A quantum computational semantics for epistemic logical operators. Part I: epistemic structures

Some critical open problems of epistemic logics can be investigated in the framework of a quantum computational approach. The basic idea is to interpret sentences like “Alice knows that Bob does not understand that π is irrational” as pieces of quantum information (generally represented by density operators of convenient Hilbert spaces). Logical epistemic operators (to understand, to know. . .) are dealt with as (generally irreversible) quantum operations, which are, in a sense, similar to measurement-procedures. This approach permits us to model some characteristic epistemic processes, that concern both human and artificial intelligence. For instance, the operation of “memorizing and retrieving information” can be formally represented, in this framework, by using a quantum teleportation phenomenon

Automated Verification of Quantum Protocols using MCMAS

We present a methodology for the automated verification of quantum protocols using MCMAS, a symbolic model checker for multi-agent systems The method is based on the logical framework developed by D'Hondt and Panangaden for investigating epistemic and temporal properties, built on the model for Distributed Measurement-based Quantum Computation (DMC), an extension of the Measurement Calculus to distributed quantum systems. We describe the translation map from DMC to interpreted systems, the typical formalism for reasoning about time and knowledge in multi-agent systems. Then, we introduce dmc2ispl, a compiler into the input language of the MCMAS model checker. We demonstrate the technique by verifying the Quantum Teleportation Protocol, and discuss the performance of the tool.Comment: In Proceedings QAPL 2012, arXiv:1207.055

Quantum objects are vague objects

[FIRST PARAGRAPHS] Is vagueness a feature of the world or merely of our representations of the world? Of course, one might respond to this question by asserting that insofar as our knowledge of the world is mediated by our representations of it, any attribution of vagueness must attach to the latter. However, this is to trivialize the issue: even granted the point that all knowledge is representational, the question can be re-posed by asking whether vague features of our representations are ultimately eliminable or not. It is the answer to this question which distinguishes those who believe that vagueness is essentially epistemic from those who believe that it is, equally essentially, ontic. The eliminability of vague features according to the epistemic view can be expressed in terms of the supervenience of ‘vaguely described facts’ on ‘precisely describable facts’: If two possible situations are alike as precisely described in terms of physical measurements, for example, then they are alike as vaguely described with words like ‘thin’. It may therefore be concluded that the facts themselves are not vague, for all the facts supervene on precisely describable facts. (Williamson 1994, p. 248; see also pp. 201- 204) It is the putative vagueness of certain identity statements in particular that has been the central focus of claims that there is vagueness ‘in’ the world (Parfit 1984, pp. 238-241; Kripke 1972, p. 345 n. 18). Thus, it may be vague as to who is identical to whom after a brain-swap, to give a much discussed example. Such claims have been dealt a forceful blow by the famous Evans-Salmon argument which runs as follows: suppose for reductio that it is indeterminate whether a = b. Then b definitely possesses the property that it is indeterminate whether it is identical with a, but a definitely does not possess this property since it is surely not indeterminate whether a=a. Therefore, by Leibniz’s Law, it cannot be the case that a=b and so the identity cannot be indeterminate (Evans 1978; Salmon 1982)

Inadequacy of Modal Logic in Quantum Settings

We test the principles of classical modal logic in fully quantum settings. Modal logic models our reasoning in multi-agent problems, and allows us to solve puzzles like the muddy children paradox. The Frauchiger-Renner thought experiment highlighted fundamental problems in applying classical reasoning when quantum agents are involved; we take it as a guiding example to test the axioms of classical modal logic. In doing so, we find a problem in the original formulation of the Frauchiger-Renner theorem: a missing assumption about unitarity of evolution is necessary to derive a contradiction and prove the theorem. Adding this assumption clarifies how different interpretations of quantum theory fit in, i.e., which properties they violate. Finally, we show how most of the axioms of classical modal logic break down in quantum settings, and attempt to generalize them. Namely, we introduce constructions of trust and context, which highlight the importance of an exact structure of trust relations between agents. We propose a challenge to the community: to find conditions for the validity of trust relations, strong enough to exorcise the paradox and weak enough to still recover classical logic.Comment: In Proceedings QPL 2018, arXiv:1901.0947