore, meanings are always supposed to be precise and nonambiguous. As a consequence, classical semantics turns out to hardly applicable to an adequate formal analysis either of natural languages or of the languages of art, where contextuality and ambiguity seem to represent essential features. The quantum-theoretic formalism, instead, gives rise to some characteristic entangled states of knowledge where our information about the whole determines our information about the parts, but not the other way around. The entanglement phenomenon (one of the most striking feature of quantum mechanics) can be thought of as a semantic resource that gives rise to surprising holistic features of the logic underpinning quantum computational logic. In particular, we will see how some usual “classical” connectives (AND, XOR) admit of both a “compositional” and a “holistic” quantum counterpart.
1) M.L. Dalla Chiara, R. Giuntini, R. Greechie, Reasoning in Quantum Theory, Kluwer, 2004.
2) M.L. Dalla Chiara, R. Giuntini, R. Leporini, “Holism, ambiguity and approximation in the logics of quantum computation. A survey”, International Journal of General Systems 40, pp. 85-99, 2011.
3) M.L. Dalla Chiara, R. Giuntini, E. Negri, R. A. Luciani, From Quantum Information to Musical Semantics, College Publications, London, 2012.
4) M.L. Dalla Chiara, R. Giuntini, A. Ledda, G. Sergioli, “The Toffoli- Hadamard gate system: an algebraic approach”, Journal of Philosophical Logic 42, pp. 467-481, 2013.