Inducing Classification and Regression Trees in First Order Logic

2001 ◽  
pp. 140-159 ◽  
Author(s):  
Stefan Kramer ◽  
Gerhard Widmer
Keyword(s):  
Regression Trees ◽  
Classification And Regression Trees ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Classification And Regression

First-Order Logic Reasoning Support for the Semantic Web

2009 ◽  
Vol 19 (12) ◽  
pp. 3091-3099 ◽  
Author(s):  
Gui-Hong XU ◽  
Jian ZHANG
Keyword(s):  
Semantic Web ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Logic Reasoning

Boolean-valued structures

2018 ◽  
Author(s):  
Tim Button ◽  
Sean Walsh
Keyword(s):  
Model Theory ◽  
Order Logic ◽  
First Order Logic ◽  
Inference Rules ◽  
Mathematical Concepts ◽  
Semantic Framework ◽  
First Order ◽  
Standard Models ◽  
Boolean Valued Model ◽  
Semantic Values

Chapters 6-12 are driven by questions about the ability to pin down mathematical entities and to articulate mathematical concepts. This chapter is driven by similar questions about the ability to pin down the semantic frameworks of language. It transpires that there are not just non-standard models, but non-standard ways of doing model theory itself. In more detail: whilst we normally outline a two-valued semantics which makes sentences True or False in a model, the inference rules for first-order logic are compatible with a four-valued semantics; or a semantics with countably many values; or what-have-you. The appropriate level of generality here is that of a Boolean-valued model, which we introduce. And the plurality of possible semantic values gives rise to perhaps the ‘deepest’ level of indeterminacy questions: How can humans pin down the semantic framework for their languages? We consider three different ways for inferentialists to respond to this question.

scholarly journals GAMES AND CARDINALITIES IN INQUISITIVE FIRST-ORDER LOGIC

2021 ◽  
pp. 1-28
Author(s):  
IVANO CIARDELLI ◽  
GIANLUCA GRILLETTI
Keyword(s):  
Order Logic ◽  
First Order Logic ◽  
First Order

scholarly journals Extensions in graph normal form

2020 ◽  
Author(s):  
Michał Walicki
Keyword(s):  
Normal Form ◽  
Fixed Points ◽  
Propositional Logic ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Special Cases

Abstract Graph normal form, introduced earlier for propositional logic, is shown to be a normal form also for first-order logic. It allows to view syntax of theories as digraphs, while their semantics as kernels of these digraphs. Graphs are particularly well suited for studying circularity, and we provide some general means for verifying that circular or apparently circular extensions are conservative. Traditional syntactic means of ensuring conservativity, like definitional extensions or positive occurrences guaranteeing exsitence of fixed points, emerge as special cases.

Preoperative hematocrit and platelet count are associated with blood loss during spinal fusion for children with neuromuscular scoliosis

2021 ◽  
pp. 175045892096263
Author(s):  
Margaret O Lewen ◽  
Jay Berry ◽  
Connor Johnson ◽  
Rachael Grace ◽  
Laurie Glader ◽  
...  
Keyword(s):  
Platelet Count ◽  
Blood Loss ◽  
Spinal Fusion ◽  
Regression Trees ◽  
Classification And Regression Trees ◽  
Neuromuscular Scoliosis ◽  
Independent Variables ◽  
Estimated Blood Loss ◽  
Laboratory Results ◽  
Classification And Regression

Aim To assess the relationship of preoperative hematology laboratory results with intraoperative estimated blood loss and transfusion volumes during posterior spinal fusion for pediatric neuromuscular scoliosis. Methods Retrospective chart review of 179 children with neuromuscular scoliosis undergoing spinal fusion at a tertiary children’s hospital between 2012 and 2017. The main outcome measure was estimated blood loss. Secondary outcomes were volumes of packed red blood cells, fresh frozen plasma, and platelets transfused intraoperatively. Independent variables were preoperative blood counts, coagulation studies, and demographic and surgical characteristics. Relationships between estimated blood loss, transfusion volumes, and independent variables were assessed using bivariable analyses. Classification and Regression Trees were used to identify variables most strongly correlated with outcomes. Results In bivariable analyses, increased estimated blood loss was significantly associated with higher preoperative hematocrit and lower preoperative platelet count but not with abnormal coagulation studies. Preoperative laboratory results were not associated with intraoperative transfusion volumes. In Classification and Regression Trees analysis, binary splits associated with the largest increase in estimated blood loss were hematocrit ≥44% vs. <44% and platelets ≥308 vs. <308 × 109/L. Conclusions Preoperative blood counts may identify patients at risk of increased bleeding, though do not predict intraoperative transfusion requirements. Abnormal coagulation studies often prompted preoperative intervention but were not associated with increased intraoperative bleeding or transfusion needs.

