F - Teaching-WIKI
... • Given the truth values of all symbols in a sentence, it can be “evaluated” to determine its truth value (True or False) • A model for a KB is a “possible world” (assignment of truth values to propositional symbols) in which each sentence in the KB is True • A valid sentence or tautology is a sente ...
... • Given the truth values of all symbols in a sentence, it can be “evaluated” to determine its truth value (True or False) • A model for a KB is a “possible world” (assignment of truth values to propositional symbols) in which each sentence in the KB is True • A valid sentence or tautology is a sente ...
Bitwise Operators
... Bitwise Operators Bitwise operator works on bits and performs bit-by-bit operation. Assume if a = 60; and b = 13; a = 0011 1100 b = 0000 1101 & (bitwise and) ...
... Bitwise Operators Bitwise operator works on bits and performs bit-by-bit operation. Assume if a = 60; and b = 13; a = 0011 1100 b = 0000 1101 & (bitwise and) ...
Lesson 2
... A set of formulas {A1,…,An} is satisfiable iff there is a valuation v such that v is a model of every formula Ai, i = 1,...,n. The valuation v is then a model of the set {A1,…,An}. Mathematical Logic ...
... A set of formulas {A1,…,An} is satisfiable iff there is a valuation v such that v is a model of every formula Ai, i = 1,...,n. The valuation v is then a model of the set {A1,…,An}. Mathematical Logic ...
Transparencies
... Also sounds good, but requires a fixed causal structure. (Terno reports on some developments) What is an event when we sum over causal histories? Maybe quantum theory should come from quantum gravity and not the other way around?? ...
... Also sounds good, but requires a fixed causal structure. (Terno reports on some developments) What is an event when we sum over causal histories? Maybe quantum theory should come from quantum gravity and not the other way around?? ...
4 slides/page
... arguments such as the following: Borogroves are mimsy whenever it is brillig. It is now brillig and this thing is a borogrove. Hence this thing is mimsy. Propositional logic is good for reasoning about • conjunction, negation, implication (“if . . . then . . . ”) Amazingly enough, it is also useful ...
... arguments such as the following: Borogroves are mimsy whenever it is brillig. It is now brillig and this thing is a borogrove. Hence this thing is mimsy. Propositional logic is good for reasoning about • conjunction, negation, implication (“if . . . then . . . ”) Amazingly enough, it is also useful ...
Standard Model at the LHC (Lecture 1: Theoretical Recap) M. Schott
... × (phasespace) flux flux given by experiment phase space : ’easy’ QM consideration M : matrix element σ= ...
... × (phasespace) flux flux given by experiment phase space : ’easy’ QM consideration M : matrix element σ= ...
pdf
... What causes the gap between NP and PSPACE here? We show that, in a precise sense, it is the negative introspection axiom: ¬Kϕ ⇒ K¬Kϕ. It easily follows from Ladner’s proof of PSPACE-hardness that for any modal logic L between K and S4, there exists a family of formulas ϕn , all consistent with L suc ...
... What causes the gap between NP and PSPACE here? We show that, in a precise sense, it is the negative introspection axiom: ¬Kϕ ⇒ K¬Kϕ. It easily follows from Ladner’s proof of PSPACE-hardness that for any modal logic L between K and S4, there exists a family of formulas ϕn , all consistent with L suc ...
F - Teaching-WIKI
... • Given the truth values of all symbols in a sentence, it can be “evaluated” to determine its truth value (True or False) • A model for a KB is a “possible world” (assignment of truth values to propositional symbols) in which each sentence in the KB is True • A valid sentence or tautology is a sente ...
... • Given the truth values of all symbols in a sentence, it can be “evaluated” to determine its truth value (True or False) • A model for a KB is a “possible world” (assignment of truth values to propositional symbols) in which each sentence in the KB is True • A valid sentence or tautology is a sente ...
Word Document - sdsu
... 3) “Reality is, when unobserved, only approximate is its nature: it is a probability function or wave function specifying a number of possible states which it might assume if challenged, at which time the packet of uncertainty that constitutes a particle before it is measured is collapsed--forced r ...
... 3) “Reality is, when unobserved, only approximate is its nature: it is a probability function or wave function specifying a number of possible states which it might assume if challenged, at which time the packet of uncertainty that constitutes a particle before it is measured is collapsed--forced r ...
Lecture 14 - ChemWeb (UCC)
... This is obviously correct for any state of the particle in the box if you look at the diagrams of the wavefunctions. (It is more interesting to consider the average position of the particle in the left hand side of the box, between 0 and L/2. This is L/4 for n = even and is a function of n for n = o ...
... This is obviously correct for any state of the particle in the box if you look at the diagrams of the wavefunctions. (It is more interesting to consider the average position of the particle in the left hand side of the box, between 0 and L/2. This is L/4 for n = even and is a function of n for n = o ...
The Uniform Density of Sets of Integers and Fermat`s Last Theorem
... and so, by Faltings’ Theorem, each odd prime p divides only finitely many elements of F (since an= p must assume at most finitely many values with a > 1). Therefore Fp is finite and so, by Lemma 2, F has uniform density 0. It is apparently still unknown whether or not Fermat’s Last Theorem is true f ...
... and so, by Faltings’ Theorem, each odd prime p divides only finitely many elements of F (since an= p must assume at most finitely many values with a > 1). Therefore Fp is finite and so, by Lemma 2, F has uniform density 0. It is apparently still unknown whether or not Fermat’s Last Theorem is true f ...
Computation of hadronic two-point functions in Lattice QCD
... field theories: not directly measurable parameters need to be adjusted as functions of a scale µ at which QCD is evaluated, to keep physical observables (e.g. hadron masses) constant and well defined. In QCD this is possible and no new terms need to be introduced as µ is sent to infinity. QCD is a r ...
