bucephalus.org
bucephalus.org on logic
http://www.bucephalus.org/text/TheoAlgAxioms/TheoAlgAxioms.html
Axioms of theory algebras. Content: 1. Preliminaries, 2. Definitions of theory algebras, 3. Models of theory algebras, 4. Appendix: The axiom system of a complete theory algebra. October 2002, 10 pages.
bucephalus.org
bucephalus.org on logic
http://www.bucephalus.org/text/TheoryAlgebras/TheoryAlgebras.html
From propositional logic to theory algebra. Quick remainder on the syntax and semantics of propositional logic. A = {p,q,r,s}. And the set of. Two example formulas are [1]. Psi; := p → q. Upsilon; := ¬(p ∧ ¬ q)&and (r → r). The semantic of a formula is given by its. For the two example formulas, that is. B := {0,1}. The set of boolean values and. The atom set of a formula. Then formally speaking, the truth table of. Is a function of type. Phi; → B) → B. P ⇒ p ∨ ¬r. Not;p ∨ r ⇔ p → r. X ∧ y. Not(p ∨...
bucephalus.org
bucephalus.org on logic
http://www.bucephalus.org/text/BucanonScreenshots/BucanonScreenshots.html
Screenshots and samples of the bucanon applet in action. The plain bucanon panel. This is the plain panel. Of the bucanon applet. Which appears if the browser understands Java and everything works fine. The features may vary a little from system to system. The example here is taken from a Windows XP machine. First, insert a boolean formula, say. A,b] = ['a;'b] ]. Then call an action, e.g. eval. And view the result in the output area:. Input (in stroke notation):. A,b] = ['a;'b] ]. So the result is! Which...
bucephalus.org
bucephalus.org on logic
http://www.bucephalus.org/text/BucanonSyntax/BucanonSyntax.html
The grammar of formulas, i.e. the language accepted by the bucanon applet. September 2002, one single page.
bucephalus.org
bucephalus.org on logic
http://www.bucephalus.org/text/BucanonIntroContinued/BucanonIntroContinued.html
Bucanon introduction, continued: Motivating theory algebras. Next to the common algebraization of propositional logic as boolean algebra. We introduce our modified algebraization as a theory algebra. Based on not only one, but two order structures: the semantic and the syntactic (i.e. atomic) order. The paradigmatic model of this kind of theory algebra is the structure of (binary) worlds. September 2002, 3 pages.
bucephalus.org
bucephalus.org on logic
http://www.bucephalus.org/projectlist.html
Was the name of Alexander the Great's horse. In the centuries afterwards, this frequently served as a proper name example in many classic text books of philosophy and logic. Here and now,. Is the title of an ongoing research project in logic, which went online as. Major and minor projects. Current division into major projects. By now we have an effectively computable propositional logic system. This comes with an algebraic abstraction of propositional logic as a. Theory algebra of relations. Ie a kind of...
bucephalus.org
bucephalus.org on logic
http://www.bucephalus.org/text/Meaning/Meaning.html
A logical concept of meaning. Elaboration of the ideas introduced in The introduction to a logical concept of meaning. And Die Einführung eines logischen Bedeutungsbegriffs. Finished May 1997, published November 1999, 59 pages.
bucephalus.org
bucephalus.org on logic
http://www.bucephalus.org/textlist.html
List of papers and books. Introduction to a logical concept of meaning. Einführung eines logischen Bedeutungsbegriffs. A logical concept of meaning. Theory algebra of relations. Axioms of theory algebras. Theory and implementation of efficient canonical systems for sentential calculus, based on Prime Normal Forms. The Haskell PropLogic package. Installing the PropLogic package. A little program for propositional logic. Brief introduction to PropLogic. Guide to the bucanon software and documentation.
bucephalus.org
bucephalus.org on logic
http://www.bucephalus.org/text/IntroMeaning/IntroMeaning.html
The introduction to a logical concept of meaning. The traditional semantic is based on the supposition of two ontological levels - a world. And understands semantic symptoms as mutual mappings between the phenomena of the world and the expressions of the language: expressions express phenomena on the one hand, phenomena are the meanings of the expressions on the other. Semantic relations do only exist as relations between the signs of a given system. The fundamental principle. Is thus: the meaning. Can a...
