Related papers: Boole's Method I. A Modern Version
To determine Euler numbers modulo powers of two seems to be a difficult task. In this paper we achieve this and apply the explicit congruence to give a new proof of a classical result due to M. A. Stern.
In this work, a novel quaternary algebra has been proposed that can be used to implement an arbitrary quaternary logic function in more than one systematic ways. The proposed logic has evolved from and is closely related to the Boolean…
The goal of this modern presentation, followed by an English translation from the German, is to make available some parts of Lie's very systematic mathematical thought which deserve to join the contemporary literature, and above all also,…
Algebraic logic studies algebraic theories related to proposition and first-order logic. A new algebraic approach to first-order logic is sketched in this paper. We introduce the notion of a quantifier theory, which is a functor from the…
We present a method for the solution of polynomial equations. We do not intend to present one more method among several others, because today there are many excellent methods. Our main aim is educational. Here we attempt to present a method…
Several open problems in algebraic logic are solved.
This paper from 2008 is the first in a series of three related papers on modal methods in interpretability logics and applications. In this first paper the foundations are laid for later results. These foundations consist of a thorough…
"The hardest logic puzzle ever" presented by George Boolos became a target for philosophers and logicians who tried to modify it and make it even tougher. I propose further modification of the original puzzle where part of the available…
We provide a complete axiomatization of modal inclusion logic - team-based modal logic extended with inclusion atoms. We review and refine an expressive completeness and normal form theorem for the logic, define a natural deduction proof…
Boolean calculus has been studied extensively in the past in the context of switching circuits, error-correcting codes etc. This work generalizes several approaches to defining a differential calculus for Boolean functions. A unified theory…
We present a slightly more general version of Boole's additive formula for factorials as a simple consequence of Lagrange's Interpolating Polynomial theorem.
Most discussions of G\"odel's theorems fall into one of two types: either they emphasize perceived philosophical, cultural "meanings" of the theorems, and perhaps sketch some of the ideas of the proofs, usually relating G\"odel's proofs to…
An alternative proof of the completeness of relational algebra with respect to allowed formulas of first-order logic is presented. The proof relies on the well-known embedding of relational algebra into cylindric algebra, which makes it…
An existing solvability result for relaxed one-sided Lipschitz algebraic inclusions is substantially improved. This enhanced solvability result allows the design of a very robust numerical method for the approximation of a solution of the…
We proove a Bloch's theorem in an almost complex projective plane.
The most recent wave of applications of logic to operator algebras is a young and rapidly developing field. This is a snapshot of the current state of the art.
We propose a new modal logic endowed with a simple deductive system to interpret Aristotle's theory of the modal syllogism. While being inspired by standard propositional modal logic it is also a logic of terms that admits a (sound)…
It is well-known that a Hilbert-style deduction system for first-order classical logic is sound and complete for a model theory built using all Boolean algebras as truth-value algebras if and only if it is sound and complete for a model…
In this note we comment on part of a recent article by B. Schroer and H.-W. Wiesbrock. Therein they calculate some new modular structure for the U(1)-current-algebra (Weyl-algebra). We point out that their findings are true in a more…
The article explores the arithmetic of multiplication as a model of many valued projective logic. It is demonstrated that closed numerical intervals within this framework constitute Heyting algebras. The conditions for these algebras to be…