Theorem proving with abstraction, part I /

"UILU-ENG 79-1706."

Our foreign relations : showing present perils from England and France, the nature and conditions of intervention by mediation, and also by recognition, the impossibility of any recognition of a new power with slavery as a corner-stone, and the wrongful concession of ocean belligerency. Speech of Hon. Charles Sumner, before the citizens of New York, at the Cooper Institute, Sept. 10, 1863.

Mode of access: Internet.

The impossibility of social democracy, being a supplement to "The quintessence of socialism",

"Translated from the fourth German Edition, by A. C. Morant."

Binomial theorem and logarithms. For the use of the midshipmen at the naval school, Philadelphia.

Preface signed: William Chauvenet.

The true intellectual system of the universe : wherein all the reason and philosophy of atheism is confuted, and its impossibility demonstrated. A treatise on immutable morality; with a discourse concerning the true notion of the Lord's supper: and two sermons on 1. John 2: 3, 4, and 1. Cor. 15: 27.

Mode of access: Internet.

The philosophical significance of Cox's theorem

Cox's theorem states that, under certain assumptions, any measure of belief is isomorphic to a probability measure. This theorem, although intended as a justification of the subjectivist interpretation of probability theory, is sometimes presented as an argument for more controversial theses. Of particular interest is the thesis that the only coherent means of representing uncertainty is via the probability calculus. In this paper I examine the logical assumptions of Cox's theorem and I show how these impinge on the philosophical conclusions thought to be supported by the theorem. I show that the more controversial thesis is not supported by Cox's theorem. (C) 2003 Elsevier Inc. All rights reserved.

No(i)stalgia: On the impossibility of recognising noise in the present

Starting from a comparison between the process of writing by hand and writing to screen, this paper contends that there is a continuity between the former, apparently archaic form of writing, and the latter, supposedly more modern form of writing. It will be suggested that, rather than being truly archaic, writing by hand perhaps constitutes a nostalgic act which attempts to bypass the perceived virtuality of the postmodern condition. As such, it will be claimed, via Baudrillard, that nostalgia of this kind is a type of hyper-simulacrum that relies on a misinterpretation of the noise created by the very act of expression. It will be claimed, however, that if interpreted without the sort of wilful misinterpretation to which noise often falls prey, many kinds of noise grafted onto contemporary cultural objects bear testimony to a certain continuity across historical eras as well as to the fact that we are ultimately incapable of recognising many cultural products' noise (and thus the products themselves in their entirety) in their own era. This paper therefore calls for a noisy theory which, analysing the world from an immanent position, would acknowledge the impossibility of full knowledge of the sign

Axiomatisation of an Interval Calculus for Theorem Proving

We provide an axiomatisation of the Timed Interval Calculus, a set-theoretic notation for expressing properties of time intervals. We implement the axiomatisation in the Ergo theorem prover in order to allow the machine-checked proof of laws for reasoning about predicates expressed using interval operators. These laws can be then used in the machine-assisted verification of real-time applications.

Improvements on the Juxtaposing Theorem

A new class of binary constant weight codes is presented. We establish new lower bound and exact values on A(n1 +n2; 2(a1 +a2); n2) ≥ min {M1;M2}+1, if A(n1; 2a1; a1 +b1) = M1 and A(n2; 2b2; a2 +b2) = M2, in particular, A(30; 16; 15) = 16 and A(33; 18; 15) = 11.

On the Various Bisection Methods Derived from Vincent’s Theorem

In 2000 A. Alesina and M. Galuzzi presented Vincent’s theorem “from a modern point of view” along with two new bisection methods derived from it, B and C. Their profound understanding of Vincent’s theorem is responsible for simplicity — the characteristic property of these two methods. In this paper we compare the performance of these two new bisection methods — i.e. the time they take, as well as the number of intervals they examine in order to isolate the real roots of polynomials — against that of the well-known Vincent-Collins-Akritas method, which is the first bisection method derived from Vincent’s theorem back in 1976. Experimental results indicate that REL, the fastest implementation of the Vincent-Collins-Akritas method, is still the fastest of the three bisection methods, but the number of intervals it examines is almost the same as that of B. Therefore, further research on speeding up B while preserving its simplicity looks promising.

On a New Approach to Williamson's Generalization of Pólya's Enumeration Theorem

Pólya’s fundamental enumeration theorem and some results from Williamson’s generalized setup of it are proved in terms of Schur- Macdonald’s theory (S-MT) of “invariant matrices”. Given a permutation group W ≤ Sd and a one-dimensional character χ of W , the polynomial functor Fχ corresponding via S-MT to the induced monomial representation Uχ = ind|Sdv/W (χ) of Sd , is studied. It turns out that the characteristic ch(Fχ ) is the weighted inventory of some set J(χ) of W -orbits in the integer-valued hypercube [0, ∞)d . The elements of J(χ) can be distinguished among all W -orbits by a maximum property. The identity ch(Fχ ) = ch(Uχ ) of both characteristics is a consequence of S-MT, and is equivalent to a result of Williamson. Pólya’s theorem can be obtained from the above identity by the specialization χ = 1W , where 1W is the unit character of W.