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What can logic learn from quantum mechanics
, 2005
"... We give a logical analysis of quantum measurements as forms of information update. We enumerate some of the “lessons ” that Logic can learn from Quantum Mechanics: (1) the importance of logical dynamics; (2) the fact that quantum physics does not require any modification of the classical laws of “st ..."
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We give a logical analysis of quantum measurements as forms of information update. We enumerate some of the “lessons ” that Logic can learn from Quantum Mechanics: (1) the importance of logical dynamics; (2) the fact that quantum physics does not require any modification of the classical laws of “static ” propositional logic, but only a nonclassical dynamics of information flow; (3) the fact that all informationgathering actions have ontic sideeffects; (4) the fact that this ontic impact might in its turn affect the flow of information, leading to nonclassical epistemic effects and to states of “objectively imperfect information”. 1
Logic and quantum physics
 Journal of the Indian Council of Philosophical Research
, 2011
"... Current research in Logic is no longer confined to the traditional study of logical consequence or valid inference. As can be witnessed by the range of topics covered in this special issue, the subject matter of logic encompasses several kinds of informational processes ranging from proofs and infer ..."
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Current research in Logic is no longer confined to the traditional study of logical consequence or valid inference. As can be witnessed by the range of topics covered in this special issue, the subject matter of logic encompasses several kinds of informational processes ranging from proofs and inferences to dialogues, observations, measurements, communication and computation. What interests us here is its application to quantum physics: how does logic handle informational processes such as observations and measurements of quantum systems? What are the basic logical principles fit to handle and reason about quantum physical processes? These are the central questions in this paper. It is my aim to provide the reader with some food for thought and to give some pointers to the literature that provide an easy access to this field of research. In the next section I give a brief historical sketch of the origin of the quantum logic project. Next I will explain the theory of orthomodular lattices in section 2. Section 3 covers the syntax and semantics of traditional
Automated quantum reasoning: Nonlogic ❀ semilogic ❀ hyperlogic
 Proceedings of AAAI Spring Symposium on Quantum Interaction
"... Quantum theory does not necessitate the breakdown of fullblown deduction. On the contrary, it comes with substantially enhanced logical reasoning power as compared to its classical counterpart. It features a codeductive mechanism besides a deductive one, resulting in a sound purely graphical calcu ..."
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Quantum theory does not necessitate the breakdown of fullblown deduction. On the contrary, it comes with substantially enhanced logical reasoning power as compared to its classical counterpart. It features a codeductive mechanism besides a deductive one, resulting in a sound purely graphical calculus which admits an informationflow interpretation. (Abramsky & Coecke 2004; Coecke 2005a; 2005b; Coecke & Pavlovic 2006). The key physical concept represented by the logic is the interaction of quantum systems i.e. the tensor product structure, contra (Birkhoff & von Neumann 1936)logic which only addresses individual systems. The trace structure, important in IR applications (van Rijsbergen 2004), is an intrincic part of the logic, together with many other quantitative concepts, again contra BvNlogic where the trace only arises indirectly via Gleason’s theorem. Hence we provide a powerful highlevel formalism for designing, controlling and even automating quantum informatic tasks, which can involve multiple agents. We also mention several existing applications to nonquantum domains such as linguistics, multiagent systems and concurrency.
Quantum Probabilistic Dyadic SecondOrder Logic ⋆
"... Abstract. We propose an expressive but decidable logic for reasoning about quantum systems. The logic is endowed with tensor operators to capture properties of composite systems, and with probabilistic predication formulas P ≥r (s), saying that a quantum system in state s will yield the answer ‘yes ..."
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Abstract. We propose an expressive but decidable logic for reasoning about quantum systems. The logic is endowed with tensor operators to capture properties of composite systems, and with probabilistic predication formulas P ≥r (s), saying that a quantum system in state s will yield the answer ‘yes ’ (i.e. it will collapse to a state satisfying property P) with a probability at least r whenever a binary measurement of property P is performed. Besides firstorder quantifiers ranging over quantum states, we have two secondorder quantifiers, one ranging over quantumtestable properties, the other over quantum “actions”. We use this formalism to express the correctness of some quantum programs. We prove decidability, via translation into the firstorder logic of real numbers. 1