V.R. Pratt. Linear logic for generalized quantum mechanics. In Proc. of Workshop on Physics and Computation (PhysComp'92), pages 166--180, Dallas, Oct 1992. IEEE.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....computing promises to open fresh vistas for computer science almost 100 years after quantum mechanics revolutionized physics. We expect that logical methods will play a key role in the development of quantum computer systems, much like the role they have played in classical computing. Pratt [Pra92] has also argued that logical support for reasoning about quantum e#ects may become essential in the next ten years to designers of classical hardware. In this paper, we study what is potentially one of the building blocks of modal logics for quantum computing, by developing a logic for ....

V.R. Pratt. Linear logic for generalized quantum mechanics. In Proc. of Workshop on Physics and Computation (PhysComp'92), pages 166--180, Dallas, Oct 1992. IEEE.

....and symmetric. It is possible to de ne an operation called orthocomplementation X that gives the most general proposition that represents a state that cannot be confused with X. Orthocomplementation satis es most of the laws of classical negation, but does not satisfy distributivity. Pratt[8] showed that full classical linear logic can be regarded as an extension of quantum logic, in which the additive operators and negation correspond to the and , or , and negation of quantum logic. Pratt casts these as static operators describing xed situations. The multiplicative operators ....

V. R. Pratt. Linear logic for generalized quantum mechanics. In Proc. Workshop on Physics and Computation (PhysComp'92), pages 166-180, Dallas, 1993. IEEE. 11

.... B turns out to be the common denominator of basic orthologic and linear logic. On this basis, we obtain a whole gamma of quantum logics, which are all cut free. The last of our logics, B tr, seems to be a good candidate in order to represent a linear quantum logic in the sense of Pratt ([12]) So far we have only dealt with a fragment of basic logic, which has no implication connective. With this linguistic restriction, we have easily proved the equivalence between our calculi and the usual formulations of paraconsistent quantum logic and of orthologic. However, the same methods can ....

V. R. Pratt, Linear logic for generalized quantum mechanics, in Proc. Workshop on Physics and Computation (PhysComp'92), Dallas, 1993, IEEE, pp. 166--180.

....of a framework whose sheer novelty at the time already presented enough of a conceptual challenge. 2 In fact even more so, Chu spaces viewed equivalently as either matrices or Boolean propositions being conceptually simpler than ortholattices. discussed at length at the previous meeting [Pra93a], linear logic resembles quantum logic in some respects while improving on it in others. The resemblances are in details such as rejection of distributivity of conjunction over disjunction and acceptance of double negation, differentiating both logics from Boolean logic (which accepts the former) ....

.... loss of generality in passing from Chu(V; k) to Chu(Set; K) appears to be negligible in practice in comparison with what is lost in the passage from V (any symmetric closed category with pullbacks) to Set (a very constrained instance of such a V ) This model also picks up where we left off in [Pra93a], where we proposed linear logic as an extension of quantum logic that equipped it with a dynamics, a glaring omission from Birkhoff and von Neumann s original formulation [BvN36] At the end of that paper we briefly hinted at partial distributive lattices as a potentially superior model to the ....

V.R. Pratt. Linear logic for generalized quantum mechanics. In Proc. Workshop on Physics and Computation (PhysComp'92), pages 166--180, Dallas, 1993. IEEE.

....of any station b 2 XB we see the same sequence A of trains, and vice versa when we watch the stations go by from any train a 2 XA . We have been using A only relatively recently [Pra92b, Pra92a] as the basic link between schedules and automata, and as complementarity in quantum mechanics [Pra93]. Automata express behavior as graphs with states as vertices and events as edges; schedules dualize this by interchanging them, with A denoting the automaton form of the schedule A. The generalization of the event spaces of [Pra92b, Pra92a] to the Chu spaces of this paper is anticipated by ....

....with states as vertices and events as edges; schedules dualize this by interchanging them, with A denoting the automaton form of the schedule A. The generalization of the event spaces of [Pra92b, Pra92a] to the Chu spaces of this paper is anticipated by the partial distributive lattices of [Pra93, x5], which are essentially Chu spaces, whose role in this application we defer to a separate paper. 3 Chu Spaces and Transforms We now imbue a binary relation with a spatial character by taking its domain to be its point set, and its codomain to be its degrees of freedom or states, reflected in the ....

V.R. Pratt. Linear logic for generalized quantum mechanics. In Proc. Workshop on Physics and Computation (PhysComp'92), Dallas, 1993. IEEE.

....Hilbert space. Furthermore the progression from automata to Chu spaces recapitulates the progression from Langrangian mechanics retaining even some of the essential properties of the Legendre transform by which this passage is standardly accomplished. Some of these connections are developed in [Pra93a, Pra94b], although the details of this second point of contact have only become clear to us since then. These connections get considerably closer to the essence of quantum mechanics than does quantum logic [BvN36] which abstracts away from complementarity to capture just the underlying projective ....

V.R. Pratt. Linear logic for generalized quantum mechanics. In Proc. Workshop on Physics and Computation (PhysComp'92), pages 166--180, Dallas, 1993. IEEE.

No context found.

V.R. Pratt (1993a), Linear Logic for Generalized Quantum Mechanics. In Proceedings Workshop on Physics and Computation, Dallas, IEEE Computer Society.

No context found.

PRATT V. (1993), Linear Logic for Generalized Quantum Mechanics, in Proc. Workshop on Physics and Computation (PhysComp'92), Dallas, IEEE, 166180.

No context found.

V.R. Pratt (1993a), Linear Logic for Generalized Quantum Mechanics. In Proceedings Workshop on Physics and Computation, Dallas, IEEE Computer Society.

No context found.

V.R. Pratt (1993), Linear Logic for Generalized Quantum Mechanics. In Proceedings Workshop on Physics and Computation, Dallas, IEEE Computer Society.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC