Proof Theory of the Cut Rule

2018 ◽  
Author(s):  
J. R. B. Cockett ◽  
R. A. G. Seely
Keyword(s):  
Proof Theory ◽  
Graphical Representation ◽  
Basic Component ◽  
Graphical Representations ◽  
Mathematical Language ◽  
Basic Logic ◽  
Cut Rule ◽  
Structural Rules ◽  
The One ◽  
Categorical Semantics

This chapter describes the categorical proof theory of the cut rule, a very basic component of any sequent-style presentation of a logic, assuming a minimum of structural rules and connectives, in fact, starting with none. It is shown how logical features can be added to this basic logic in a modular fashion, at each stage showing the appropriate corresponding categorical semantics of the proof theory, starting with multicategories, and moving to linearly distributive categories and *-autonomous categories. A key tool is the use of graphical representations of proofs (“proof circuits”) to represent formal derivations in these logics. This is a powerful symbolism, which on the one hand is a formal mathematical language, but crucially, at the same time, has an intuitive graphical representation.

scholarly journals On the correspondence between nested calculi and semantic systems for intuitionistic logics

2020 ◽  
Author(s):  
Tim Lyon
Keyword(s):  
Intuitionistic Logic ◽  
Structural Rules ◽  
First Order ◽  
Constant Domains ◽  
The Relationship ◽  
Intuitionistic Logics

Abstract This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is shown that Fitting’s nested calculi naturally arise from their corresponding labelled calculi—for each of the aforementioned logics—via the elimination of structural rules in labelled derivations. The translational correspondence between the two types of systems is leveraged to show that the nested calculi inherit proof-theoretic properties from their associated labelled calculi, such as completeness, invertibility of rules and cut admissibility. Since labelled calculi are easily obtained via a logic’s semantics, the method presented in this paper can be seen as one whereby refined versions of labelled calculi (containing nested calculi as fragments) with favourable properties are derived directly from a logic’s semantics.

On-Line Chinese Character Recognition Via a Representation of Spatial Relationships Between Strokes

1997 ◽  
Vol 11 (03) ◽  
pp. 329-357 ◽  
Author(s):  
Ju-Wei Chen ◽  
Suh-Yin Lee
Keyword(s):  
Character Recognition ◽  
Chinese Character ◽  
Spatial Relationship ◽  
Spatial Relations ◽  
Chinese Characters ◽  
Spatial Relationships ◽  
Matching Problem ◽  
Structural Rules ◽  
Chinese Character Recognition ◽  
On Line

Chinese characters are constructed by basic strokes based on structural rules. In handwritten characters, the shapes of the strokes may vary to some extent, but the spatial relations and geometric configurations of the strokes are usually maintained. Therefore these spatial relations and configurations could be regarded as invariant features and could be used in the recognition of handwritten Chinese characters. In this paper, we investigate the structural knowledge in Chinese characters and propose the stroke spatial relationship representation (SSRR) to describe Chinese characters. An On-Line Chinese Character Recognition (OLCCR) method using the SSRR is also presented. With SSRR, each character is processed and is represented by an attribute graph. The process of character recognition is thereby transformed into a graph matching problem. After careful analysis, the basic spatial relationship between strokes can be characterized into five classes. A bitwise representation is adopted in the design of the data structure to reduce storage requirements and to speed up character matching. The strategy of hierarchical search in the preclassification improves the recognition speed. Basically, the attribute graph model is a generalized character representation that provides a useful and convenient representation for newly added characters in an OLCCR system with automatic learning capability. The significance of the structural approach of character recognition using spatial relationships is analyzed and is proved by experiments. Realistic testing is provided to show the effectiveness of the proposed method.

Structural Interface for Automated Compliance Checking

2021 ◽  
Author(s):  
Erik Arthur Bjorkner
Keyword(s):  
Cost Reduction ◽  
Design Model ◽  
3D Design ◽  
Structural Rules ◽  
Structural Interface ◽  
Compliance Checking ◽  
Contract Specification

This paper describes the benefits of cost reduction and improved schedule attainment by adding digitized regulatory structural rules and contract specification requirements to the 3D design model through Knowledge Provisioning.

scholarly journals ALGEBRAIC ASPECT AND CONSTRUCTION OF LAX OPERATORS IN QUANTUM INTEGRABLE SYSTEMS

1995 ◽  
Vol 10 (40) ◽  
pp. 3113-3117 ◽  
Author(s):  
B. BASU-MALLICK ◽  
ANJAN KUNDU
Keyword(s):  
Integrable Systems ◽  
Integrable Models ◽  
Quantum Integrable Systems ◽  
Algebraic Construction ◽  
Algebraic Aspect ◽  
Quantum Integrable Models

An algebraic construction which is more general and closely connected with that of Faddeev,1 along with its application for generating different classes of quantum integrable models is summarized to complement the recent results of Ref. 1.

