From hierarchies to well-foundedness

We highlight that the connection of well-foundedness and recursive definitions is more than just convenience. While the consequences of making well-foundedness a sufficient condition for the existence of hierarchies (of various complexity) have been extensively studied, we point out that (if parameters are allowed) well-foundedness is a necessary condition for the existence of hierarchies e.g. that even in an intuitionistic setting (Π01−CA0)α⊢wf(α)where(Π01−CA0)α stands for the iteration of Π01 comprehension (with parameters) along some ordinal α and wf(α) stands for the well-foundedness of α.

Forcing for hat inductive definitions in arithmetic

By forcing, we give a direct interpretation of inline image into Avigad's inline image. To the best of the author's knowledge, this is one of the simplest applications of forcing to “real problems”.

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<ω 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.

Realizing public announcements by justifications

Modal public announcement logics study how beliefs change after public announcements. However, these logics cannot express the reason for a new belief. Justification logics fill this gap since they can formally represent evidence and justifications for an agent's belief. We present OPAL(K) and JPAL(K) , two alternative justification counterparts of Gerbrandy–Groeneveld's public announcement logic PAL(K) . We show that PAL(K) is the forgetful projection of both OPAL(K) and JPAL(K) . We also establish that JPAL(K) partially realizes PAL(K) . The question whether a similar result holds for OPAL(K) is still open.

Logical omniscience as infeasibility

Logical theories for representing knowledge are often plagued by the so-called Logical Omniscience Problem. The problem stems from the clash between the desire to model rational agents, which should be capable of simple logical inferences, and the fact that any logical inference, however complex, almost inevitably consists of inference steps that are simple enough. This contradiction points to the fruitlessness of trying to solve the Logical Omniscience Problem qualitatively if the rationality of agents is to be maintained. We provide a quantitative solution to the problem compatible with the two important facets of the reasoning agent: rationality and resource boundedness. More precisely, we provide a test for the logical omniscience problem in a given formal theory of knowledge. The quantitative measures we use are inspired by the complexity theory. We illustrate our framework with a number of examples ranging from the traditional implicit representation of knowledge in modal logic to the language of justification logic, which is capable of spelling out the internal inference process. We use these examples to divide representations of knowledge into logically omniscient and not logically omniscient, thus trying to determine how much information about the reasoning process needs to be present in a theory to avoid logical omniscience.

Censors for Boolean Description Logic

Protecting different kinds of information has become an important area of research. One aspect is to provide effective means to avoid that secrets can be deduced from the answers of legitimate queries. In the context of atomic propositional databases several methods have been developed to achieve this goal. However, in those databases it is not possible to formalize structural information. Also they are quite restrictive with respect to the specification of secrets. In this paper we extend those methods to match the much greater expressive power of Boolean description logics. In addition to the formal framework, we provide a discussion of various kinds of censors and establish different levels of security they can provide.

Context-aware Adaptation Mechanism for Video Dissemination over Flying Ad-Hoc Networks

The user experience on watching live video se- quences transmitted over a Flying Ad-Hoc Networks (FANETs) must be considered to drop packets in overloaded queues, in scenarios with high buffer overflow and packet loss rate. In this paper, we introduce a context-aware adaptation mechanism to manage overloaded buffers. More specifically, we propose a utility function to compute the dropping probability of each packet in overloaded queues based on video context information, such as frame importance, packet deadline, and sensing relevance. In this way, the proposed mechanism drops the packet that adds the minimum video distortion. Simulation evaluation shows that the proposed adaptation mechanism provides real-time multimedia dissemination with QoE support in a multi-hop, multi-flow, and mobile network environments.

Objekte auf Kulturreise: Wie das @ in unsere Mailbox kam (Ausstellung)

Wie kam das polynesische Wort «Tabu» nach Europa, die Kalaschnikow auf die Flagge Mosambiks? Finden Sie unterhaltsame Antworten im Projekt «KulturTransfer».

The diffusion of /l/ -vocalization in Swiss German

Several western Swiss German dialects roughly grouped around the nation's capital Bern show /l/ > [u] vocalization in various contexts. The spatial boundaries of /l/-vocalization in Swiss German are suspected to have been expanding since being described in the Linguistic Atlas of German-Speaking Switzerland in the middle of the 20th century. The present study assesses the overall expansion of /l/-vocalization by means of a rapid anonymous survey in 20 urban regional centers situated just beyond the traditional boundaries of /l/-vocalization highlighted by the Atlas. Results show that the expansion of /l/-vocalization mainly progresses in southeasterly, southerly, and westerly directions, but with much less success to the north and northwest, where the equally influential dialectal areas of Basel and Zürich seem to exert opposing influences. Further analysis of the data indicates that somewhat differing constraint hierarchies are at work in the different places to which vocalization has diffused.