A Logical Foundation for Session
... the years many research attempts were made in this regard, a Curry-Howard correspondence between linear logic and concurrent computation was only found recently, bridging the proof theory of linear logic and session-typed process calculus. Building upon this work, we have developed a theory of intui ...
... the years many research attempts were made in this regard, a Curry-Howard correspondence between linear logic and concurrent computation was only found recently, bridging the proof theory of linear logic and session-typed process calculus. Building upon this work, we have developed a theory of intui ...
Indium Phosphide Quantum Dots in GaP and in
... are presented and discussed, together with their optical properties and associated carrier dynamics. The QDs are grown using gas-source molecular-beam epitaxy in and on the two materials In0.48 Ga0.52 P (lattice matched to GaAs) and GaP. Under the proper growth conditions, formation of InP dots via ...
... are presented and discussed, together with their optical properties and associated carrier dynamics. The QDs are grown using gas-source molecular-beam epitaxy in and on the two materials In0.48 Ga0.52 P (lattice matched to GaAs) and GaP. Under the proper growth conditions, formation of InP dots via ...
Document
... – (x) is preceded by no universal quantifiers, (u) is preceded by (y) and (z), and (w) by (y), (z) and (v). – Therefore, we replace the existential variable x by a constant a, u by a two-place function f(y,z), and w by a three-place function g(y,z,v). – The standard form of the formula is • ...
... – (x) is preceded by no universal quantifiers, (u) is preceded by (y) and (z), and (w) by (y), (z) and (v). – Therefore, we replace the existential variable x by a constant a, u by a two-place function f(y,z), and w by a three-place function g(y,z,v). – The standard form of the formula is • ...
Die Grundlagen der Arithmetik §§82–83
... two sections would have contained a remarkably large gap that was never filled by any argument found in Grundgesetze. In any case, it is certain that Frege did not know of this proof. We begin by discussing §§70–81. In §70, Frege begins the definition of equinumerosity by explaining the notion of a ...
... two sections would have contained a remarkably large gap that was never filled by any argument found in Grundgesetze. In any case, it is certain that Frege did not know of this proof. We begin by discussing §§70–81. In §70, Frege begins the definition of equinumerosity by explaining the notion of a ...
Simplicity, Truth, and Topology Kevin T. Kelly Konstantin Genin Hanti Lin
... The concept of stratification of a topological space is familiar in algebraic geometry (Stratification., http://www.encyclopediaofmath.org/index.php?title=Stratification), which studies the numerical stability of solutions to polynomial equations. We arrived at the concept independently, based entir ...
... The concept of stratification of a topological space is familiar in algebraic geometry (Stratification., http://www.encyclopediaofmath.org/index.php?title=Stratification), which studies the numerical stability of solutions to polynomial equations. We arrived at the concept independently, based entir ...
Introduction to Modal and Temporal Logic
... Classical (Two-Valued) Nature of Kripke Semantics Lemma 1 For any Kripke model hW, R, ϑi, any w ∈ W and any formula ϕ, either ϑ(w, ϕ) = t or else ϑ(w, ϕ) = f . Proof: Pick any Kripke model hW, R, ϑi, any w ∈ W , and any formula ϕ. Proceed by induction on the length l of ϕ. Base Case l = 1: If ϕ is ...
... Classical (Two-Valued) Nature of Kripke Semantics Lemma 1 For any Kripke model hW, R, ϑi, any w ∈ W and any formula ϕ, either ϑ(w, ϕ) = t or else ϑ(w, ϕ) = f . Proof: Pick any Kripke model hW, R, ϑi, any w ∈ W , and any formula ϕ. Proceed by induction on the length l of ϕ. Base Case l = 1: If ϕ is ...
CS 208: Automata Theory and Logic
... – Cartesian product A × B of two sets A and B is the set (of tuples) {(a, b) : a ∈ A and b ∈ B}. – A binary relation R on two sets A and B is a subset of A × B, formally we write R ⊆ A × B. Similarly n-ary relation. – A function (or mapping) f from set A to B is a binary relation on A and B such tha ...
... – Cartesian product A × B of two sets A and B is the set (of tuples) {(a, b) : a ∈ A and b ∈ B}. – A binary relation R on two sets A and B is a subset of A × B, formally we write R ⊆ A × B. Similarly n-ary relation. – A function (or mapping) f from set A to B is a binary relation on A and B such tha ...
Discrete Mathematics
... A propositional variable (lowercase letters p, q, r) is a proposition. These variables model true/false statements. The negation of a proposition P, written ¬ P, is a proposition. The conjunction (and) of two propositions, written P ∧ Q, is a proposition. The disjunction (or) of two propositions, wr ...
... A propositional variable (lowercase letters p, q, r) is a proposition. These variables model true/false statements. The negation of a proposition P, written ¬ P, is a proposition. The conjunction (and) of two propositions, written P ∧ Q, is a proposition. The disjunction (or) of two propositions, wr ...
Notes on the ACL2 Logic
... But what we are after is reasoning about programs, and while propositional logic will play an important role, we need more powerful logics. To see why, let’s simplify things for a moment and consider conjectures involving numbers and arithmetic operations. Consider the conjecture: 1. a+b = ba What d ...
... But what we are after is reasoning about programs, and while propositional logic will play an important role, we need more powerful logics. To see why, let’s simplify things for a moment and consider conjectures involving numbers and arithmetic operations. Consider the conjecture: 1. a+b = ba What d ...
