M APPING P ARAMETRIZED D IFFERENCE R EVISION O PERATORS TO B ELIEF C - - PowerPoint PPT Presentation

MAPPING PARAMETRIZED DIFFERENCE REVISION OPERATORS TO BELIEF CONTRACTION

Maria Andrikopoulou Theofanis Aravanis

ST

RUC T URE O F PRESENT AT IO N

 Be lie f C ha ng e  T

he AG M Pa ra d ig m

 Re visio n a nd C o ntra c tio n  Inte rd e fina b ility o f O p e ra tio ns  Pa ra me trize d Diffe re nc e Re visio n O p e ra to rs

(PDR O p e ra to rs)

 PDR O p e ra to rs in the Re a lm o f C o ntra c tio n  C o nc lusio ns

BEL

IEF C HANG E (REVISIO N) [1/ 2]

• Ma ry ha s just d isc o ve re d tha t G e o rg e a nd Dim itra a re no t he r

true p a re nts.

• She w a s a d o p te d w he n she w a s 6 m o nths o ld fro m a n
• rp ha na g e in Sa o Pa o lo .
• T

he ne w s re a lly sho o k Ma ry.

• Muc h o f w ha t she use d to b e lie ve a b o ut he rse lf a nd he r

fa m ily w a s w ro ng .

• She m ust, no w , p ut he r tho ug hts b a c k in o rd e r.
• M. Andrikopoulou and T. Aravanis

BEL

IEF C HANG E (REVISIO N) [2/ 2]

• A typ ic a l (a ltho ug h ra the r d ra m a tic ) insta nc e o f a

b e lie f-re visio n sc e na rio .

• A

ra tio na l a g e nt re c e ive s ne w (c o ntra d ic ting ) info rm a tio n, tha t m a ke s he r c ha ng e he r b e lie fs.

• Withd ra w so m e o f the o ld b e lie fs, b e fo re she c a n

(c o nsiste ntly) a c c o m m o d a te the ne w info rm a tio n.

• Ac c e p t the c o nse q ue nc e s tha t mig ht re sult fro m the

inte ra c tio n o f the ne w info rm a tio n w ith the o ld b e lie fs.

• M. Andrikopoulou and T. Aravanis

T

HE AG M PARADIG M [1/ 2]

• M. Andrikopoulou and T. Aravanis
• T

he stud y o f Be lie f C ha ng e c a n b e tra c e d b a c k to the e a rly ’ 80s, w ith the se m ina l wo rk

• f

Alc ho urró n, G ä rd e nfo rs, a nd Ma kinso n.

• T

he y e sta b lishe d the AG M p a ra d ig m; to this d a te , the d o m ina nt fra m e w o rk in Be lie f C ha ng e .

• Be lie fs

a re m o d e le d a s se nte nc e s (φ,

ψ)

• f

α

p ro p o sitio na l la ng ua g e .

• Be lie f se ts (Κ) a re mo d e le d a s se ts o f se nte nc e s c lo se d

und e r lo g ic a l im p lic a tio n (the o rie s).

• T

he p ro c e ss o f b e lie f c ha ng e is e nc o d e d a s a func tio n tha t m a p s a the o ry a nd a se nte nc e to a ne w the o ry.

T

HE AG M PARADIG M [2/ 2]

• M. Andrikopoulou and T. Aravanis
• T

he AG M p a ra d ig m stud ie s b o th b e lie f re visio n a nd b e lie f c o ntra c tio n.

• Be lie f Re visio n: Inc o rp o ra tio n o f a se nte nc e tha t is

inc o nsiste nt w ith a b e lie f se t.

• Be lie f C o ntra c tio n: Withd ra w a l o f a se nte nc e fro m a

b e lie f se t.

• T

he AG M p a ra d ig m c ha ra c te rize s ra tio na l b e lie f re visio n a nd b e lie f c o ntra c tio n func tio ns, b y m e a ns o f a se t o f ra tio na lity p o stula te s fo r e a c h c a se .

