Logic and Foundations Commons^™

Model-Completions And Model-Companions, Mostafa Mirabi

Mostafa Mirabi

The Feferman-Vaught Theorem, Mostafa Mirabi

Mostafa Mirabi

The Logic Of Uncertain Justifications, Robert Milnikel

Robert Milnikel

No abstract provided.

Observing, Reporting, And Deciding In Networks Of Sentences, H. Jerome Keisler, Jeffrey M. Keisler

Jeffrey Keisler

In prior work we considered networks of agents who prove facts from their knowledge bases and report them to their neighbors in their common languages in order to help a decider verify a single sentence. In report complete networks, the signatures of the agents and the links between agents are rich enough to verify any decider's sentence that can be proved from the combined knowledge base. This paper introduces a more general setting where new observations may be added to knowledge bases and the decider must choose a sentence from a set of alternatives. We consider the question of when …

Craig Interpolation For Networks Of Sentences, H Jerome Keisler, Jeffrey M. Keisler

Jeffrey Keisler

The Craig Interpolation Theorem can be viewed as saying that in first order logic, two agents who can only communicate in their common language can cooperate in building proofs. We obtain generalizations of the Craig Interpolation Theorem for finite sets of agents with the following properties. (1) The agents are vertices of a directed graph. (2) The agents have knowledge bases with overlapping signatures. (3) The agents can only communicate by sending to neighboring agents sentences that they know and that are in the common language of the two agents.

Loss Of Vision: How Mathematics Turned Blind While It Learned To See More Clearly, Bernd Buldt, Dirk Schlimm

Bernd Buldt

To discuss the developments of mathematics that have to do with the introduction of new objects, we distinguish between ‘Aristotelian’ and ‘non-Aristotelian’ accounts of abstraction and mathematical ‘top-down’ and ‘bottom-up’ approaches. The development of mathematics from the 19th to the 20th century is then characterized as a move from a ‘bottom-up’ to a ‘top-down’ approach. Since the latter also leads to more abstract objects for which the Aristotelian account of abstraction is not well-suited, this development has also lead to a decrease of visualizations in mathematical practice.

Morphogrammatics Of Reflection, Rudolf Kaehr

Rudolf Kaehr

Turning back from the studies of morphogrammatics to some open questions of reflectional programming, the recountered problematics might be put into a different light and new methods of handling formal aspects of reflection and reflectionality shall be introduced. Albeit the use of light-metaphors, morphogrammatic reflection is not sketched along the paradigm of optical metaphors. Morphograms are presenting neither propositions nor perceptions able for mirroring (representation). Exercises in defining morphogrammatic retro-grade recursion and reflection schemata are continued from the paper “Sketches to Morphogrammatic Programming”.

Memristics: Memristors, Again? – Part Ii, How To Transform Wired ‘Translations’ Between Crossbars Into Interactions?, Rudolf Kaehr

Rudolf Kaehr

The idea behind this patchwork of conceptual interventions is to show the possibility of a “buffer-free” modeling of the crossbar architecture for memristive systems on the base of a purely difference-theoretical approach. It is considered that on a nano-electronic level principles of interpretation appears as mechanisms of complementarity. The most basic conceptual approach to such a complementarity is introduced as an interchangeability of operators and operands of an operation. Therefore, the architecture of crossbars gets an interpretation as complementarity between crossbar functionality and “buffering” translation functionality. That is, the same matter functions as operator and at once, as operand – …

Memristics: Memristors, Again?, Rudolf Kaehr

Rudolf Kaehr

This collection gives first and short critical reflections on the concepts of memristics, memristors and memristive systems and the history of similar movements with an own focus on a possible interplay between memory and computing functions, at once, at the same place and time, to achieve a new kind of complementarity between computation and memory on a single chip without retarding buffering conditions.

Sketch Of A Typology Of Abstract Memristic Machines, Rudolf Kaehr

Rudolf Kaehr

A typology of memristic machines is sketched. This sketch gives an overview and orientation to the paper “Towards Abstract Memristic Machines”. It also intents to propose a concise systematization of the newly introduced terms and strategies to memristics and morphogrammatics. This sketch is introducing four types of sign-use for four types of machines of fundamentally different paradigms: 1. semiotic, 2. monomorphic, 3. polymorphic and 4. bisimilar abstract machines. Further definitions of abstract machines have to be based on those graphematic notational systems. A realization of such constructions of abstract machines, in contrast to existing abstract machines of the theory of …

Towards Abstract Memristic Machines, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

From Universe To Polyverses, Rudolf Kaehr

Rudolf Kaehr

Some thoughts about the power of speculation behind important discoveries in mathematics, physics and computer science. The exercise shows that there is no need for a compulsory ultimate unifying universe. It is speculated that just this paradigm of a single ultimate universe is unmasking itself today as the main obstacle for further development in Western science and technology.

