Fuzzy topology, Quantization and Gauge Fields
... where v(x) is w flow velocity, it is supposed to be independent of w(x) ...
... where v(x) is w flow velocity, it is supposed to be independent of w(x) ...
ppt - Harvard Condensed Matter Theory group
... Density ripples in expanding low-dimensional condensates Review of earlier work Analysis of density ripples spectrum 1d systems 2d systems ...
... Density ripples in expanding low-dimensional condensates Review of earlier work Analysis of density ripples spectrum 1d systems 2d systems ...
INTERPLAYS OF KNOWLEDGE AND NON
... is an inference rule of the system. There are many interpretations of these axioms in the literature. As it is known, they reflect logical omniscience (D), axiom of knowledge (E) and forms of introspection (F) and (G). So we have two logics and there are two non-interdefinable operators: knowledge ...
... is an inference rule of the system. There are many interpretations of these axioms in the literature. As it is known, they reflect logical omniscience (D), axiom of knowledge (E) and forms of introspection (F) and (G). So we have two logics and there are two non-interdefinable operators: knowledge ...
Partial Grounded Fixpoints
... used for example in the XNMR system [Castro and Warren, 2001]. Partial stable models are not only used for debugging. Real-life databases often contain (local) inconsistencies. The partial stable model semantics for deductive databases is more robust than the two-valued stable semantics in this case ...
... used for example in the XNMR system [Castro and Warren, 2001]. Partial stable models are not only used for debugging. Real-life databases often contain (local) inconsistencies. The partial stable model semantics for deductive databases is more robust than the two-valued stable semantics in this case ...
Quantitative Temporal Logics: PSPACE and below - FB3
... is satisfiable. Note that the length of the latter formula is polynomial in the length of ϕ. Second, for any interval I of the form (0, n), (0, n], or [0, n) with n > 1, ♦IF ϕ is [0,n−1] equivalent to ♦JF ♦F ϕ, where J is obtained from I by replacing the upper interval bound n by 1. In the following ...
... is satisfiable. Note that the length of the latter formula is polynomial in the length of ϕ. Second, for any interval I of the form (0, n), (0, n], or [0, n) with n > 1, ♦IF ϕ is [0,n−1] equivalent to ♦JF ♦F ϕ, where J is obtained from I by replacing the upper interval bound n by 1. In the following ...
Predicate logic
... Let a, b ∈ Z s.t. a and b are odd. Then by definition of odd a = 2m + 1.m ∈ Z and b = 2n + 1.n ∈ Z So ab = (2m + 1)(2n + 1) = 4mn + 2m + 2n + 1 = 2(2mn + m + n) + 1 and since m, n ∈ Z it holds that (2mn + m + n) ∈ Z, so ab = 2k + 1 for some k ∈ Z. Thus ab is odd by definition of odd. QED ...
... Let a, b ∈ Z s.t. a and b are odd. Then by definition of odd a = 2m + 1.m ∈ Z and b = 2n + 1.n ∈ Z So ab = (2m + 1)(2n + 1) = 4mn + 2m + 2n + 1 = 2(2mn + m + n) + 1 and since m, n ∈ Z it holds that (2mn + m + n) ∈ Z, so ab = 2k + 1 for some k ∈ Z. Thus ab is odd by definition of odd. QED ...
POSSIBLE WORLDS SEMANTICS AND THE LIAR Reflections on a
... Now, Kaplan’s argument shows that the principle of plenitude is incompatible with assumptions commonly made in possible worlds semantics. Here is how the argument goes: (i) There is a set W of possible worlds and a set P rop of propositions. (ii) There is, for every subset X of W , a corresponding p ...
... Now, Kaplan’s argument shows that the principle of plenitude is incompatible with assumptions commonly made in possible worlds semantics. Here is how the argument goes: (i) There is a set W of possible worlds and a set P rop of propositions. (ii) There is, for every subset X of W , a corresponding p ...
GLukG logic and its application for non-monotonic reasoning
... the replacement and deduction theorems. It should be expressive enough. If possible it should be finitely axiomatizable and somehow close to some constructive logic. If possible the logic should be many-valued. 2. Definition 1 should give the same result to our basic program B as the stable semantic ...
... the replacement and deduction theorems. It should be expressive enough. If possible it should be finitely axiomatizable and somehow close to some constructive logic. If possible the logic should be many-valued. 2. Definition 1 should give the same result to our basic program B as the stable semantic ...
Logical nihilism - University of Notre Dame
... naive procedural reading of its connectives. It also happens that structural completeness bears a precise relation to the phenomenon of Post-completeness, the situation in which any addition made to the set of theorems of some logic will trivialize the logic by making all formulas in its signature p ...
