Difference between revisions of "Introducing Grades in Deontic Logics"

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(New page: {{Paper|author=Pilar Dellunde|author2=Lluis Godo|title=Introducing Grades in Deontic Logics|journal=Lecture Notes in Computer Science |volume=5076|pages=248-262 |year=2008|preprint=http://...)
 
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{{Paper|author=Pilar Dellunde|author2=Lluis Godo|title=Introducing Grades in Deontic Logics|journal=Lecture Notes in Computer Science |volume=5076|pages=248-262 |year=2008|preprint=http://www.iiia.csic.es/files/pdfs/1659.pdf}}
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{{Paper|author=Pilar Dellunde|author2=Lluis Godo|title=Introducing Grades in Deontic Logics|journal=Lecture Notes in Computer Science |volume=5076|number=|pages=248-262 |year=2008|preprint=http://www.iiia.csic.es/files/pdfs/1659.pdf}}
  
 
== Abstract ==
 
== Abstract ==
  
 
In this paper we define a framework to introduce gradedness in Deontic logics through the use of fuzzy modalities. By way of example, we instantiate the framework to Standard Deontic logic (SDL) formulas. Given a deontic formula <math>\Phi\in SDL</math>, our language contains formulas of the form <math>\overline{r}\to N\Phi</math> or <math>\overline{r} \to P\Phi</math>, where <math>r \in [0, 1]</math>, expressing that the preference or probability degree respectively of a norm <math>\Phi</math> is at least <math>r</math>. We present sound and complete axiomatisations for these logics.
 
In this paper we define a framework to introduce gradedness in Deontic logics through the use of fuzzy modalities. By way of example, we instantiate the framework to Standard Deontic logic (SDL) formulas. Given a deontic formula <math>\Phi\in SDL</math>, our language contains formulas of the form <math>\overline{r}\to N\Phi</math> or <math>\overline{r} \to P\Phi</math>, where <math>r \in [0, 1]</math>, expressing that the preference or probability degree respectively of a norm <math>\Phi</math> is at least <math>r</math>. We present sound and complete axiomatisations for these logics.

Revision as of 17:11, 19 December 2008

Authors:
Pilar Dellunde
Lluis Godo
Title: Introducing Grades in Deontic Logics
Journal: Lecture Notes in Computer Science
Volume 5076
Number
Pages: 248-262
Year: 2008
Preprint





Abstract

In this paper we define a framework to introduce gradedness in Deontic logics through the use of fuzzy modalities. By way of example, we instantiate the framework to Standard Deontic logic (SDL) formulas. Given a deontic formula Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \Phi\in SDL} , our language contains formulas of the form Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \overline{r}\to N\Phi} or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \overline{r} \to P\Phi} , where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle r \in [0, 1]} , expressing that the preference or probability degree respectively of a norm Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \Phi} is at least Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle r} . We present sound and complete axiomatisations for these logics.