Morphogrammatics For Dummies: The Domino Approach, Rudolf Kaehr

Rudolf Kaehr

Dominoes, morphograms, cellular automata, memristics. Topics: possible continuation, coalitions, cooperations, substitution, morphic bisimilarity.

The Logic Of Bailout Strategies, Rudolf Kaehr

Rudolf Kaehr

Some thoughts about/of the logic, blend, chiasm and diamond of bailout strategies. Eliciting aspects of the maxim: “Without insurrection, no resurrection".

Diamond Semiotic Short Studies, Rudolf Kaehr

Rudolf Kaehr

A collection of papers on semiotics, polycontexturality and diamond theory

Diamond Theory Collections. A Collection Of Papers And Fragments Towards Diamond Theory 2007-2009, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

Double Cross Playing Diamonds, Rudolf Kaehr

Rudolf Kaehr

Understanding interactivity in/between bigraphs and diamonds Grammatologically, the Western notational system is not offering space in itself to place sameness and otherness necessary to realize interaction/ality. Alphabetism is not prepared to challenge the dynamics of interaction directly. The Chinese writing system in its scriptural structuration, is able to place complex differences into itself, necessary for the development and design of formal systems and programming languages of interaction. The challenge of interactionality to Western thinking, modeling and design interactivity has to be confronted with the decline of the scientific power of alpha-numeric notational systems as media of living in a complex …

Short Studies 2008. Adventures In Diamond Strategies Of Change(S), Rudolf Kaehr

Rudolf Kaehr

Modular Bolognese Paradoxes of postmodern education. A Tale of Fishes, Birds and Diamonds in Second-Order Epistemology Why it is useless to write about the mono-contexturality of alphabetism and digitalism Chez Maxime's Human rights in a polycontextural world Primary Thoughts to a Manifesto for Awareness Fashion Marketing Which Equality? How equal are equal human beings? Generalized Diamonds From monosemic to tectonic complementarity Diamond Disremption Diamond interpretation of the kenomic succession operation Diamond Web2.0? How social is social networking? Web Mobility Web computing between semiotic and kenomic spaces Double Cross Playing Diamonds Understanding interactivity in/between bigraphs and diamonds Morphogrammatics of Change A …

Actors, Objects, Contextures, Morphograms, Rudolf Kaehr

Rudolf Kaehr

Systematic and historic overview and critics of actor and object oriented programming.

From Dialogues To Polylogues, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

The Abacus Of Universal Logics, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

Place-Valued Logics Around Cybernetic Ontology, The Bcl And Afosr, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

From Ruby To Rudy, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

The Chinese Challenge. Hallucinations For Other Futures, Rudolf Kaehr

Rudolf Kaehr

The main question is: What can we learn from China that China is not teaching us? It is proposed that a study of polycontextural logic and morphogrammatics could be helpful to discover this new kind of rationality.

Enumerations Of The Kolmogorov Function, Richard Beigel, Harry Buhrman, Peter Fejer, Lance Fortnow, Piotr Grabowski, Luc Longpré, Andrej Muchnik, Frank Stephan, Leen Torenvliet

Peter Fejer

A recursive enumerator for a function h is an algorithm f which enumerates for an input x finitely many elements including h(x). f is a k(n)-enumerator if for every input x of length n, h(x) is among the first k(n) elements enumerated by f. If there is a k(n)-enumerator for h then h is called k(n)-enumerable. We also consider enumerators which are only A-recursive for some oracle A.

We determine exactly how hard it is to enumerate the Kolmogorov function, which assigns to each string x its Kolmogorov complexity:

• For every underlying universal machine U, there is a constant a …

Fibonacci In Contextures, An Application, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

Contextures. Programming Dynamic Complexity, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

Gödel Games: "Cloning Gödel's Proofs", Rudolf Kaehr

Rudolf Kaehr

Gödel's Proofs in the context of beautifying (Hehner) and re-beautifying in polycontextural logic. Deconstruction of the relevance.

Lambda Calculi In Polycontextural Situations, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

Polylogics. Towards A Formalization Of Polycontextural Logics, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.