• Princ ip le o f Minim a l C ha ng e : T

he ne w b e lie f se t d iffe rs a s little a s p o ssib le fro m the o ld b e lie f se t.

T

HE AG M PO ST UL AT ES FO R REVISIO N

• M. Andrikopoulou and T. Aravanis

T

HE AG M PO ST UL AT ES FO R C O NT RAC T IO N

• M. Andrikopoulou and T. Aravanis

INT

ERDEFINABIL IT Y O F O PERAT O RS

• Re visio n a nd c o ntra c tio n c a n b e d e fine d in te rm s o f e a c h
• the r thro ug h L

e vi a nd Ha rp e r Id e ntitie s.

• M. Andrikopoulou and T. Aravanis

C O NC RET

E REVISIO N O PERAT O RS

• M. Andrikopoulou and T. Aravanis
• Se ve ra l c o nc re te “ o ff the se lf” re visio n func tio ns

(o p e ra to rs), imp le me nting the p ro c e ss o f b e lie f re visio n, ha ve b e e n p ro p o se d .

• Amo ng the we ll-kno wn p ro p o sa ls, o nly Da la l’ s

re visio n o p e ra to r sa tisfie s the full se t o f AG M p o stula te s fo r re visio n (Κ*1) – (Κ*8).

• Simp le a nd intuitive c o nstruc tio n.

PARAMET

RIZED DIFFERENC E REVISIO N O PERAT O RS

• M. Andrikopoulou and T. Aravanis
• Intro d uc e d b y Pe p p a s a nd Willia ms (2016).
• Sa tisfy the AG M p o stula te s fo r re visio n.
• Na tura l g e ne ra liza tio ns o f Da la l’ s re visio n o p e ra to r,

with a muc h g re a te r ra ng e o f a p p lic a b ility.

• Lo w re p re se nta tio na l a nd c o mp uta tio na l c o st, tha t

ma ke s the m id e a l fo r re a l-wo rld a p p lic a tio ns.

• Ha ve b e e n a xio ma tic a lly d e fine d , ve ry re c e ntly, in

the re a lm o f re visio n.

• We p ro vid e a n a xio ma tic c ha ra c te riza tio n in the

re a lm o f c o ntra c tio n.

• M. Andrikopoulou and T. Aravanis
• PDR o p e ra to rs ha ve b e e n a xio ma tic a lly d e fine d in

the re a lm o f re visio n b y Pe p p a s a nd Willia ms (2018).

PDR O PERAT

O RS IN T HE REAL M O F REVISIO N [1/ 2]

PDR O PERAT

O RS IN T HE REAL M O F REVISIO N [2/ 2]

• M. Andrikopoulou and T. Aravanis
• PDR o p e ra to rs a re a p ro p e r sub c la ss o f the who le

c la ss o f AG M re visio n func tio ns.

PDR O PERAT

O RS IN T HE REAL M O F C O NT RAC T IO N

• M. Andrikopoulou and T. Aravanis
• We p ro vid e d the a xio ma tic c ha ra c te riza tio n o f PDR
• p e ra to rs in the re a lm o f b e lie f c o ntra c tio n.
• Le vi a nd Ha rp e r Id e ntitie s we re utilize d .

O NE- T

O- O NE C O RRESPO NDENC E

• M. Andrikopoulou and T. Aravanis

C O NC L

USIO NS

• PDR
• p e ra to rs

b ring us a ste p c lo se r to the d e ve lo p me nt o f a suc c e ssful AG M b e lie f-c ha ng e syste m, d ue to the ir fa vo ra b le p ro p e rtie s.

• We ha ve ma p p e d PDR o p e ra to rs in the re a lm o f

b e lie f c o ntra c tio n, b y me a ns o f the Le vi a nd Ha rp e r Id e ntitie s, c ha ra c te rizing the c la ss o f PDC o p e ra to rs.

• T

he a xio ma tic c ha ra c te riza tio n o f this ne w c la ss o f

• p e ra to rs ha s b e e n c o mp le te d fo r the two p ro c e sse s
• f b e lie f c ha ng e (re visio n a nd c o ntra c tio n).

Thank you!