Some Fixpoint Techniques in Algebraic Structures and Applications to Computer Science

1987 ◽  
Vol 10 (4) ◽  
pp. 387-413
Author(s):  
Irène Guessarian
Keyword(s):  
Logic Programming ◽  
Computer Science ◽  
Proof Theory ◽  
Algebraic Structures ◽  
Data Bases

This paper recalls some fixpoint theorems in ordered algebraic structures and surveys some ways in which these theorems are applied in computer science. We describe via examples three main types of applications: in semantics and proof theory, in logic programming and in deductive data bases.

scholarly journals A Modal Proof Theory for Polynomial Coalgebras

2021 ◽  
Author(s):  
◽  
David Friggens
Keyword(s):  
Modal Logic ◽  
Computer Science ◽  
Programming Languages ◽  
Data Structures ◽  
Proof Theory ◽  
Object Oriented ◽  
Object Oriented Programming ◽  
Algebraic Methods ◽  
Mathematical Structures ◽  
Finite Constant

<p>The abstract mathematical structures known as coalgebras are of increasing interest in computer science for their use in modelling certain types of data structures and programs. Traditional algebraic methods describe objects in terms of their construction, whilst coalgebraic methods describe objects in terms of their decomposition, or observational behaviour. The latter techniques are particularly useful for modelling infinite data structures and providing semantics for object-oriented programming languages, such as Java. There have been many different logics developed for reasoning about coalgebras of particular functors, most involving modal logic. We define a modal logic for coalgebras of polynomial functors, extending Rößiger’s logic [33], whose proof theory was limited to using finite constant sets, by adding an operator from Goldblatt [11]. From the semantics we define a canonical coalgebra that provides a natural construction of a final coalgebra for the relevant functor. We then give an infinitary axiomatization and syntactic proof relation that is sound and complete for functors constructed from countable constant sets.</p>

scholarly journals Induction as a Search Procedure

2008 ◽  
pp. 166-216 ◽  
Author(s):  
Stasinos Konstantopoulos ◽  
Rui Camacho ◽  
Nuno A. Fonseca ◽  
Vítor Santos Costa
Keyword(s):  
Logic Programming ◽  
Computer Science ◽  
Inductive Logic Programming ◽  
Inductive Logic ◽  
Search Space ◽  
Search Algorithms ◽  
Stochastic Algorithms ◽  
Search Procedure ◽  
Formal Definition ◽  
Version Spaces

This chapter introduces Inductive Logic Programming (ILP) from the perspective of search algorithms in Computer Science. It first briefly considers the Version Spaces approach to induction, and then focuses on Inductive Logic Programming: from its formal definition and main techniques and strategies, to priors used to restrict the search space and optimized sequential, parallel, and stochastic algorithms. The authors hope that this presentation of the theory and applications of Inductive Logic Programming will help the reader understand the theoretical underpinnings of ILP, and also provide a helpful overview of the State-of-the-Art in the domain.

Categories for the Working Philosopher

2018 ◽  
Keyword(s):  
Mathematical Modeling ◽  
Computer Science ◽  
Category Theory ◽  
Proof Theory ◽  
Scientific Theories ◽  
General Audience ◽  
Seminal Work ◽  
The World

Borrowing from the title of Saunders Mac Lane’s seminal work Categories for the Working Mathematician, this book aims to bring the concepts of category theory to philosophers working in areas ranging from mathematics to proof theory to computer science to ontology, from physics to biology to cognition, from mathematical modeling to the structure of scientific theories to the structure of the world. Moreover, it aims to do this in a way that is accessible to a general audience. Each chapter is written by either a category-theorist or a philosopher working in one of the represented areas, and in a way that is accessible and is intended to build on the concepts already familiar to those philosophers working in these areas.

scholarly journals Exploiting Game Theory for Analysing Justifications

2020 ◽  
Vol 20 (6) ◽  
pp. 880-894
Author(s):  
SIMON MARYNISSEN ◽  
BART BOGAERTS ◽  
MARC DENECKER
Keyword(s):  
Game Theory ◽  
Logic Programming ◽  
Computer Science ◽  
Central Concept ◽  
Semantic Framework ◽  
The Third ◽  
The Past ◽  
Theoretical Foundations

AbstractJustification theory is a unifying semantic framework. While it has its roots in non-monotonic logics, it can be applied to various areas in computer science, especially in explainable reasoning; its most central concept is a justification: an explanation why a property holds (or does not hold) in a model.In this paper, we continue the study of justification theory by means of three major contributions. The first is studying the relation between justification theory and game theory. We show that justification frameworks can be seen as a special type of games. The established connection provides the theoretical foundations for our next two contributions. The second contribution is studying under which condition two different dialects of justification theory (graphs as explanations vs trees as explanations) coincide. The third contribution is establishing a precise criterion of when a semantics induced by justification theory yields consistent results. In the past proving that such semantics were consistent took cumbersome and elaborate proofs.We show that these criteria are indeed satisfied for all common semantics of logic programming.

scholarly journals Introducing Computer Science to High School Students Through Logic Programming

2018 ◽  
Vol 19 (2) ◽  
pp. 204-228 ◽  
Author(s):  
TIMOTHY T. YUEN ◽  
MARITZA REYES ◽  
YUANLIN ZHANG
Keyword(s):  
High School ◽  
High School Students ◽  
Logic Programming ◽  
Computer Science ◽  
School Students ◽  
Introductory Computer Science ◽  
Cyclical Process ◽  
K 12 ◽  
Novice Students ◽  
Traditional Approaches

AbstractThis paper investigates how high school students in an introductory computer science (CS) course approach computing in the logic programming (LP) paradigm. This qualitative study shows how novice students operate within the LP paradigm while engaging in foundational computing concepts and skills: students are engaged in a cyclical process of abstraction, reasoning, and creating representations of their ideas in code while also being informed by the (procedural) requirements and the revision/debugging process. As these computing concepts and skills are also expected in traditional approaches to introductory K-12 CS courses, this paper asserts that LP is a viable paradigm choice for high school novices.

Free ordered algebraic structures towards proof theory

2001 ◽  
Vol 66 (2) ◽  
pp. 597-608
Author(s):  
Andreja Prijatelj
Keyword(s):  
Classical Logic ◽  
Proof Theory ◽  
Algebraic Structures ◽  
Ordered Algebras

AbstractIn this paper, constructions of free ordered algebras on one generator are given that correspond to some one-variable fragments of affine propositional classical logic and their extensions with n-contraction (n ≥ 2). Moreover, embeddings of the already known infinite free structures into the algebras introduced below are furnished with; thus, solving along the respective cardinality problems.

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