A Labeled Deduction System for the Logic UB

Caleiro, Carlos; Viganò, Luca; Volpe, Marco

doi:10.1109/time.2013.14

Cited by 5 publications

(8 citation statements)

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“…In addition to the works on DTL, and in particular the labeled tableaux system given in [5], our starting points for N(QBDTL) are the labeled natural deduction system for the logic UB (i.e., the until-free fragment of CTL) given in [11] and the approach developed in [27,28], where a labeled modal deduction system with specific modalities able to describe quantum state transformations is given. Fittingly, in N(QBDTL), we consider composed labels (i, x, q) that represent an agent/qubit i, a time instant x, and the quantum information q in the underlying semantics.…”

Section: Contributionsmentioning

confidence: 99%

“…We can classify them into four categories: (i) local life-cycle rules (inspired to the deduction system for the logic UB given in [11]), (ii) distributed life-cycle rules (reminiscent of the global labeled tableaux developed for DTL in [5]), (iii) quantum transformations rules (actually a fragment of the deduction systems studied in [28]) and (iv) interaction rules.…”

Section: The Rules Of N(qbdtl)mentioning

confidence: 99%

“…The case of ∃ E and ∃ E is similar but complicated by the fact that the universal linear-time operator ( or ) is preceded by an existential path quantifier (∃), which prevents us from inferring the conclusion for a successor along an arbitrary relation. Our solution is based on the idea (originally proposed in [11]) of using Skolem functions as names for particular relations, e.g., r(i, x, A) denotes a relation passing at x and such that if ∃ A holds in x, then A holds at each successor of x along r(x, A).…”

Section: Local Life-cycle Rules (Figure 1)mentioning

confidence: 99%

“…This modeling of the induction principle is inspired to the one proposed in [11] and it is reminiscent of deduction systems for Peano Arithmetic. An example of use of the rule ind∃ can be found in Figure 5, as we discuss below.…”

Section: Local Life-cycle Rules (Figure 1)mentioning

confidence: 99%

“…The base case is when (i, x, q) : A ∈ Γ and is trivial. There is one step case for every rule (where, for what concerns local life-cycle rules, we refer to [11], whose treatment can be quite easily adapted to work here). We show a few representative step cases.…”

Section: Soundnessmentioning

confidence: 99%

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A branching distributed temporal logic for reasoning about entanglement-free quantum state transformations

Viganò

Volpe

Zorzi

2017

Information and Computation

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The Distributed Temporal Logic DTL allows one to reason about temporal properties of a distributed system from the local point of view of the system's agents, which are assumed to execute independently and to interact by means of event sharing. In this paper, we introduce the Quantum Branching Distributed Temporal Logic QBDTL, a variant of DTL able to represent (entanglement-free) quantum state transformations in an abstract, qualitative way. In QBDTL, each agent represents a distinct quantum bit (the unit of quantum information theory), which evolves by means of quantum transformations and possibly interacts with other agents, and n-ary quantum operators act as communication/synchronization points between agents. We endow QBDTL with a DTL-style semantics, which fits the intrinsically distributed nature of quantum computing, we formalize a labeled deduction system for QBDTL, and we prove the soundness and completeness of this deduction system with respect to the given semantics. We give a number of examples and, finally, we discuss possible extensions of our logic in order to reason about entanglement phenomena.

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Section: Contributionsmentioning

confidence: 99%

Section: The Rules Of N(qbdtl)mentioning

confidence: 99%

Section: Local Life-cycle Rules (Figure 1)mentioning

confidence: 99%

Section: Local Life-cycle Rules (Figure 1)mentioning

confidence: 99%

Section: Soundnessmentioning

confidence: 99%

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