A Restriction-Centered Theory of Reasoning and Computation to materialize a Web 3.0

Researchers suggest that personalization on the Semantic Web adds up to a Web 3.0 eventually. In this Web, personalized agents process and thus generate the biggest share of information rather than humans. In the sense of emergent semantics, which supplements traditional formal semantics of the Semantic Web, this is well conceivable. An emergent Semantic Web underlying fuzzy grassroots ontology can be accomplished through inducing knowledge from users' common parlance in mutual Web 2.0 interactions [1]. These ontologies can also be matched against existing Semantic Web ontologies, to create comprehensive top-level ontologies. On the Web, if augmented with information in the form of restrictions andassociated reliability (Z-numbers) [2], this collection of fuzzy ontologies constitutes an important basis for an implementation of Zadeh's restriction-centered theory of reasoning and computation (RRC) [3]. By considering real world's fuzziness, RRC differs from traditional approaches because it can handle restrictions described in natural language. A restriction is an answer to a question of the value of a variable such as the duration of an appointment. In addition to mathematically well-defined answers, RRC can likewise deal with unprecisiated answers as "about one hour." Inspired by mental functions, it constitutes an important basis to leverage present-day Web efforts to a natural Web 3.0. Based on natural language information, RRC may be accomplished with Z-number calculation to achieve a personalized Web reasoning and computation. Finally, through Web agents' understanding of natural language, they can react to humans more intuitively and thus generate and process information.

Relative Predicativity and dependent recursion in second-order set theory and higher-orders theories

This article reports that some robustness of the notions of predicativity and of autonomous progression is broken down if as the given infinite total entity we choose some mathematical entities other than the traditional ��. Namely, the equivalence between normal transfinite recursion scheme and new dependent transfinite recursion scheme, which does hold in the context of subsystems of second order number theory, does not hold in the context of subsystems of second order set theory where the universe V of sets is treated as the given totality (nor in the contexts of those of n+3-th order number or set theories, where the class of all n+2-th order objects is treated as the given totality).

Explicit mathematics and operational set theory: some ontological comparisons

We discuss several ontological properties of explicit mathematics and operational set theory: global choice, decidable classes, totality and extensionality of operations, function spaces, class and set formation via formulas that contain the definedness predicate and applications.

A note on the theory SID<�� of stratified induction

We introduce and analyse a theory of finitely stratified general inductive definitions over the natural numbers, inline image, and establish its proof theoretic ordinal, inline image. The definition of inline image bears some similarities with Leivant's ramified theories for finitary inductive definitions.

A feasible theory of truth over combinatory algebra

We define an applicative theory of truth TPT which proves totality exactly for the polynomial time computable functions. TPT has natural and simple axioms since nearly all its truth axioms are standard for truth theories over an applicative framework. The only exception is the axiom dealing with the word predicate. The truth predicate can only reflect elementhood in the words for terms that have smaller length than a given word. This makes it possible to achieve the very low proof-theoretic strength. Truth induction can be allowed without any constraints. For these reasons the system TPT has the high expressive power one expects from truth theories. It allows embeddings of feasible systems of explicit mathematics and bounded arithmetic. The proof that the theory TPT is feasible is not easy. It is not possible to apply a standard realisation approach. For this reason we develop a new realisation approach whose realisation functions work on directed acyclic graphs. In this way, we can express and manipulate realisation information more efficiently.

A new model construction by making a detour via intuitionistic theories I: Operational set theory without choice is ��1-equivalent to KP

We introduce a version of operational set theory, OST���, without a choice operation, which has a machinery for ��0��0 separation based on truth functions and the separation operator, and a new kind of applicative set theory, so-called weak explicit set theory WEST, based on G��del operations. We show that both the theories and Kripke���Platek set theory KPKP with infinity are pairwise ��1��1 equivalent. We also show analogous assertions for subtheories with ���-induction restricted in various ways and for supertheories extended by powerset, beta, limit and Mahlo operations. Whereas the upper bound is given by a refinement of inductive definition in KPKP, the lower bound is by a combination, in a specific way, of realisability, (intuitionistic) forcing and negative interpretations. Thus, despite interpretability between classical theories, we make ���a detour via intuitionistic theories���. The combined interpretation, seen as a model construction in the sense of Visser's miniature model theory, is a new way of construction for classical theories and could be said the third kind of model construction ever used which is non-trivial on the logical connective level, after generic extension �� la Cohen and Krivine's classical realisability model.

Coordinating Platform-Based Multi-Sourcing: Introducing the Theory of Convention

Spurred by the consumer market, companies increasingly deploy smartphones or tablet computers in their operations. However, unlike private users, companies typically struggle to cover their needs with existing applications, and therefore expand mobile software platforms through customized applications from multiple software vendors. Companies thereby combine the concepts of multi-sourcing and software platform ecosystems in a novel platform-based multi-sourcing setting. This implies, however, the clash of two different approaches towards the coordination of the underlying one-to-many inter-organizational relationships. So far, however, little is known about impacts of merging coordination approaches. Relying on convention theory, we addresses this gap by analyzing a platform-based multi-sourcing project between a client and six software vendors, that develop twenty-three custom-made applications on a common platform (Android). In doing so, we aim to understand how unequal coordination approaches merge, and whether and for what reason particular coordination mechanisms, design decisions, or practices disappear, while new ones emerge.

Concepts of Bitemporal Database Theory and the Evolution of Web-Documents

A vast amount of temporal information is provided on the Web. Even though many facts expressed in documents are time-related, the temporal properties of Web presentations have not received much attention. In database research, temporal databases have become a mainstream topic in recent years. In Web documents, temporal data may exist as meta data in the header and as user-directed data in the body of a document. Whereas temporal data can easily be identified in the semi-structured meta data, it is more difficult to determine temporal data and its role in the body. We propose procedures for maintaining temporal integrity of Web pages and outline different approaches of applying bitemporal data concepts for Web documents. In particular, we regard desirable functionalities of Web repositories and other Web-related tools that may support the Webmasters in managing the temporal data of their Web documents. Some properties of a prototype environment are described.