Tag Archives: Logical Graphs

How To Succeed In Proof Business Without Really Trying

Posted on July 15, 2013 by Jon Awbrey

Re: R.J. Lipton • Surely You Are Joking? Comment 1 Even at the mailroom entry point of propositional calculus, there is a qualitative difference between insight proofs and routine proofs.  Human beings can do either sort, as a rule, but … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Automatic Theorem Proving, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Graph Theory, Logic, Logical Graphs, Minimal Negation Operators, Model Theory, Peirce, Praeclarum Theorema, Proof Theory, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , , , , , , , , | 7 Comments

Special Classes of Propositions

Posted on May 31, 2013 by Jon Awbrey

Adapted from Differential Propositional Calculus • Special Classes of Propositions A basic proposition, coordinate proposition, or simple proposition in the universe of discourse is one of the propositions in the set Among the propositions in are several families of propositions … Continue reading →

Posted in Boolean Functions, Computational Complexity, Differential Logic, Equational Inference, Functional Logic, Indication, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , | 2 Comments

Finding a Needle in a Cactus Patch

Posted on April 30, 2013 by Jon Awbrey

Re: R.J. Lipton • Sex, Lies, And Quantum Computers Don’t know much about quantum computation, but my ventures in graphical syntaxes for propositional calculus did turn up a logical operator whose evaluation process reminded me a little of the themes … Continue reading →

Posted in Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Graph Theory, Logic, Logical Graphs, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Quantum Computing, Semiotics | Tagged , , , , , , , , , , , , | 4 Comments

Propositions As Types Analogy • 1

Posted on January 29, 2013 by Jon Awbrey

Re: R.J. Lipton • Mathematical Tricks One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy. And I see hints the 2‑part analogy can be extended to a … Continue reading →

Posted in Animata, C.S. Peirce, Combinator Calculus, Combinatory Logic, Curry–Howard Isomorphism, Graph Theory, Lambda Calculus, Logic, Logical Graphs, Mathematics, Proof Theory, Propositions As Types Analogy, Type Theory | Tagged , , , , , , , , , , , , | 3 Comments

Paradisaical Logic and the After Math

Posted on April 9, 2012 by Jon Awbrey

Re: Peter Cameron • Cultures, Tribes, or Just an Illusion? Re: Peirce List • (1) (2) (3) (4) Not too coincidentally with the mention of Peirce’s existential graphs, a tangent of discussion elsewhere brought to mind an old favorite passage … Continue reading →

Posted in Amphecks, C.S. Peirce, Critical Thinking, Inquiry, Logic, Logic of Relatives, Logical Graphs, Logical Reflexion, Mathematics, Peirce, Relation Theory, Second Intentions, Semiotics, Sign Relations, Truth Theory, Visualization | Tagged , , , , , , , , , , , , , , , | 2 Comments

C.S. Peirce • Relatives of Second Intention

Posted on April 7, 2012 by Jon Awbrey

Selections from C.S. Peirce, “The Logic of Relatives”, CP 3.456–552 488.   The general method of graphical representation of propositions has now been given in all its essential elements, except, of course, that we have not, as yet, studied any truths … Continue reading →

Posted in Abstraction, Amphecks, C.S. Peirce, Cognition, Experience, Inquiry, Logic, Logic of Relatives, Logical Graphs, Logical Reflexion, Mathematics, Peirce, Relation Theory, Second Intentions, Semiotics, Sign Relations, Truth Theory | Tagged , , , , , , , , , , , , , , , , | 7 Comments

Peirce’s Law

Posted on October 6, 2008 by Jon Awbrey

Peirce’s law is a logical proposition that states a non-obvious truth of classical logic and affords a novel way of defining classical propositional calculus. Continue reading →

Posted in C.S. Peirce, Equational Inference, Laws of Form, Logic, Logical Graphs, Mathematics, Peirce, Peirce's Law, Proof Theory, Propositional Calculus, Propositions As Types Analogy, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , | 15 Comments

Praeclarum Theorema

Posted on October 5, 2008 by Jon Awbrey

The praeclarum theorema, or splendid theorem, is a theorem of propositional calculus that was noted and named by G.W. Leibniz. Continue reading →

Posted in Abstraction, Animata, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Form, Graph Theory, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Painted Cacti, Peirce, Praeclarum Theorema, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown | Tagged , , , , , , , , , , , , , , , , , , , , , | 17 Comments

Logical Graphs • Formal Development

Posted on September 19, 2008 by Jon Awbrey

Logical graphs are next presented as a formal system by going back to the initial elements and developing their consequences in a systematic manner. Continue reading →

Posted in Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , | 41 Comments

Hypostatic Abstraction

Posted on August 8, 2008 by Jon Awbrey

Hypostatic Abstraction (HA) is a formal operation on a subject–predicate form that preserves its information while introducing a new subject and upping the “arity” of its predicate. To cite a notorious example, HA turns “Opium is drowsifying” into “Opium has dormitive virtue”. Continue reading →

Posted in Abstraction, Article, C.S. Peirce, Hypostatic Abstraction, Logic, Logic of Relatives, Logical Graphs, Mathematics, Molière, Peirce, Reification, Relation Theory | Tagged , , , , , , , , , , , | 5 Comments