The Natural Order-Generic Collapse for ω
... Since it is more convenient for our proof, we will talk about structures instead of databases. A structure can be viewed as a database whose database schema may contain not only relation symbols but also constant symbols. This allows us to restrict ourselves to boolean queries (which are formulated ...
... Since it is more convenient for our proof, we will talk about structures instead of databases. A structure can be viewed as a database whose database schema may contain not only relation symbols but also constant symbols. This allows us to restrict ourselves to boolean queries (which are formulated ...
Logic in the Finite - CIS @ UPenn
... In what follows, we will analyze and compare the logical and computational complexity of queries relative to classes of nite structures. It will be convenient to introduce, for each signature ; a canonical countable set of nite structures F which contains, up to isomorphism, every nite structu ...
... In what follows, we will analyze and compare the logical and computational complexity of queries relative to classes of nite structures. It will be convenient to introduce, for each signature ; a canonical countable set of nite structures F which contains, up to isomorphism, every nite structu ...
Massachusetts Institute of Technology Spring 2014
... where a† and a are a raising and a lowering operator of photons respectively, and N is a photon number operator. In the absence of coupling, the eigenstates of the uncoupled Hamiltonian or the bare states are simply a ground or excited state with photons. For example, the bare states can be labeled ...
... where a† and a are a raising and a lowering operator of photons respectively, and N is a photon number operator. In the absence of coupling, the eigenstates of the uncoupled Hamiltonian or the bare states are simply a ground or excited state with photons. For example, the bare states can be labeled ...
Sub-Planckian black holes and the Generalized Uncertainty Principle
... Compton wavelength, RC = ~/(M c), which can be obtained from the HUP with the substitution ∆x → R and ∆p → cM but without the factor of 2. Similarly, a key feature of the macroscopic domain is the existence of black holes, a spherically symmetric object of mass M forming an event horizon if it falls ...
... Compton wavelength, RC = ~/(M c), which can be obtained from the HUP with the substitution ∆x → R and ∆p → cM but without the factor of 2. Similarly, a key feature of the macroscopic domain is the existence of black holes, a spherically symmetric object of mass M forming an event horizon if it falls ...
In order to define the notion of proof rigorously, we would have to
... Then, it is convenient to define the negation of P as P ⇒⊥ and to abbreviate it as ¬P (or sometimes ∼ P ). Thus, ¬P (say: not P ) is just a shorthand for P ⇒⊥. This interpretation of negation may be confusing at first. The intuitive idea is that ¬P = (P ⇒⊥) is true if and only if P is not true becau ...
... Then, it is convenient to define the negation of P as P ⇒⊥ and to abbreviate it as ¬P (or sometimes ∼ P ). Thus, ¬P (say: not P ) is just a shorthand for P ⇒⊥. This interpretation of negation may be confusing at first. The intuitive idea is that ¬P = (P ⇒⊥) is true if and only if P is not true becau ...
Informal Proceedings of the 30th International Workshop on
... predicate variables see [16], [3], and they require restrictions concerning individual variables. Secondly, superintuitionistic predicate logics in general suer from lack of adequate semantics, both algebraic and relational (Kripke). We list some important logics that are Kripke complete: Q-INT (S. ...
... predicate variables see [16], [3], and they require restrictions concerning individual variables. Secondly, superintuitionistic predicate logics in general suer from lack of adequate semantics, both algebraic and relational (Kripke). We list some important logics that are Kripke complete: Q-INT (S. ...
Provability as a Modal Operator with the models of PA as the Worlds
... Theorem 4: If MB is non-terminal at some world A then MB has no negative-introspection. Proof: By theorem 3 MB , A (⊥ → ⊥) → ⊥. Because A is non-terminal, the consequent is false, and therefore MB , A ¬(¬⊥). However, because MB , A ¬⊥ and MB , A(¬⊥), negative introspection does not ho ...
... Theorem 4: If MB is non-terminal at some world A then MB has no negative-introspection. Proof: By theorem 3 MB , A (⊥ → ⊥) → ⊥. Because A is non-terminal, the consequent is false, and therefore MB , A ¬(¬⊥). However, because MB , A ¬⊥ and MB , A(¬⊥), negative introspection does not ho ...
Realizing the Harper Hamiltonian with Laser
... shaken lattice (no Raman beams), this was studied in Ref. [36]. Analyzing the expansion of the cloud gives a tunneling rate of 0:4 0:1 Hz, comparable to the nextnearest-neighbor tunneling rate in an untilted lattice, 0:8 Hz in our system. However, in an untilted lattice, next-nearest-neighbor tun ...
... shaken lattice (no Raman beams), this was studied in Ref. [36]. Analyzing the expansion of the cloud gives a tunneling rate of 0:4 0:1 Hz, comparable to the nextnearest-neighbor tunneling rate in an untilted lattice, 0:8 Hz in our system. However, in an untilted lattice, next-nearest-neighbor tun ...