... field theories: not directly measurable parameters need to be adjusted as functions of a scale µ at which QCD is evaluated, to keep physical observables (e.g. hadron masses) constant and well defined. In QCD this is possible and no new terms need to be introduced as µ is sent to infinity. QCD is a r ...
Propositional logic
... unsatisfiable wff is also called a contradiction. If s(a) = T for every assignment s, then a is a tautology. Definition: a set of wffs S logically implies a wff a, S |= a, provided that for each assignment s such that s(b) = T for each bŒS, s(a) = T (if S = ∅, write |= a and a is a tautology). ...
... unsatisfiable wff is also called a contradiction. If s(a) = T for every assignment s, then a is a tautology. Definition: a set of wffs S logically implies a wff a, S |= a, provided that for each assignment s such that s(b) = T for each bŒS, s(a) = T (if S = ∅, write |= a and a is a tautology). ...
Quantum spin liquids
... SU(2) spins. This process, which for the anyon theories is often called fusion, has to obey very similar rules as those for combining two conventional SU(2) spins. In particular, they have to obey the so-called fusion rules which also incorporate the cut-off k in a consistent way min[i+j,2k i j] ...
... SU(2) spins. This process, which for the anyon theories is often called fusion, has to obey very similar rules as those for combining two conventional SU(2) spins. In particular, they have to obey the so-called fusion rules which also incorporate the cut-off k in a consistent way min[i+j,2k i j] ...
Predicate Logic - Teaching-WIKI
... sentences would just be a represented by some proposition, say P, Q and R. What relationship is there between these propositions? We can say P /\ Q → R Then, given P /\ Q, we could indeed conclude R. But now, suppose we were told Pat is standing in the rain. ...
... sentences would just be a represented by some proposition, say P, Q and R. What relationship is there between these propositions? We can say P /\ Q → R Then, given P /\ Q, we could indeed conclude R. But now, suppose we were told Pat is standing in the rain. ...
text - Physics Department, Princeton University
... ignorance, and paradoxically, for this reason it is more fundamental than any other theory. indeed, although we always are learning more, there is much more that we do not know. For example, we do not know exactly where all the molecules in a gas are and which way they move. We can only give a stati ...
... ignorance, and paradoxically, for this reason it is more fundamental than any other theory. indeed, although we always are learning more, there is much more that we do not know. For example, we do not know exactly where all the molecules in a gas are and which way they move. We can only give a stati ...
characterization of classes of frames in modal language
... If a logic consists of K, φ → φ, φ → φ, grz, then it is characterized by the class of reflexive, transitive and antisymmetric Kripke frames which do not contain any infinite ascending chains of distinct points. S4 is valid in frames defined by grz. S4 laws in K ∪ grz were proved around 1979 by W. J ...
... If a logic consists of K, φ → φ, φ → φ, grz, then it is characterized by the class of reflexive, transitive and antisymmetric Kripke frames which do not contain any infinite ascending chains of distinct points. S4 is valid in frames defined by grz. S4 laws in K ∪ grz were proved around 1979 by W. J ...
Lesson 2
... A set of formulas {A1,…,An} is satisfiable iff there is a valuation v such that v is a model of every formula Ai, i = 1,...,n. The valuation v is then a model of the set {A1,…,An}. Introduction to Logic ...
... A set of formulas {A1,…,An} is satisfiable iff there is a valuation v such that v is a model of every formula Ai, i = 1,...,n. The valuation v is then a model of the set {A1,…,An}. Introduction to Logic ...
Quantum mechanics and path integrals
... If we try to pursue this program, then there are some problems one will run into. For example, it is far from clear that different approximation schemes for any given action functional S will result in the same path integral. In fact, there is indeed such an ambiguity in quantum mechanics – a given ...
... If we try to pursue this program, then there are some problems one will run into. For example, it is far from clear that different approximation schemes for any given action functional S will result in the same path integral. In fact, there is indeed such an ambiguity in quantum mechanics – a given ...
Quantum gravitational contributions to quantum electrodynamics
... is signalled by g(E) → 0 as E → ∞, requiring β < 0 in this limit. In the standard model of particle physics gravity is usually ignored as it plays an inessential role in most calculations of interest. Additionally, if we view Einstein’s theory of gravity as a fundamental theory it exhibits the undes ...
... is signalled by g(E) → 0 as E → ∞, requiring β < 0 in this limit. In the standard model of particle physics gravity is usually ignored as it plays an inessential role in most calculations of interest. Additionally, if we view Einstein’s theory of gravity as a fundamental theory it exhibits the undes ...
Sequent calculus - Wikipedia, the free encyclopedia
... Consider, for example, the rule (∧L 1). It says that, whenever one can prove that Δ can be concluded from some sequence of formulae that contain A, then one can also conclude Δ from the (stronger) assumption, that A∧B holds. Likewise, the rule (¬R) states that, if Γ and A suffice to conclude Δ, then ...
... Consider, for example, the rule (∧L 1). It says that, whenever one can prove that Δ can be concluded from some sequence of formulae that contain A, then one can also conclude Δ from the (stronger) assumption, that A∧B holds. Likewise, the rule (¬R) states that, if Γ and A suffice to conclude Δ, then ...
slides - Computer and Information Science
... proposition by prefixing it with: It is true that . . . and seeing whether the result makes grammatical sense. • Atomic propositions. Intuitively, these are the set of smallest propositions. • Definition: An atomic proposition is one whose truth or falsity does not depend on the truth or falsity of ...
... proposition by prefixing it with: It is true that . . . and seeing whether the result makes grammatical sense. • Atomic propositions. Intuitively, these are the set of smallest propositions. • Definition: An atomic proposition is one whose truth or falsity does not depend on the truth or falsity of ...