... naive procedural reading of its connectives. It also happens that structural completeness bears a precise relation to the phenomenon of Post-completeness, the situation in which any addition made to the set of theorems of some logic will trivialize the logic by making all formulas in its signature p ...
chapter 16
... — A universal proof (or universal derivation) is an ordered list of sentences in which every sentence is either a premise or is derived from earlier lines (not within a completed subproof) using an inference rule. If we are able to prove Φ(xʹ) where xʹ does not appear free in any line above the univ ...
... — A universal proof (or universal derivation) is an ordered list of sentences in which every sentence is either a premise or is derived from earlier lines (not within a completed subproof) using an inference rule. If we are able to prove Φ(xʹ) where xʹ does not appear free in any line above the univ ...
Propositional Logic - faculty.cs.tamu.edu
... Proof. We will show by induction on the degree of a proposition that an interpretation v0 : S → B has an extension to a valuation v : Prop → B. The uniqueness of this extension is obvious from Theorem 1. We set v(a) = v0 (a) for all a of degree 0. Then v is certainly a valuation on the set of degree ...
... Proof. We will show by induction on the degree of a proposition that an interpretation v0 : S → B has an extension to a valuation v : Prop → B. The uniqueness of this extension is obvious from Theorem 1. We set v(a) = v0 (a) for all a of degree 0. Then v is certainly a valuation on the set of degree ...
Variation of the Gravitational Constant and its Consequences
... Compton wavelength before the process must end either by repaying the energy debt or forcing the electron to sink back into the negative energy space from which it arose11. However the original electron is annihilated together with the positron, so the energy debt to the vacuum is repaid and the new ...
... Compton wavelength before the process must end either by repaying the energy debt or forcing the electron to sink back into the negative energy space from which it arose11. However the original electron is annihilated together with the positron, so the energy debt to the vacuum is repaid and the new ...
Point-free geometry, Approximate Distances and Verisimilitude of
... equip the class of possible scientific theories with a structure of approximate metric space and we define the verisimilitude of a theory as a function of its approximate distance from the truth (see also the definition of verisimilitude proposed in [5]). The motivation of such a choice is that usua ...
... equip the class of possible scientific theories with a structure of approximate metric space and we define the verisimilitude of a theory as a function of its approximate distance from the truth (see also the definition of verisimilitude proposed in [5]). The motivation of such a choice is that usua ...
Tautologies Arguments Logical Implication
... A formula A logically implies B if A ⇒ B is a tautology. Theorem: An argument is valid iff the conjunction of its premises logically implies the conclusion. Proof: Suppose the argument is valid. We want to show (A1 ∧ . . . ∧ An) ⇒ B is a tautology. • Do we have to try all 2k truth assignments (where ...
... A formula A logically implies B if A ⇒ B is a tautology. Theorem: An argument is valid iff the conjunction of its premises logically implies the conclusion. Proof: Suppose the argument is valid. We want to show (A1 ∧ . . . ∧ An) ⇒ B is a tautology. • Do we have to try all 2k truth assignments (where ...
ABSTRACT ENTANGLEMENT AND INFORMATION IN ALGEBRAIC QUANTUM THEORIES
... The purpose of this dissertation is to address some philosophical questions arising in the algebraic approach. In particular, as the title indicates, I focus on some issues concerning entanglement and information. The original part of the work is based on a few papers that I have already published ...
... The purpose of this dissertation is to address some philosophical questions arising in the algebraic approach. In particular, as the title indicates, I focus on some issues concerning entanglement and information. The original part of the work is based on a few papers that I have already published ...
Monday, Nov. 6, 2006
... • This QN is found to be conserved in strong interactions • But not conserved in EM or Weak interactions • Third component of the isospin QN is assigned to be positive for the particles with larger electric charge • Isospin is not a space-time symmetry • Cannot be assigned uniquely to leptons and ph ...
... • This QN is found to be conserved in strong interactions • But not conserved in EM or Weak interactions • Third component of the isospin QN is assigned to be positive for the particles with larger electric charge • Isospin is not a space-time symmetry • Cannot be assigned uniquely to leptons and ph ...
Admissible rules in the implication-- negation fragment of intuitionistic logic
... It can be checked, following [23], that for any intermediate logic L and finite set of implicational formulas {ϕ1 , . . . , ϕn }, the substitution σ p = ϕ1 → (ϕ2 → (· · · → (ϕn → p) · · · ) is an L-projective unifier. So by Lemma 2.3, the implicational fragment of any intermediate logic is (heredita ...
... It can be checked, following [23], that for any intermediate logic L and finite set of implicational formulas {ϕ1 , . . . , ϕn }, the substitution σ p = ϕ1 → (ϕ2 → (· · · → (ϕn → p) · · · ) is an L-projective unifier. So by Lemma 2.3, the implicational fragment of any intermediate logic is (heredita ...