scholarly journals Regional Mapping of Groundwater Potential in Ar Rub Al Khali, Arabian Peninsula Using the Classification and Regression Trees Model

2021 ◽  
Vol 13 (12) ◽  
pp. 2300
Author(s):  
Samy Elmahdy ◽  
Tarig Ali ◽  
Mohamed Mohamed
Keyword(s):  
Machine Learning ◽  
Regional Scale ◽  
Regression Trees ◽  
Classification And Regression Trees ◽  
Groundwater Potential ◽  
Machine Learning Algorithms ◽  
Conditioning Factors ◽  
Potential Mapping ◽  
Classification And Regression ◽  
Groundwater Potential Mapping

Mapping of groundwater potential in remote arid and semi-arid regions underneath sand sheets over a very regional scale is a challenge and requires an accurate classifier. The Classification and Regression Trees (CART) model is a robust machine learning classifier used in groundwater potential mapping over a very regional scale. Ten essential groundwater conditioning factors (GWCFs) were constructed using remote sensing data. The spatial relationship between these conditioning factors and the observed groundwater wells locations was optimized and identified by using the chi-square method. A total of 185 groundwater well locations were randomly divided into 129 (70%) for training the model and 56 (30%) for validation. The model was applied for groundwater potential mapping by using optimal parameters values for additive trees were 186, the value for the learning rate was 0.1, and the maximum size of the tree was five. The validation result demonstrated that the area under the curve (AUC) of the CART was 0.920, which represents a predictive accuracy of 92%. The resulting map demonstrated that the depressions of Mondafan, Khujaymah and Wajid Mutaridah depression and the southern gulf salt basin (SGSB) near Saudi Arabia, Oman and the United Arab Emirates (UAE) borders reserve fresh fossil groundwater as indicated from the observed lakes and recovered paleolakes. The proposed model and the new maps are effective at enhancing the mapping of groundwater potential over a very regional scale obtained using machine learning algorithms, which are used rarely in the literature and can be applied to the Sahara and the Kalahari Desert.

Relational Chase Procedures Interpreted as Resolution with Paramodulation1

1991 ◽  
Vol 15 (2) ◽  
pp. 123-138
Author(s):  
Joachim Biskup ◽  
Bernhard Convent
Keyword(s):  
Alternative Interpretation ◽  
Order Logic ◽  
First Order Logic ◽  
Inference Problem ◽  
First Order ◽  
Inference Problems ◽  
The One ◽  
The Relationship ◽  
Theoretical Foundations ◽  
Insight Into

In this paper the relationship between dependency theory and first-order logic is explored in order to show how relational chase procedures (i.e., algorithms to decide inference problems for dependencies) can be interpreted as clever implementations of well known refutation procedures of first-order logic with resolution and paramodulation. On the one hand this alternative interpretation provides a deeper insight into the theoretical foundations of chase procedures, whereas on the other hand it makes available an already well established theory with a great amount of known results and techniques to be used for further investigations of the inference problem for dependencies. Our presentation is a detailed and careful elaboration of an idea formerly outlined by Grant and Jacobs which up to now seems to be disregarded by the database community although it definitely deserves more attention.

scholarly journals Formula size games for modal logic and μ-calculus

2019 ◽  
Vol 29 (8) ◽  
pp. 1311-1344 ◽  
Author(s):  
Lauri T Hella ◽  
Miikka S Vilander
Keyword(s):  
Modal Logic ◽  
Optimal Strategy ◽  
Order Logic ◽  
First Order Logic ◽  
Kripke Models ◽  
First Order ◽  
Modal Operators ◽  
Crucial Difference ◽  
Definition Of ◽  
Person Game

Abstract We propose a new version of formula size game for modal logic. The game characterizes the equivalence of pointed Kripke models up to formulas of given numbers of modal operators and binary connectives. Our game is similar to the well-known Adler–Immerman game. However, due to a crucial difference in the definition of positions of the game, its winning condition is simpler, and the second player does not have a trivial optimal strategy. Thus, unlike the Adler–Immerman game, our game is a genuine two-person game. We illustrate the use of the game by proving a non-elementary succinctness gap between bisimulation invariant first-order logic $\textrm{FO}$ and (basic) modal logic $\textrm{ML}$. We also present a version of the game for the modal $\mu $-calculus $\textrm{L}_\mu $ and show that $\textrm{FO}$ is also non-elementarily more succinct than $\textrm{L}_\mu $.

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