A E-Business Case of Study

2017 ◽  
Vol 8 (3) ◽  
pp. 1-20
Author(s):  
Maria Vargas-Vera ◽  
Camilo Salles ◽  
Joaquin Parot ◽  
Sebastian Letelier
Keyword(s):  
Chemical Composition ◽  
Red Wine ◽  
Business Case ◽  
Order Logic ◽  
Wine Industry ◽  
First Order Logic ◽  
Qualitative Properties ◽  
Wine Quality ◽  
First Order

The main purpose of this research was to find relations between the chemical composition of the wines and the wine testers' opinions on the wine quality. We used in our study a dataset which contains examples of red wine from Vinho Verde, Portugal. Firstly, we did an analysis on the attributes of the examples, in the dataset, to find correlations between quantitative and qualitative properties in wines. Secondly, we performed clustering using the algorithms k-means and x-means. Additionally, we used the J48 algorithm for getting a decision tree and then to extract first order logic rules. We concluded that, there is a relation between physicochemical properties and quality of wines. This result opens the possibility of further analysis and perhaps this could lead to use fewer wine testers and therefore, our research could bring benefit to the wine industry.

scholarly journals FOL Learning for Knowledge Discovery in Documents

2012 ◽  
pp. 1237-1262
Author(s):  
Stefano Ferilli ◽  
Floriana Esposito ◽  
Marenglen Biba ◽  
Teresa M.A. Basile ◽  
Nicola Di Mauro
Keyword(s):  
Order Logic ◽  
Learning Performance ◽  
First Order Logic ◽  
Machine Learning Techniques ◽  
Document Processing ◽  
First Order ◽  
Real World Application ◽  
Learning Techniques ◽  
Viable Solution

This chapter proposes the application of machine learning techniques, based on first-order logic as a representation language, to the real-world application domain of document processing. First, the tasks and problems involved in document processing are presented, along with the prototypical system DOMINUS and its architecture, whose components are aimed at facing these issues. Then, a closer look is provided for the learning component of the system, and the two sub-systems that are in charge of performing supervised and unsupervised learning as a support to the system performance. Finally, some experiments are reported that assess the quality of the learning performance. This is intended to prove to researchers and practitioners of the field that first-order logic learning can be a viable solution to tackle the domain complexity, and to solve problems such as incremental evolution of the document repository.

scholarly journals Different Proofs are Good Proofs

10.29007/kwk9 ◽  
2018 ◽  
Author(s):  
Geoff Sutcliffe ◽  
Cynthia Chang ◽  
Li Ding ◽  
Deborah McGuinness ◽  
Paulo Pinheiro da Silva
Keyword(s):  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Problem Library

In order to compare the quality of proofs, it is necessary to measure artifacts of the proofs, and evaluate the measurements to determine differences between the proofs. This paper discounts the approach of ranking measurements of proof artifacts, and takes the position that different proofs are good proofs. The position is based on proofs in the TSTP solution library, which are generated by Automated Theorem Proving (ATP) systems applied to first-order logic problems in the TPTP problem library.

scholarly journals FOL Learning for Knowledge Discovery in Documents

2010 ◽  
pp. 348-374
Author(s):  
Stefano Ferilli ◽  
Floriana Esposito ◽  
Marenglen Biba ◽  
Teresa M.A. Basile ◽  
Nicola Di Mauro
Keyword(s):  
Order Logic ◽  
Learning Performance ◽  
First Order Logic ◽  
Machine Learning Techniques ◽  
Document Processing ◽  
First Order ◽  
Real World Application ◽  
Learning Techniques ◽  
Viable Solution

This chapter proposes the application of machine learning techniques, based on first-order logic as a representation language, to the real-world application domain of document processing. First, the tasks and problems involved in document processing are presented, along with the prototypical system DOMINUS and its architecture, whose components are aimed at facing these issues. Then, a closer look is provided for the learning component of the system, and the two sub-systems that are in charge of performing supervised and unsupervised learning as a support to the system performance. Finally, some experiments are reported that assess the quality of the learning performance. This is intended to prove to researchers and practitioners of the field that first-order logic learning can be a viable solution to tackle the domain complexity, and to solve problems such as incremental evolution of the document repository.

scholarly journals Learning from Multiple Proofs: First Experiments

10.29007/nb2g ◽  
2018 ◽  
Author(s):  
Daniel Kuehlwein ◽  
Josef Urban
Keyword(s):  
Explicit Knowledge ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Selection Algorithms ◽  
Lateral Thinking

Mathematical textbooks typically present only one proof for most of the theorems. However, there are infinitely many proofs for each theorem in first-order logic, and mathematicians are often aware of (and even invent new) important alternative proofs and use such knowledge for (lateral) thinking about new problems.In this paper we start exploring how the explicit knowledge of multiple (human and ATP) proofs of the same theorem can be used in learning-based premise selection algorithms in large-theory mathematics.Several methods and their combinations are defined, and their effect on the ATP performance is evaluated on the MPTP2078 large-theory benchmark.Our first findings are that the proofs used for learning significantly influence the number of problems solved, and that the quality of the proofs is more important than the quantity.

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 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.

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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