Fatigue Assessment of Welded Joints Taking Into Account Effects of Residual Stress

2010 ◽  
Author(s):  
Nur Syahroni ◽  
Stig Berge
Keyword(s):  
Residual Stress ◽  
Fatigue Strength ◽  
Welded Joints ◽  
Fatigue Testing ◽  
International Association ◽  
Hot Spot ◽  
Mean Stress ◽  
Element Analysis ◽  
Structural Rules ◽  
Fatigue Design

Residual stress may have a significant effect on the fatigue strength of welded joints. As a non-fluctuating stress, it has an effect similar to that of the mean stress. Recently the International Association of Ship Classification Societies (IACS) has issued Common Structural Rules (CSR) for respectively tankers (IACS 2006a) and bulk carriers (IACS 2006b). The effect of mean stress in fatigue design is taken into account in both sets of rules. However, the treatment is quite different, in particular with regard to residual stress and shakedown effects. In the present paper a comparative study of fatigue design procedures of the IACS rules is reported, with emphasis on residual stress effects. Testing was carried out with longitudinal attachment welds in the as-welded condition. The initial residual stress was measured by a sectioning method using strain gages. Hot spot stress was determined experimentally by strain gauges and numerically by finite element analysis using different types of elements. Fatigue testing was carried out and SN-curves were plotted according to the relevant stress as specified by the rules. In order to investigate the shake-down effect of residual stress, testing was performed for several pre-load conditions which could be taken to represent maximum load levels in a load history. The aim of the study is to contribute towards better understanding of the effect of residual stress and shakedown on fatigue strength of welded joints.

scholarly journals ANALYSIS OF CORROSION DEPTH PERCENTAGE ON THE INNER BOTTOM PLATES OF AGING BULK CARRIERS WITH AN AIM TO OPTIMIZE CORROSION MARGIN

Brodogradnja ◽  
2021 ◽  
Vol 72 (3) ◽  
pp. 81-95
Author(s):  
Špiro Ivošević ◽  
◽  
Nataša Kovač ◽  
Nikola Momčilović ◽  
Goran Vukelić ◽  
...  
Keyword(s):  
Fuel Consumption ◽  
Alternative Energy ◽  
Structural Integrity ◽  
Linear Models ◽  
Metal Plate ◽  
Fuel Oil ◽  
Corrosion Depth ◽  
Structural Rules ◽  
Bulk Carriers ◽  
Simple Conversion

To ensure the better structural integrity and maximum safety of bulk carriers in the ship design phase, an appropriate corrosion margin is introduced by the classification societies, which should enable the exploitation of ships during the projected 25-year life cycle. The new Common Structural Rules introduce even higher corrosion margin value to ensure the structural integrity of the ship. This directly affects the increase in hull weight and thus the need for more total installed power and higher fuel consumption. Higher fuel consumption results in increased emissions which directly affects environmental pollution. For these reasons, efforts are being made to introduce alternative energy sources, cleaner fuel, ship weight reduction, and the overall economic efficiency of ships. Therefore, using experimental data collected on aging bulk carriers, the paper explores the corrosion margin reduction potential considering its impact on hull weight. Assuming that the corrosive processes occur after four years of operation, a linear model that describes the percentage of plate wear as a function of the as build-in the thickness of inner bottom plates (IBP) of fuel oil tanks (FOT) located on the double bottom of aging bulk carriers, is analyzed. Over the course of 25 years, the IBP segment was monitored on 36 different ships surveys. In this way, 520 input data describing the depth of corrosion were formed. At the same time, records were kept on the mean thickness of the original metal plate, which enabled systematization of the empirical database and grouping of measured values by intervals of original plate thicknesses, and simple conversion of corrosion depth into adequate percentage values. Depth corrosion percentages were represented by standard linear models known in the literature. Based on this analysis, representative numerical and graphical results were obtained. Conclusions from the paper can assist to optimize corrosion margin and the energy efficiency of future vessels.

scholarly journals Language statistical learning responds to reinforcement learning principles rooted in the striatum

PLoS Biology ◽  
2021 ◽  
Vol 19 (9) ◽  
pp. e3001119
Author(s):  
Joan Orpella ◽  
Ernest Mas-Herrero ◽  
Pablo Ripollés ◽  
Josep Marco-Pallarés ◽  
Ruth de Diego-Balaguer
Keyword(s):  
Reinforcement Learning ◽  
Language Learning ◽  
Statistical Learning ◽  
Dorsal Striatum ◽  
Rule Learning ◽  
Prediction Errors ◽  
Neural Basis ◽  
Structural Rules ◽  
Learning Principles ◽  
Striatal Function

Statistical learning (SL) is the ability to extract regularities from the environment. In the domain of language, this ability is fundamental in the learning of words and structural rules. In lack of reliable online measures, statistical word and rule learning have been primarily investigated using offline (post-familiarization) tests, which gives limited insights into the dynamics of SL and its neural basis. Here, we capitalize on a novel task that tracks the online SL of simple syntactic structures combined with computational modeling to show that online SL responds to reinforcement learning principles rooted in striatal function. Specifically, we demonstrate—on 2 different cohorts—that a temporal difference model, which relies on prediction errors, accounts for participants’ online learning behavior. We then show that the trial-by-trial development of predictions through learning strongly correlates with activity in both ventral and dorsal striatum. Our results thus provide a detailed mechanistic account of language-related SL and an explanation for the oft-cited implication of the striatum in SL tasks. This work, therefore, bridges the long-standing gap between language learning and reinforcement learning phenomena.

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