24,387 research outputs found
Basic Logic and Quantum Entanglement
As it is well known, quantum entanglement is one of the most important
features of quantum computing, as it leads to massive quantum parallelism,
hence to exponential computational speed-up. In a sense, quantum entanglement
is considered as an implicit property of quantum computation itself. But...can
it be made explicit? In other words, is it possible to find the connective
"entanglement" in a logical sequent calculus for the machine language? And
also, is it possible to "teach" the quantum computer to "mimic" the EPR
"paradox"? The answer is in the affirmative, if the logical sequent calculus is
that of the weakest possible logic, namely Basic logic. A weak logic has few
structural rules. But in logic, a weak structure leaves more room for
connectives (for example the connective "entanglement"). Furthermore, the
absence in Basic logic of the two structural rules of contraction and weakening
corresponds to the validity of the no-cloning and no-erase theorems,
respectively, in quantum computing.Comment: 10 pages, 1 figure,LaTeX. Shorter version for proceedings
requirements. Contributed paper at DICE2006, Piombino, Ital
The Eightfold Way: Why Analyticity, Apriority and Necessity are Independent
This paper concerns the three great modal dichotomies: (i) the necessary/contingent dichotomy; (ii) the a priori/empirical dichotomy; and (iii) the analytic/synthetic dichotomy. These can be combined to produce a tri-dichotomy of eight modal categories. The question as to which of the eight categories house statements and which do not is a pivotal battleground in the history of analytic philosophy, with key protagonists including Descartes, Hume, Kant, Kripke, Putnam and Kaplan. All parties to the debate have accepted that some categories are void. This paper defends the contrary view that all eight categories house statementsâa position I dub âoctopropositionalismâ. Examples of statements belonging to all eight categories are given
Tonk Strikes Backâ
What is a logical constant? In which terms should we characterize the meaning of logical words like âandâ, âorâ, âimpliesâ? An attractive answer is: in terms of their inferential roles, i.e. in terms of the role they play in building inferences. More precisely, we favor an approach, going back to Dosen and Sambin, in which the inferential role of a logical constant is captured by a double line rule which introduces it as reflecting structural links (for example, multiplicative conjunction reflects comma on the right of the turnstyle). Rule-based characterizations of logical constants are subject to the well known objection of Priorâs fake connective, tonk. We show that some double line rules also give rise to such pseudo logical constants. But then, we are able to find a property of a double line rules which guarantee that it defines a genuine logical constant. Thus we provide an alternative answer to Belnapâs requirement of conservatity in terms of a local requirement on double line rules
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