Introduction Śivas¯ utras task method German praty¯ ah¯ aras¯ utras Outlook On the generalizability of P¯ an . ini’s praty¯ ah¯ ara-technique to other languages Wiebke Petersen Silke Hamann Heinrich-Heine University Düsseldorf (Germany) 4th Int. Sanskrit Computational Linguistics Symposium, Dec. 10–12 2010 Petersen & Hamann On the generalizability of P¯ an . ini’s praty¯ ah¯ ara-technique 1
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Introduction Śivasutras task method German pratyaharasutras Outlook
On the generalizability of Pan. ini’spratyahara-technique to other languages
glottal stop epenthesis (right context){Y, 5, @, I, E, œ, O, U, a, i, e, o, u, y, ø, a:, i:, o:, u:, y:, ø:, e:, aI
“, OI
“, aU
“, E:}
vowel shortening input {i:, y:, e:, ø:, u:, o:}
vowel shortening output {i, y, e, ø, u, o}
palatal fricative assimilation {a:, a, u:, U, o:, O, aU“
}
Petersen & Hamann On the generalizability of Pan. ini’s pratyahara-technique 7
Introduction Śivasutras task method German pratyaharasutras Outlook
Main theorem on pratyaharasutras
task
Given a set of sound classes find a list of the sounds in the style ofPan. ini’s Śivasutras (called pratyaharasutras) which provides apratyahara for each sound class.
main theorem
A set of sound classes has pratyaharasutras in which no sound occursmore than once⇔the concept lattice of the set of sound classes is planar and eachsound occurs on its boundary.
Petersen (2009): On the Construction of Śivasutra-Alphabets. In Proc. of the 3rd Int. Sanskrit Comp. Ling. Symp.
Petersen & Hamann On the generalizability of Pan. ini’s pratyahara-technique 8
Introduction Śivasutras task method German pratyaharasutras Outlook
Example: concept lattice
{{d , e}, {a, b}, {b, c , d , f , g , h, i}, {f , i}, {c , d , e, f , g , h, i}, {g , h}}
e
d
c
if
hg
b
a
{d, e}
{d}
{c, d, f , g, h, i}
{f , i} {g, h}
{b}
{a, b}
{ }
{a, b, c, d, e, f , g, h, i}
{c, d, e, f , g, h, i} {b, c, d, f , g, h, i}
Petersen & Hamann On the generalizability of Pan. ini’s pratyahara-technique 9
Introduction Śivasutras task method German pratyaharasutras Outlook
Example: concept lattice
{{d , e}, {a, b}, {b, c , d , f , g , h, i}, {f , i}, {c , d , e, f , g , h, i}, {g , h}}
e
d
c
if
hg
b
a
Petersen & Hamann On the generalizability of Pan. ini’s pratyahara-technique 9
Introduction Śivasutras task method German pratyaharasutras Outlook
Pratyaharasutras with a minimal number of markers
e
d
c
if
hg
b
a
Petersen & Hamann On the generalizability of Pan. ini’s pratyahara-technique 10
Introduction Śivasutras task method German pratyaharasutras Outlook
Pratyaharasutras with a minimal number of markers
e
d
c
if
hg
b
a
Petersen & Hamann On the generalizability of Pan. ini’s pratyahara-technique 11
Introduction Śivasutras task method German pratyaharasutras Outlook
Pratyaharasutras with a minimal number of markers
e
d
c
if
hg
b
a
e
Petersen & Hamann On the generalizability of Pan. ini’s pratyahara-technique 11
Introduction Śivasutras task method German pratyaharasutras Outlook
Pratyaharasutras with a minimal number of markers
e
d
c
if
hg
b
a
ee
e
Petersen & Hamann On the generalizability of Pan. ini’s pratyahara-technique 11
Introduction Śivasutras task method German pratyaharasutras Outlook
Pratyaharasutras with a minimal number of markers
e
d
c
if
hg
b
a
e
dd
ed
Petersen & Hamann On the generalizability of Pan. ini’s pratyahara-technique 11
Introduction Śivasutras task method German pratyaharasutras Outlook
Pratyaharasutras with a minimal number of markers
e
d
c
if
hg
b
a
e
d
•cc
edM1c
Petersen & Hamann On the generalizability of Pan. ini’s pratyahara-technique 11
Introduction Śivasutras task method German pratyaharasutras Outlook
Pratyaharasutras with a minimal number of markers
e
d
c
if
hg
b
a
e
d
•c
if
c
if
edM1cfi
Petersen & Hamann On the generalizability of Pan. ini’s pratyahara-technique 11
Introduction Śivasutras task method German pratyaharasutras Outlook
Pratyaharasutras with a minimal number of markers
e
d
c
if
hg
b
a
e
d
•c
if
c
•
edM1cfiM2
Petersen & Hamann On the generalizability of Pan. ini’s pratyahara-technique 11
Introduction Śivasutras task method German pratyaharasutras Outlook
Pratyaharasutras with a minimal number of markers
e
d
c
if
hg
b
a
e
d
•c
if
c
•
hg
c• b
• a
•
edM1cfiM2ghM3bM4aM5
Petersen & Hamann On the generalizability of Pan. ini’s pratyahara-technique 11
Introduction Śivasutras task method German pratyaharasutras Outlook
Set of 10 German sound classes that have to be described