Delete operations and Horn formulas

2005 ◽  
pp. 329-343 ◽  
Author(s):  
Rüdiger Schätz
Keyword(s):  
Horn Formulas

scholarly journals The joy of implications, aka pure Horn formulas: Mainly a survey

2017 ◽  
Vol 658 ◽  
pp. 264-292 ◽  
Author(s):  
Marcel Wild
Keyword(s):  
Horn Formulas

Chapter 29. Theory of Quantified Boolean Formulas

2021 ◽  
Author(s):  
Hans Kleine Büning ◽  
Uwe Bubeck
Keyword(s):  
Normal Form ◽  
Boolean Function ◽  
Expressive Power ◽  
Modeling Language ◽  
Complex Problems ◽  
Quantified Boolean Formulas ◽  
Horn Formulas ◽  
Boolean Formulas ◽  
Function Models ◽  
Resolution Calculus

Quantified Boolean formulas (QBF) are a generalization of propositional formulas by allowing universal and existential quantifiers over variables. This enhancement makes QBF a concise and natural modeling language in which problems from many areas, such as planning, scheduling or verification, can often be encoded in a more compact way than with propositional formulas. We introduce in this chapter the syntax and semantics of QBF and present fundamental concepts. This includes normal form transformations and Q-resolution, an extension of the propositional resolution calculus. In addition, Boolean function models are introduced to describe the valuation of formulas and the behavior of the quantifiers. We also discuss the expressive power of QBF and provide an overview of important complexity results. These illustrate that the greater capabilities of QBF lead to more complex problems, which makes it interesting to consider suitable subclasses of QBF. In particular, we give a detailed look at quantified Horn formulas (QHORN) and quantified 2-CNF (Q2-CNF).

Learning orthogonal F-Horn formulas

1995 ◽  
pp. 110-122
Author(s):  
Akira Miyashiro ◽  
Eiji Takimoto ◽  
Yoshifumi Sakai ◽  
Akira Maruoka
Keyword(s):  
Horn Formulas

scholarly journals Learning orthogonal F-Horn formulas

1997 ◽  
Vol 185 (1) ◽  
pp. 177-190
Author(s):  
Eiji Takimoto ◽  
Akira Miyashiro ◽  
Akira Maruoka ◽  
Yoshifumi Sakai
Keyword(s):  
Horn Formulas

scholarly journals Learning definite Horn formulas from closure queries

2017 ◽  
Vol 658 ◽  
pp. 346-356 ◽  
Author(s):  
Marta Arias ◽  
José L. Balcázar ◽  
Cristina Tîrnăucă
Keyword(s):  
Horn Formulas

A representation of recursively enumerable sets through Horn formulas in higher recursion theory

2016 ◽  
Vol 73 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Juan A. Nido Valencia ◽  
Julio E. Solís Daun ◽  
Luis M. Villegas Silva
Keyword(s):  
Recursion Theory ◽  
Recursively Enumerable ◽  
Horn Formulas ◽  
Recursively Enumerable Sets

Modus Ponens and Derivation from Horn Formulas

1967 ◽  
Vol 13 (3-5) ◽  
pp. 33-54
Author(s):  
William Craig
Keyword(s):  
Modus Ponens ◽  
Horn Formulas

Parametric algebraic specifications with Gentzen formulas – from quasi-freeness to free functor semantics

1995 ◽  
Vol 5 (1) ◽  
pp. 69-111 ◽  
Author(s):  
Michael Löwe ◽  
Uwe Wolter
Keyword(s):  
Function Spaces ◽  
Data Type ◽  
Finite Function ◽  
Practical Applications ◽  
Free Objects ◽  
Algebraic Specifications ◽  
Free Construction ◽  
Horn Formulas ◽  
Type Constructor ◽  
Parametric Case

Inspired by the work of S. Kaplan on positive/negative conditional rewriting, we investigate initial semantics for algebraic specifications with Gentzen formulas. Since the standard initial approach is limited to conditional equations (i.e. positive Horn formulas), the notion of semi-initial and quasi-initial algebras is introduced, and it is shown that all specifications with (positive) Gentzen formulas admit quasi-initial models.The whole approach is generalized to the parametric case where quasi-initiality generalizes to quasi-freeness. Since quasi-free objects need not be isomorphic, the persistency requirement is added to obtain a unique semantics for many interesting practical examples. Unique persistent quasi-free semantics can be described as a free construction if the homomorphisms of the parameter category are suitably restricted. Furthermore, it turns out that unique persistent quasi-free semantics applies especially to specifications where the Gentzen formulas can be interpreted as hierarchical positive/negative conditional equations. The data type constructor of finite function spaces is used as an example that does not admit a correct initial semantics, but does admit a correct unique persistent quasi-initial semantics. The example demonstrates that the concepts introduced in this paper might be of some importance in practical applications.

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