admissible and derivable rules in intuitionistic logic
... rules. This problem seems to be related with some constructive features of intuitionism (disjunction and existence property) but appear also in modal logics. We study here a particular case of this phenomenon, admissible rules in propositional calculus. G.E.Mints in [Mi 72] give sufficients conditio ...
... rules. This problem seems to be related with some constructive features of intuitionism (disjunction and existence property) but appear also in modal logics. We study here a particular case of this phenomenon, admissible rules in propositional calculus. G.E.Mints in [Mi 72] give sufficients conditio ...
The prime divisors of the number of points on abelian
... Note, this map distinguishes for each p ∈ S whether ` divides or not the positive integer #A(kp ). We also write E := EndK̄ (A) ⊗ Q. We repeatedly make use of the following: If A is an elliptic curve without CM then for all but finitely many ` we have G` = GL2 (F` ), see [9, Thm. 2]. If A is an elli ...
... Note, this map distinguishes for each p ∈ S whether ` divides or not the positive integer #A(kp ). We also write E := EndK̄ (A) ⊗ Q. We repeatedly make use of the following: If A is an elliptic curve without CM then for all but finitely many ` we have G` = GL2 (F` ), see [9, Thm. 2]. If A is an elli ...
Divide and congruence applied to eta-bisimulation
... equivalence consists of a class C of modal formulas such that two processes are equivalent if and only if they make true the same formulas in C. For instance, Hennessy-Milner logic [14] is the modal characterisation of bisimulation. Larsen and Liu [15] introduced a method for decomposing formulas fr ...
... equivalence consists of a class C of modal formulas such that two processes are equivalent if and only if they make true the same formulas in C. For instance, Hennessy-Milner logic [14] is the modal characterisation of bisimulation. Larsen and Liu [15] introduced a method for decomposing formulas fr ...
The Stochastic Geometric Machine Model1
... computation in familiar vector spaces. For that, a stochastic number is conceived as a gaussian random variable (in the continuous space) with a known mean value (real number) and a known standard deviation (nonnegative real number). This notion of (proper, usual) deviation is generalized and improp ...
... computation in familiar vector spaces. For that, a stochastic number is conceived as a gaussian random variable (in the continuous space) with a known mean value (real number) and a known standard deviation (nonnegative real number). This notion of (proper, usual) deviation is generalized and improp ...
A Crevice on the Crane Beach: Finite-Degree
... • The graph of any nondecreasing unbounded function is exactly one power of two strictly greater than x, using the f : N → N defines a finite-degree predicate, since f −1 (n) monadic predicate true on powers of two. Moreover, we can is a finite set for all n; define formulas trans(i) (x, y), 1 ≤ i ≤ ...
... • The graph of any nondecreasing unbounded function is exactly one power of two strictly greater than x, using the f : N → N defines a finite-degree predicate, since f −1 (n) monadic predicate true on powers of two. Moreover, we can is a finite set for all n; define formulas trans(i) (x, y), 1 ≤ i ≤ ...
Temporal Here and There - Computational Cognition Lab
... are interpreted by the precedence relation between integers. For this reason, we had to redefine the filtration method in an appropriate way (see Sect. 6 for details). Moreover, the determinisation of the filtrated model requires, in the case of ordinary temporal logic, the use of a characteristic fo ...
... are interpreted by the precedence relation between integers. For this reason, we had to redefine the filtration method in an appropriate way (see Sect. 6 for details). Moreover, the determinisation of the filtrated model requires, in the case of ordinary temporal logic, the use of a characteristic fo ...
Document
... Notice that the inverse of g (x) = x 3 is a function, but that the inverse of f (x) = x 2 is not a function. On the other hand, the graph of g (x) = xf3(xcannot ) = x 2 be intersected twice with a horizontal line and its inverse is a function. ...
... Notice that the inverse of g (x) = x 3 is a function, but that the inverse of f (x) = x 2 is not a function. On the other hand, the graph of g (x) = xf3(xcannot ) = x 2 be intersected twice with a horizontal line and its inverse is a function. ...
Chapter 4 - Functions
... I will not examine you on ‘functions of two variables’ like this, I have just included it for interest. Example 4.2.7. It may also be the case that the graph cannot be represented as a picture. For example, a function could have the plane as its domain and as its codomain. In this case we would need ...
... I will not examine you on ‘functions of two variables’ like this, I have just included it for interest. Example 4.2.7. It may also be the case that the graph cannot be represented as a picture. For example, a function could have the plane as its domain and as its codomain. In this case we would need ...
R The Topology of Chapter 5 5.1
... Definition 5.2.2. A set S ⊂ R is disconnected if there are two open intervals U and V such that U ∩ V = ∅, U ∩ S ̸= ∅, V ∩ S ̸= ∅ and S ⊂ U ∪ V . Otherwise, it is connected. The sets U ∩ S and V ∩ S are said to be a separation of S. In other words, S is disconnected if it can be written as the union ...
... Definition 5.2.2. A set S ⊂ R is disconnected if there are two open intervals U and V such that U ∩ V = ∅, U ∩ S ̸= ∅, V ∩ S ̸= ∅ and S ⊂ U ∪ V . Otherwise, it is connected. The sets U ∩ S and V ∩ S are said to be a separation of S. In other words, S is disconnected if it can be written as the union ...
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... We briefly review the five standard systems of reverse mathematics. For completeness, we include systems stronger than arithmetical comprehension, but these will play no part in this paper. Details, general background, and results, as well as many examples of reversals, can be found in Simpson [1999 ...
... We briefly review the five standard systems of reverse mathematics. For completeness, we include systems stronger than arithmetical comprehension, but these will play no part in this paper. Details, general background, and results, as well as many examples of reversals, can be found in Simpson [1999 ...
