Canonical proof nets for classical logic

Proof nets provide abstract counterparts to sequent proofs modulo rule permutations; the idea being that if two proofs have the same underlying proof-net, they are in essence the same proof. Providing a convincing proof-net counterpart to proofs in the classical sequent calculus is thus an important step in understanding classical sequent calculus proofs. By convincing, we mean that (a) there should be a canonical function from sequent proofs to proof nets, (b) it should be possible to check the correctness of a net in polynomial time, (c) every correct net should be obtainable from a sequent calculus proof, and (d) there should be a cut-elimination procedure which preserves correctness. Previous attempts to give proof-net-like objects for propositional classical logic have failed at least one of the above conditions. In Richard McKinley (2010) [22], the author presented a calculus of proof nets (expansion nets) satisfying (a) and (b); the paper defined a sequent calculus corresponding to expansion nets but gave no explicit demonstration of (c). That sequent calculus, called LK∗ in this paper, is a novel one-sided sequent calculus with both additively and multiplicatively formulated disjunction rules. In this paper (a self-contained extended version of Richard McKinley (2010) [22]), we give a full proof of (c) for expansion nets with respect to LK∗, and in addition give a cut-elimination procedure internal to expansion nets – this makes expansion nets the first notion of proof-net for classical logic satisfying all four criteria.

Children's performance estimation in mathematics and science tests over a school year: A pilot study

The metacognitve ability to accurately estimate ones performance in a test, is assumed to be of central importance for initializing task-oriented effort. In addition activating adequate problem-solving strategies, and engaging in efficient error detection and correction. Although school children's' ability to estimate their own performance has been widely investigated, this was mostly done under highly-controlled, experimental set-ups including only one single test occasion. Method: The aim of this study was to investigate this metacognitive ability in the context of real achievement tests in mathematics. Developed and applied by a teacher of a 5th grade class over the course of a school year these tests allowed the exploration of the variability of performance estimation accuracy as a function of test difficulty. Results: Mean performance estimations were generally close to actual performance with somewhat less variability compared to test performance. When grouping the children into three achievement levels, results revealed higher accuracy of performance estimations in the high achievers compared to the low and average achievers. In order to explore the generalization of these findings, analyses were also conducted for the same children's tests in their science classes revealing a very similar pattern of results compared to the domain of mathematics. Discussion and Conclusion: By and large, the present study, in a natural environment, confirmed previous laboratory findings but also offered additional insights into the generalisation and the test dependency of students' performances estimations.

When language of instruction and language of application differ: Cognitive costs of bilingual mathematics learning

Bilingual education programs implicitly assume that the acquired knowledge is represented in a language-independent way. This assumption, however, stands in strong contrast to research findings showing that information may be represented in a way closely tied to the specific language of instruction and learning. The present study aims to examine whether and to which extent cognitive costs appear during arithmetic learning when language of instruction and language of retrieving differ. Thirty-nine high school students participating in a bilingual education program underwent a four-day training on multiplication and subtraction problems in one language (German or French), followed by a test session in which they had to solve trained as well as untrained problems in both languages. We found that cognitive costs related to language switching appeared for both arithmetic operations. Implications of our findings are discussed with respect to bilingual education as well as to cognitive mechanisms underlying different arithmetic operations.

A pure population of lung alveolar epithelial type II cells derived from human embryonic stem cells.

Alveolar epithelial type II (ATII) cells are small, cuboidal cells that constitute approximately 60% of the pulmonary alveolar epithelium. These cells are crucial for repair of the injured alveolus by differentiating into alveolar epithelial type I cells. ATII cells derived from human ES (hES) cells are a promising source of cells that could be used therapeutically to treat distal lung diseases. We have developed a reliable transfection and culture procedure, which facilitates, via genetic selection, the differentiation of hES cells into an essentially pure (>99%) population of ATII cells (hES-ATII). Purity, as well as biological features and morphological characteristics of normal ATII cells, was demonstrated for the hES-ATII cells, including lamellar body formation, expression of surfactant proteins A, B, and C, alpha-1-antitrypsin, and the cystic fibrosis transmembrane conductance receptor, as well as the synthesis and secretion of complement proteins C3 and C5. Collectively, these data document the successful generation of a pure population of ATII cells derived from hES cells, providing a practical source of ATII cells to explore in disease models their potential in the regeneration and repair of the injured alveolus and in the therapeutic treatment of genetic diseases affecting the lung.

REST-based sensor networks with OData

RESTful services gained a lot of attention recently, even in the enterprise world, which is traditionally more web-service centric. Data centric RESfFul services, as previously mainly known in web environments, established themselves as a second paradigm complementing functional WSDL-based SOA. In the Internet of Things, and in particular when talking about sensor motes, the Constraint Application Protocol (CoAP) is currently in the focus of both research and industry. In the enterprise world a protocol called OData (Open Data Protocol) is becoming the future RESTful data access standard. To integrate sensor motes seamlessly into enterprise networks, an embedded OData implementation on top of CoAP is desirable, not requiring an intermediary gateway device. In this paper we introduce and evaluate an embedded OData implementation. We evaluate the OData protocol in terms of performance and energy consumption, considering different data encodings, and compare it to a pure CoAP implementation. We were able to demonstrate that the additional resources needed for an OData/JSON implementation are reasonable when aiming for enterprise interoperability, where OData is suggested to solve both the semantic and technical interoperability problems we have today when connecting systems

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 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.

Proof internalization in generalized Frege systems for classical logic

We present a general method for inserting proofs in Frege systems for classical logic that produces systems that can internalize their own proofs.

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.

Colors in Mind: A Novel Paradigm to Investigate Pure Color Imagery

Mental color imagery abilities are commonly measured using paradigms that involve naming, judging, or comparing the colors of visual mental images of well-known objects (e.g., “Is a sunflower darker yellow than a lemon”?). Although this approach is widely used in patient studies, differences in the ability to perform such color comparisons might simply reflect participants’ general knowledge of object colors rather than their ability to generate accurate visual mental images of the colors of the objects. The aim of the present study was to design a new color imagery paradigm. Participants were asked to visualize a color for 3 s and then to determine a visually presented color by pressing 1 of 6 keys. The authors reasoned that participants would react faster when the imagined and perceived colors were congruent than when they were incongruent. In Experiment 1, participants were slower in incongruent than congruent trials but only when they were instructed to visualize the colors. The results in Experiment 2 demonstrate that the congruency effect reported in Experiment 1 cannot be attributed to verbalization of the color that had to be visualized. Finally, in Experiment 3, the congruency effect evoked by mental imagery correlated with performance in a perceptual version of the task. The authors discuss these findings with respect to the mechanisms that underlie mental imagery and patients suffering from color imagery deficits.

A new model construction by making a detour via intuitionistic theories I: Operational set theory without choice is Π1-equivalent to KP

We introduce a version of operational set theory, OST−, without a choice operation, which has a machinery for Δ0Δ0 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 Gödel operations. We show that both the theories and Kripke–Platek set theory KPKP with infinity are pairwise Π1Π1 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 à la Cohen and Krivine's classical realisability model.