Labeled Natural Deduction for Temporal Logics
... For instance, adapting natural deduction systems for classical (or intuitionistic) logic to modal logic is not straightforward and, in fact, it is not trivial to define systems that enjoy properties (i) and (ii) mentioned above. Fortunately, in the last decades some interesting proposals for modal p ...
... For instance, adapting natural deduction systems for classical (or intuitionistic) logic to modal logic is not straightforward and, in fact, it is not trivial to define systems that enjoy properties (i) and (ii) mentioned above. Fortunately, in the last decades some interesting proposals for modal p ...
On a Density for Sets of Integers 1 Introduction 2 A
... In the following, we obtain computational approximations for the asymptotic density and the dis- where li(·) denotes the logarithmic integral [16]. The cussed density. The approximate densities are nu- curves displayed in Figure 4 correspond to the calmerically evaluated as T increases in the range ...
... In the following, we obtain computational approximations for the asymptotic density and the dis- where li(·) denotes the logarithmic integral [16]. The cussed density. The approximate densities are nu- curves displayed in Figure 4 correspond to the calmerically evaluated as T increases in the range ...
here - Department of Physics and Astronomy
... [3 hours] Properties of the atomic nucleus and the nucleon-nucleon interaction, models for the structure of the nucleus, analysis of nuclear decay and nuclear reactions with applications to interdisciplinary areas. Prerequisite: PHYS 6330 or consent of instructor PHYS 6790 CURRENT ISSUES IN ATOMIC, ...
... [3 hours] Properties of the atomic nucleus and the nucleon-nucleon interaction, models for the structure of the nucleus, analysis of nuclear decay and nuclear reactions with applications to interdisciplinary areas. Prerequisite: PHYS 6330 or consent of instructor PHYS 6790 CURRENT ISSUES IN ATOMIC, ...
PDF of this page - Miami bulletin
... Summary of Summarizes known particles and their properties, and uses relativistic and non-relativistic quantum mechanics to describe their interaction. Quantum field theory and Feynman diagrams are discussed with emphasis on quantum electrodynamics. Prerequisite: instructor permission. PHY 437/PHY 5 ...
... Summary of Summarizes known particles and their properties, and uses relativistic and non-relativistic quantum mechanics to describe their interaction. Quantum field theory and Feynman diagrams are discussed with emphasis on quantum electrodynamics. Prerequisite: instructor permission. PHY 437/PHY 5 ...
briancox
... • Selection rules mean that central system is (to a good approx) 0++ • If you see a new particle produced exclusively with proton tags you know its quantum numbers • CP violation in the Higgs sector shows up directly as azimuthal asymmetries • Proton tagging may be the discovery channel in certain r ...
... • Selection rules mean that central system is (to a good approx) 0++ • If you see a new particle produced exclusively with proton tags you know its quantum numbers • CP violation in the Higgs sector shows up directly as azimuthal asymmetries • Proton tagging may be the discovery channel in certain r ...
full text (.pdf)
... From a practical standpoint, many simple program manipulations such as loop unwinding and basic safety analysis do not require the full power of PDL, but can be carried out in a purely equational subsystem using the axioms of Kleene algebra. However, tests are an essential ingredient for modeling r ...
... From a practical standpoint, many simple program manipulations such as loop unwinding and basic safety analysis do not require the full power of PDL, but can be carried out in a purely equational subsystem using the axioms of Kleene algebra. However, tests are an essential ingredient for modeling r ...
a semantic perspective - Institute for Logic, Language and
... algebras with operators. And modal logic can be given a topological semantics, so it can also be viewed as a tool for talking about topologies. But although we briefly discuss algebraic and topological semantics, for the most part this chapter focuses on modal logic as a tool for talking about graph ...
... algebras with operators. And modal logic can be given a topological semantics, so it can also be viewed as a tool for talking about topologies. But although we briefly discuss algebraic and topological semantics, for the most part this chapter focuses on modal logic as a tool for talking about graph ...
Independence logic and tuple existence atoms
... Definition R relation, ~x , ~y , ~z tuples of attributes. Then R |= ~x ~y | ~z if and only if, for all r , r 0 ∈ R such that r (~x ) = r 0 (~x ) there exists a r 00 ∈ R such that r 00 (~x ~y ) = r (~x ~y ) and r 00 (~x ~z ) = r (~x ~z ). Huge literature on the topic; If ~x ~y ~z contains all attri ...
... Definition R relation, ~x , ~y , ~z tuples of attributes. Then R |= ~x ~y | ~z if and only if, for all r , r 0 ∈ R such that r (~x ) = r 0 (~x ) there exists a r 00 ∈ R such that r 00 (~x ~y ) = r (~x ~y ) and r 00 (~x ~z ) = r (~x ~z ). Huge literature on the topic; If ~x ~y ~z contains all attri ...
Chapter 13 BOOLEAN ALGEBRA
... is unique. The same is true of a least upper bound, if it exists. Proof: Let g and g' be greatest lower bounds of a and b. We will prove that g = g '. (1) g a greatest lower bound of a and b g is a lower bound of a and b. (2) g ' a greatest lower bound of a and b and g a lower bound of a and b g ...
... is unique. The same is true of a least upper bound, if it exists. Proof: Let g and g' be greatest lower bounds of a and b. We will prove that g = g '. (1) g a greatest lower bound of a and b g is a lower bound of a and b. (2) g ' a greatest lower bound of a and b and g a lower bound of a and b g ...