Related papers: On The Composition Lemma
This paper introduces and studies the sequential composition and decomposition of propositional logic programs. We show that acyclic programs can be decomposed into single-rule programs and provide a general decomposition result for…
We introduce a principle of local collection for compositional truth predicates and show that it is conservative over the classically compositional theory of truth in the arithmetical setting. This axiom states that upon restriction to…
In this paper, we will study the simplest kind of beauty that can be found in a simple piece of music and can be appreciated universally. The proposed approach shows that aesthetically appealing patterns deliver higher amount of information…
The need for rigorous process composition is encountered in many situations pertaining to the development and analysis of complex systems. We discuss the use of Classical Linear Logic (CLL) for correct-by-construction resource-based process…
We make two observations regarding a recent tight example for a composition theorem for randomized query complexity: (1) it implies general randomized query-to-communication lifting is not always true if one allows relations, (2) it is in a…
We present a new, easy, and elementary proof of Jensen's Theorem on the uniqueness of infinity harmonic functions. The idea is to pass to a finite difference equation by taking maximums and minimums over small balls.
We prove two theorems on cohomologically complete complexes. These theorems are inspired by, and yield an alternative proof of, a recent theorem of P. Schenzel on complete modules.
We give a one-sentence elementary proof of the combinatorial Fa\`a di Bruno's formula.
In logic there is a clear concept of what constitutes a proof and what not. A proof is essentially defined as a finite sequence of formulae which are either axioms or derived by proof rules from formulae earlier in the sequence.…
We exhibit how the Rasiowa-Sikorski Lemma simplifies, in a sense, proofs of results that make use of the technique known as back-and-forth, often resulting in not very illustrative arguments. The first two sections seek to show one simple…
In this note, we provide a simple derivation of expressions for the restricted partition function and its polynomial part. Our proof relies on elementary algebra on rational functions and a lemma that expresses the polynomial part as an…
In this note we give a short, direct proof of the well known Combinatorial Nullstellensatz.
Scientific studies of consciousness rely on objects whose existence is assumed to be independent of any consciousness. On the contrary, we assume consciousness to be fundamental, and that one of the main features of consciousness is…
A very simple but useful almost sure convergence theorem of probability is given.
In this paper we give two theorems from the Propositional Calculus of the Boolean Logic with their consequences and applications and we prove them axiomatically.
This paper explores verification of constituent systems within the context of the Symphony tool platform for Systems of Systems (SoS). Our SoS modelling language, CML, supports various contractual specification elements, such as state…
Every system of any significant size is created by composition from smaller sub-systems or components. It is thus fruitful to analyze the fault-tolerance of a system as a function of its composition. In this paper, two basic types of system…
We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.
The sets used to construct other mathematical objects are pure sets, which means that all of their elements are sets, which are themselves pure. One set may therefore be within another, not as an element, but as an element of an element, or…
We obtain simple proofs of certain inequalites for bivariate means.