A Proof Theory for Generic Judgments
... for many examples. We will present a sequent calculus which provides this local notion of prooflevel abstraction via generic judgment and a new quantifier, ∇, which explicitly manipulates such local scope. Intuitionistic logic extended with ∇ satisfies cut-elimination even when the logic is addition ...
... for many examples. We will present a sequent calculus which provides this local notion of prooflevel abstraction via generic judgment and a new quantifier, ∇, which explicitly manipulates such local scope. Intuitionistic logic extended with ∇ satisfies cut-elimination even when the logic is addition ...
Automata vs. Logics on Data Words
... into equivalent automaton-based specifications, easing, in this way, the various reasoning tasks. Different models of automata which process words over infinite alphabets have been proposed and studied in the literature (see, for instance, the surveys [6, 7]). Pebble automata [8] use special markers ...
... into equivalent automaton-based specifications, easing, in this way, the various reasoning tasks. Different models of automata which process words over infinite alphabets have been proposed and studied in the literature (see, for instance, the surveys [6, 7]). Pebble automata [8] use special markers ...
Intuitionistic and Modal Logic
... Intuitionism, Platonism, Formalism • Intuitionism is as one of the three basic points of view opposed to Platonism and formalism. View that mathematics and mathematical truths are creations of the human mind: true = provable. N.B! provable in the informal, not formal sense. • Platonism. Most famous ...
... Intuitionism, Platonism, Formalism • Intuitionism is as one of the three basic points of view opposed to Platonism and formalism. View that mathematics and mathematical truths are creations of the human mind: true = provable. N.B! provable in the informal, not formal sense. • Platonism. Most famous ...
The Taming of the (X)OR
... 1, . . ., ⊕Cn = 1, where each variable is assigned a value 0 or 1, ⊕ is addition modulo 2, and ¬A is A ⊕ 1. In this view, the overall strategy to determine whether X is satisfiable is first to derive (if possible) a triangular form of X . For this, select a clause with a literal, say L, and eliminat ...
... 1, . . ., ⊕Cn = 1, where each variable is assigned a value 0 or 1, ⊕ is addition modulo 2, and ¬A is A ⊕ 1. In this view, the overall strategy to determine whether X is satisfiable is first to derive (if possible) a triangular form of X . For this, select a clause with a literal, say L, and eliminat ...
pdf - at www.arxiv.org.
... infinite stream of zeros at infinity. However, this approach did not result in implementation as no procedure for (semi-)deciding this property was given. An alternative solution was proposed in [6, 22]: subgoals produced in the course of an infinite SLDderivation are memorized, and if any two subgo ...
... infinite stream of zeros at infinity. However, this approach did not result in implementation as no procedure for (semi-)deciding this property was given. An alternative solution was proposed in [6, 22]: subgoals produced in the course of an infinite SLDderivation are memorized, and if any two subgo ...
Topological aspects of real-valued logic
... Theorem 1.0.3. Let S be a two-sorted metric signature, and let L be a countable fragment of Lω1 ,ω (S). Let T be an L-theory and let M = h M, V, . . . i be a model of T where M has density κ and V has density λ, with κ > λ ≥ ℵ0 . Then there is a model N = h N, W, . . . i ≡L M with N of density ℵ1 an ...
... Theorem 1.0.3. Let S be a two-sorted metric signature, and let L be a countable fragment of Lω1 ,ω (S). Let T be an L-theory and let M = h M, V, . . . i be a model of T where M has density κ and V has density λ, with κ > λ ≥ ℵ0 . Then there is a model N = h N, W, . . . i ≡L M with N of density ℵ1 an ...
Majorana returns - MIT Center for Theoretical Physics
... Neutrinos were Majorana’s own candidates for Majorana fermions, and although they look more promising than ever in that regard, no longer are they unique. Other problems at the frontier of fundamental physics seem to call for more Majorana fermions. Supersymmetry is a leading proposal to improve the ...
... Neutrinos were Majorana’s own candidates for Majorana fermions, and although they look more promising than ever in that regard, no longer are they unique. Other problems at the frontier of fundamental physics seem to call for more Majorana fermions. Supersymmetry is a leading proposal to improve the ...
Page 12 - at www.arxiv.org.
... depends on the choice of the spin-orientation to be measured on the other particle, and its outcome thereof. Relativistic locality is not necessarily violated in this experiment, as it allows either Alice’s choices to affect Bob's, or vice versa. This reciprocity, however, does not hold for a combin ...
... depends on the choice of the spin-orientation to be measured on the other particle, and its outcome thereof. Relativistic locality is not necessarily violated in this experiment, as it allows either Alice’s choices to affect Bob's, or vice versa. This reciprocity, however, does not hold for a combin ...
